NDA II 2026 General Ability Test with Solutions
Q.1 [English — Antonyms]
During the trial, the witness's deposition was equivocal.
Select the word that is opposite in meaning to the underlined word.
Equivocal = open to more than one interpretation; deliberately vague. Its opposite is explicit — stated clearly and in detail, leaving no room for doubt.
Ambiguous, evasive and guarded all lean the same way as the key word. In an antonym item, the option that stands apart from the other three is usually the answer.
Q.2 [English — Antonyms]
The professor is known for his characteristic reticence.
Select the word that is opposite in meaning to the underlined word.
Reticence = a reluctance to speak; reserve in expressing oneself. The opposite is communicativeness — readiness to talk and share.
Reserve and restraint are near-synonyms of the key word; diffidence (lack of self-confidence) is a cause of reticence, not its opposite.
Q.3 [English — Antonyms]
Observers noted the officials' increasingly capricious approach to administrative reforms.
Select the word that is opposite in meaning to the underlined word.
Capricious = given to sudden, unaccountable changes of mood or behaviour. The opposite is steadfast — firm, unwavering, consistent.
Erratic and whimsical are synonyms; ceremonial is unrelated.
Q.4 [English — Antonyms]
The novel presents an idealistic view of the ongoing political reform.
Select the word that is opposite in meaning to the underlined word.
Idealistic = guided by ideals rather than by practical considerations. Its standard opposite is pragmatic — dealing with things realistically and practically.
Visionary, utopian and romantic are all clustered on the idealistic side.
Q.5 [English — Antonyms]
The speaker's tone became increasingly caustic during the debate.
Select the word that is opposite in meaning to the underlined word.
Caustic literally means burning or corrosive; of speech it means sarcastic in a biting way. The opposite is conciliatory — intended to pacify or win goodwill.
Sarcastic, acerbic and acrimonious are all synonyms of the key word — three synonyms and one antonym is the standard build of this item type.
Q.6 [English — Antonyms]
The note drew attention to the fallacious assumptions underlying the proposals.
Select the word that is opposite in meaning to the underlined word.
Fallacious = based on a mistaken belief; false or misleading. The opposite is veracious — truthful, accurate.
Misleading and erroneous are synonyms. Do not confuse veracious (truthful) with voracious (having a huge appetite) — a pair UPSC has tested before.
Q.7 [English — Antonyms]
The activist was sceptical with regard to the antecedents of the newly discovered documents.
Select the word that is opposite in meaning to the underlined word.
Sceptical = inclined to doubt; not easily convinced. The opposite is credulous — too ready to believe things.
Guarded and restrained describe caution, which sits close to scepticism rather than against it; circumlocutory means roundabout in speech and is off the point entirely.
Q.8 [English — Antonyms]
The panel found the conclusion somewhat speculative.
Select the word that is opposite in meaning to the underlined word.
Speculative = based on conjecture rather than firm evidence. The opposite is substantiated — supported by proof.
Conjectural and hypothetical are synonyms of the key word.
Q.9 [English — Antonyms]
After the mishap, the mood was sombre among the survivors.
Select the word that is opposite in meaning to the underlined word.
Sombre = dark, gloomy, grave in mood. Its opposite is buoyant — cheerful and optimistic.
Shady and dingy pick up only the 'dark' sense of the word and are therefore near-synonyms in the physical sense, not antonyms of the mood.
Q.10 [English — Antonyms]
He is a professional artist.
Select the word that is opposite in meaning to the underlined word.
The settled antonym pair in English is professional / amateur — one who does something for a living against one who does it for love of it.
Dilettante is the near-miss: it means a dabbler and carries a note of superficiality, so it is a shade of 'amateur' rather than its plain opposite. Apprentice and aspirant describe stages on the way to becoming a professional, not the opposite of one.
Q.11 [English — Synonyms]
The controversial policy received the committee's imprimatur.
Select the word that is nearest in meaning to the underlined word.
Imprimatur is Latin for 'let it be printed' — originally a licence to publish, now any official sanction or approval.
Appraisal (an assessment) is the trap: an assessment may be favourable or unfavourable, whereas an imprimatur is always an endorsement.
Q.12 [English — Synonyms]
The archaeologist was fascinated by the annular design of the ancient monument.
Select the word that is nearest in meaning to the underlined word.
Annular comes from Latin annulus, a ring — hence ring-shaped or circular. The familiar use is the annular solar eclipse, where a ring of the Sun remains visible.
Funicular relates to a rope or cable (as in a funicular railway) and is a pure sound-alike.
Q.13 [English — Synonyms]
The nobility is not known for its munificence.
Select the word that is nearest in meaning to the underlined word.
Munificence = great generosity in giving, especially on a lavish scale.
Graciousness is the near-miss — it is about courtesy and kindness of manner, not about giving. The root munus (gift) is the clue.
Q.14 [English — Synonyms]
The goods kept in the storage facility were declared to be contraband.
Select the word that is nearest in meaning to the underlined word.
Contraband = goods that are illegal to import, export or possess; smuggled goods.
Taxable is the trap for candidates who associate the word loosely with customs. Contraband is not merely dutiable — it is banned.
Q.15 [English — Synonyms]
The judge ruled on the egregious violations of human rights by the authorities.
Select the word that is nearest in meaning to the underlined word.
Egregious = outstandingly bad; conspicuously wrong. Flagrant carries exactly that sense of an offence committed openly and shamelessly.
Subtle, inadvertent and concealed all point to something hidden or unintended — the opposite of what the word means.
Q.16 [English — Foreign Phrases]
Select the alternative which provides the correct meaning of the foreign phrase used in English : Ipso facto
Latin ipso facto — 'by that very fact'. It marks a consequence that follows automatically from a fact, without any further proof.
Example: A person convicted of treason is ipso facto disqualified from holding office.
Q.17 [English — Foreign Phrases]
Select the alternative which provides the correct meaning of the foreign phrase used in English : Via media
Latin via media — literally 'the middle road'; a compromise between two extremes.
Options (a) and (b) exploit the resemblance to the English word media, which is a different (though related) Latin plural altogether.
Q.18 [English — Foreign Phrases]
Select the alternative which provides the correct meaning of the foreign phrase used in English : Quid pro quo
Latin quid pro quo — 'something for something'; a favour granted in return for another.
Option (a) is status quo, (b) is ergo, and (d) is close to pro bono — the item is really testing four phrases at once.
Q.19 [English — Foreign Phrases]
Select the alternative which provides the correct meaning of the foreign phrase used in English : A posteriori
A posteriori reasoning moves from observed effects back to causes — knowledge derived from experience.
Its counterpart, a priori, is reasoning from theory or first principles, independent of experience. Option (a) 'at the very beginning' is closer to ab initio.
Q.20 [English — Foreign Phrases]
Select the alternative which provides the correct meaning of the foreign phrase used in English : Modus operandi
Latin modus operandi — a person's characteristic way of doing something, often used of a criminal's method.
Option (a) hints at mot juste, and the related phrase modus vivendi means a practical arrangement for living together.
Q.21 [English — Idioms]
Select the most appropriate meaning of the idiom/phrase : 'Burn your bridges'
The image is military — an army that burns the bridges behind it cannot retreat. The idiom means to destroy your means of going back on a decision.
Example: He resigned in anger and burned his bridges with the whole department.
Q.22 [English — Idioms]
Select the most appropriate meaning of the idiom/phrase : 'Make no bones about something'
To make no bones about something is to say plainly what you think, without hesitation or apology.
Option (d) is its exact inversion — a favourite distractor design.
Q.23 [English — Idioms]
Select the most appropriate meaning of the idiom/phrase : 'A blot on the landscape'
The phrase is used of an eyesore — a building, dump or hoarding that disfigures an otherwise pleasant view.
(a) and (b) read the words literally; (c) confuses it with the separate idiom black sheep.
Q.24 [English — Idioms]
Select the most appropriate meaning of the idiom/phrase : 'A bone of contention'
The image is of two dogs quarrelling over a bone. A bone of contention is the subject that keeps a dispute alive.
Option (a) is the exact reverse.
Q.25 [English — Idioms]
Select the most appropriate meaning of the idiom/phrase : 'Pour oil on troubled waters'
Oil spread on choppy water genuinely flattens the waves — sailors once used the trick, and the idiom took it over for peacemaking.
Option (c) is the deliberate reversal; do not confuse this with adding fuel to the fire, which is what (c) describes.
Q.26 [English — Parts of Speech]
Despite the heavy rain, the match continued as scheduled.
Identify the word class the underlined word belongs to.
Despite is followed here by the noun phrase the heavy rain, and a word that governs a noun phrase is a preposition.
The concessive conjunction with the same meaning is although/though, which must be followed by a clause: Although it rained heavily, the match continued. That contrast is exactly what the item tests.
Q.27 [English — Parts of Speech]
He gave both candidates an equal opportunity to present their case.
Identify the word class the underlined word belongs to.
Here both stands before the noun candidates and specifies it — the job of a determiner, like the, some, each, every.
Both would be a pronoun if it stood alone in place of a noun: Both were given an equal opportunity. The test is whether a noun follows.
Q.28 [English — Parts of Speech]
The old woman sat on the bench, knitting in silence.
Identify the word class the underlined word belongs to.
Silence is the object of the preposition in, and only a noun (or pronoun/gerund) can fill that slot.
The phrase in silence as a whole functions adverbially — which is the trap in option (c). The word class of silence itself is still a noun.
Q.29 [English — Parts of Speech]
The injured soldier crawled forward in spite of debilitating pain.
Identify the word class the underlined word belongs to.
Forward here modifies the verb crawled, telling us in which direction — the work of an adverb.
The same word is an adjective in a forward movement and a noun in football (he plays as a forward); word class is decided by the job the word does in the sentence, not by the word itself.
Q.30 [English — Parts of Speech]
The results were beyond everyone's expectation.
Identify the word class the underlined word belongs to.
Beyond governs the noun phrase everyone's expectation, so it is a preposition.
It can be an adverb when nothing follows it (the hills and the plain beyond), but here a noun phrase follows and settles the matter.
Q.31 [English — Sentence Ordering]
Reorder the PQRS set to create the most appropriate meaningful sentence.
The findings were
P : that had long been accepted
Q : because they fundamentally challenged the assumptions
R : met with considerable resistance at first
S : by the mainstream scientific community
Full sentence: The findings were met with considerable resistance at first because they fundamentally challenged the assumptions that had long been accepted by the mainstream scientific community.
R must come first — only it supplies a verb phrase to complete 'The findings were…'.
Q follows because because introduces the reason for that resistance.
P is a relative clause modifying the assumptions at the end of Q, so it must sit next to it.
S completes P: the assumptions were accepted by the mainstream scientific community.
The trap is to attach S to R — 'resistance … by the mainstream scientific community' also reads well, but then P is left with nothing to modify.
Q.32 [English — Sentence Ordering]
Reorder the PQRS set to create the most appropriate meaningful sentence.
It is often argued that
P : are not the result of innate talent alone
Q : but rather the product of
R : extraordinary achievements
S : sustained effort and deliberate practice
Full sentence: It is often argued that extraordinary achievements are not the result of innate talent alone but rather the product of sustained effort and deliberate practice.
R supplies the subject the clause needs; P is its verb phrase.
P and Q are locked together by the correlative pair not … but rather.
S is the noun phrase that completes the product of.
Q.33 [English — Sentence Ordering]
Reorder the PQRS set to create the most appropriate meaningful sentence.
The historian noted that
P : had been systematically erased
Q : the memory of certain communities
R : and replaced with a sanitized narrative
S : from the official records of the colonial period
Full sentence: The historian noted that the memory of certain communities had been systematically erased from the official records of the colonial period and replaced with a sanitized narrative.
Q is the only subject available; P the verb.
S completes erased from ….
R begins with and, so it must be the last element of the compound predicate.
Q.34 [English — Sentence Ordering]
Reorder the PQRS set to create the most appropriate meaningful sentence.
Critics have long maintained that
P : literature's true power lies in its
Q : assumptions and not in the mere
R : ability to disturb comfortable
S : reproduction of social reality
Full sentence: Critics have long maintained that literature's true power lies in its ability to disturb comfortable assumptions and not in the mere reproduction of social reality.
Work from the fragments: its at the end of P demands a noun, supplied by ability in R; comfortable at the end of R demands a noun, supplied by assumptions in Q; the mere at the end of Q demands a noun, supplied by reproduction in S.
Each fragment ends on a word that cannot stand alone — that chain fixes the order without any guesswork.
Q.35 [English — Sentence Ordering]
Reorder the PQRS set to create the most appropriate meaningful sentence.
The movie
P : it was hardly possible
Q : were so humorous that
R : to keep a straight face
S : had many scenes which
Full sentence: The movie had many scenes which were so humorous that it was hardly possible to keep a straight face.
S supplies the main verb after the subject 'The movie'.
Q follows because the relative pronoun which at the end of S needs its verb.
P and R then complete the so … that construction, with R the infinitive that completes it was hardly possible.
Q.36 [English — Sentence Correction]
Select the most appropriate correct sentence.
Verbs of demand and proposal — insist, suggest, demand, recommend, propose, urge — are followed by the subjunctive: that + subject + bare infinitive, with no -s even for a third-person singular subject.
Hence that he apologise, not apologises (a), not apologised (d), and not with a modal may (c). The alternative acceptable form is that he should apologise.
Q.37 [English — Sentence Correction]
Select the most appropriate correct sentence.
Two rules are being tested at once.
1. Police is a plural collective noun in English and takes a plural verb — which rules out (a).
2. A definite past-time adverbial such as last night cannot go with the present perfect, which rules out (b). The past perfect in (d) needs a second, later past action to be anterior to.
The simple past in (c) is the only fit.
Q.38 [English — Sentence Correction]
Select the most appropriate correct sentence.
Causative verbs follow fixed patterns:
• make + object + bare infinitive — made the students rewrite (so (a), with to, is wrong)
• have + object + bare infinitive — had the students rewrite ✓
• get + object + to-infinitive — got the students to rewrite (so (c) is wrong)
Only (d) matches its pattern exactly.
Q.39 [English — Sentence Correction]
Select the most appropriate correct sentence.
Again two points.
1. Collocation: one bases a decision on something, not about or to it — which removes (b) and (d).
2. Embedded question: an indirect question keeps normal statement order, so it is how much free time I can manage, not can I manage — which removes (a).
Q.40 [English — Sentence Correction]
Select the most appropriate correct sentence.
The sentence refers to one specific, known situation, so the definite article is required: the situation. (a) uses the indefinite a, which makes the reference vague and the sentence odd.
(b) has no verb in the subordinate clause. (c) uses however, an adverb, where a conjunction of reason is needed.
Q.41 [English — Error Spotting]
A sentence is given in three parts (a), (b) and (c). Find out which part of the sentence has an error. If there is no error, mark your option (d).
(a) He is a honest man
(b) who has served
(c) this institution for twenty years
(d) No error
Rule: the choice between a and an is decided by the sound that follows, not by the letter. In honest the h is silent, so the word begins with a vowel sound and takes an.
Correct: He is an honest man who has served this institution for twenty years.
The same rule gives an hour, an heir, an honour — and, in the other direction, a university, a European, a one-rupee coin, where the spelling starts with a vowel but the sound does not.
Q.42 [English — Error Spotting]
A sentence is given in three parts (a), (b) and (c). Find out which part of the sentence has an error. If there is no error, mark your option (d).
(a) The jury has delivered
(b) its verdict after
(c) long and careful deliberations
(d) No error
Jury is a collective noun. When the body acts as a single unit — as it does in delivering one verdict — the singular verb and the singular pronoun are correct: the jury has delivered its verdict. The sentence is internally consistent on this point, which is the clearest sign that it is right.
(The plural would be used only when the members are thought of separately: the jury were divided among themselves.)
Deliberations in the plural is standard English for the discussions of a body.
Q.43 [English — Voice]
Read the following pairs :
| Active Voice | Passive Voice | |
|---|---|---|
| I. | These grapes taste sour. | These grapes are sour when they are tasted. |
| II. | Forget the past. | Let the past be forgotten. |
Pair I. Taste here is a verb of perception used statively, and such verbs have no ordinary passive. The standard transformation used for them is exactly the one given: These grapes are sour when they are tasted. ✓
Pair II. An imperative is turned into the passive with Let + object + be + past participle: Forget the past → Let the past be forgotten. ✓
Both transformations follow their rules, so the answer is (c).
Q.44 [English — Voice]
Read the following pairs :
| Active Voice | Passive Voice | |
|---|---|---|
| I. | They asked me my name. | My name was asked by them. |
| II. | They found him guilty. | He found them guilty. |
Pair I ✓. Ask takes two objects (me, my name); either can become the subject of the passive. Taking the direct object gives My name was asked by them. (Taking the indirect object gives I was asked my name by them.) Both are legitimate.
Pair II ✗. He found them guilty is not a passive at all — it is a fresh active sentence with the roles reversed. The correct passive is He was found guilty by them.
A passive must carry be + past participle; if that is missing, the pair is wrong however plausible it sounds.
Q.45 [English — Narration]
Read the following pairs :
| Direct Speech | Indirect Speech | |
|---|---|---|
| I. | He said, "Bravo! You have written the best answer." | He applauded him saying that he had written the best answer. |
| II. | "The sun rises in the East," said the teacher. | The teacher said that the sun rose in the East. |
Pair I ✓. The exclamation Bravo! is reported by a suitable reporting verb — applauded — and the present perfect have written correctly backshifts to the past perfect had written.
Pair II ✗. This is the classic exception: a universal truth is not backshifted. The sun's rising in the east is permanently true, so the correct reported form keeps the present tense — The teacher said that the sun rises in the East.
The other standing exceptions to backshift are habitual facts and statements still true at the moment of reporting.
Q.46 [English — Narration]
Read the following pairs :
| Direct Speech | Indirect Speech | |
|---|---|---|
| I. | He said to him, "Wait here until I return." | He ordered him to wait here until he returned. |
| II. | He said, "Alas! I am undone." | He exclaimed sadly that he was undone. |
Pair II ✓. Alas! is reported by the verb exclaimed sadly, and I am backshifts correctly to he was.
Pair I ✗. The tense change and the reporting verb are right, but the adverb of place has not been changed. In reported speech here becomes there, just as this becomes that, now becomes then and tomorrow becomes the next day.
Correct: He ordered him to wait there until he returned.
Q.47 [English — One-word Substitution]
Read the following pairs :
| Group of words | One-word substitution | |
|---|---|---|
| I. | One who studies handwriting | Graphologist |
| II. | One who draws maps | Cartographer |
| III. | One who studies flags | Vexillologist |
Graphology is the study of handwriting, especially as a supposed guide to character.
Cartography (Greek chartes, map) is the drawing of maps.
Vexillology (Latin vexillum, a flag) is the study of flags.
When each pair checks out independently, 'all of the above' is the answer — candidates lose this mark by assuming at least one must be planted.
Q.48 [English — One-word Substitution]
Read the following pairs :
| Group of words | One-word substitution | |
|---|---|---|
| I. | One who knows everything | Omnipotent |
| II. | One who is all powerful | Omniscient |
| III. | One who abandons religious faith | Apostate |
I ✗ and II ✗ — the two words have been swapped.
Omniscient (scire, to know) = knowing everything.
Omnipotent (potens, powerful) = all powerful.
So 'one who knows everything' is omniscient, not omnipotent, and 'one who is all powerful' is omnipotent, not omniscient.
III ✓. An apostate is one who renounces a religious or political belief. (The third member of the family is omnipresent — present everywhere.)
Q.49 [English — Phrasal Verbs]
Fill in the blanks with the most appropriate phrasal verb.
The car tended to __________ every time the rains decided to __________.
Act up = to behave badly or, of a machine, to function erratically — exactly what a car does in the rain.
Come down = to fall, said of rain (the rain came down in sheets).
Act out means to perform or to express feelings through behaviour, and come in means to arrive or enter — neither fits.
Both blanks must be right for the option to stand, so check the second before marking.
Q.50 [English — Phrasal Verbs]
Fill in the blanks with the most appropriate phrasal verb.
He was eager to __________ after having resigned his position, but was advised to __________ his next move given the prevailing market situation.
Move on = to leave a situation behind and go forward with one's life — the natural verb after a resignation.
Hold off = to delay or postpone, which is what the market situation calls for.
Move off is used of a vehicle starting to move, and hold on means to wait a moment or to grip something — close in sense but not the idiom used with a planned 'next move'.
Q.51 [Physics]
A bicycle racing track is a level circular road of radius 10 m. Three cyclists P, Q and R with identical cycles are cycling on the track with speeds 2 m/s, 3 m/s and 5 m/s respectively. If the coefficient of friction between the tyres and the road is $0\cdot1$, then which cyclist will slip? (Take $g=10$ m/s$^2$)
$\dfrac{mv^2}{r}\le\mu mg\ \Rightarrow\ v\le\sqrt{\mu g r}.$
$v_{\max}=\sqrt{0\cdot1\times10\times10}=\sqrt{10}\approx3\cdot16$ m/s.
P at 2 m/s and Q at 3 m/s are below this limit; R at 5 m/s exceeds it and slips. Option (c).
Note that the mass cancels — which is why 'identical cycles' is stated but never needed.
Q.52 [Physics]
The bob of a simple pendulum is displaced from its mean position and then released from rest $0\cdot20$ m above its mean position. What is the speed of the bob as it passes through the mean position? (Take $g=10$ m/s$^2$)
$mgh=\tfrac12mv^2\ \Rightarrow\ v=\sqrt{2gh}.$
$v=\sqrt{2\times10\times0\cdot20}=\sqrt4=2$ m/s. Option (c).
Neither the mass of the bob nor the length of the string is needed — only the vertical drop.
Q.53 [Physics]
A tennis ball of mass 350 g is thrown vertically upwards at a speed of 4 m/s. If M is the maximum gravitational potential energy of the ball and H is the maximum height it reaches, then which one of the following is correct? (Take $g=10$ m/s$^2$)
$H=\dfrac{u^2}{2g}=\dfrac{4^2}{2\times10}=\dfrac{16}{20}=0\cdot8$ m.
Potential energy at the top: all the initial kinetic energy has been converted, so
$M=mgH=0\cdot350\times10\times0\cdot8=2\cdot8$ J.
(Equivalently $M=\tfrac12mu^2=\tfrac12(0\cdot35)(16)=2\cdot8$ J.) Option (d).
The mass must be converted to kilograms — using 350 directly is what produces the inflated 5·6 J options.
Q.54 [Physics]
Which of the following is correct regarding the total internal reflection at the interface between two different optical media?
1. Light must travel from a denser medium to a rarer one (high $\mu$ to low $\mu$);
2. The angle of incidence must exceed the critical angle $C$, where $\sin C=\dfrac{\mu_{\text{rarer}}}{\mu_{\text{denser}}}$.
Only option (b) states both. Options (a) and (d) reverse the direction; option (c) gets the direction right but drops the critical-angle condition — and without it the light simply refracts out.
The phenomenon explains optical fibres, the mirage, and the sparkle of a diamond (whose critical angle is only about $24^\circ$).
Q.55 [Physics]
Consider the following statements :
I. The weight of an object is the same everywhere on the surface of the Earth, but its inertial mass could be different.
II. The inertial mass and gravitational mass of an object are proportional and the proportionality constant is the same everywhere.
III. The inertial mass and weight of an object are the same at different places on Earth.
Which of the statements given above is/are correct ?
II is true. This is the principle of equivalence: inertial mass (resistance to acceleration) and gravitational mass (response to gravity) are proportional, and by choosing units the constant is made 1 — everywhere in the universe.
III is false. Mass and weight are different physical quantities with different units (kg and newton); they are numerically related by $g$, which itself varies.
Answer (b).
Q.56 [Physics]
Consider the following :
I. Gravitational field due to a spherical body
II. Electrostatic field due to a point charge
III. Strong nuclear force field due to a proton
IV. Magnetic field due to a bar magnet
How many of the above follow the inverse square law ?
II ✓ — Coulomb's law gives $\dfrac{1}{4\pi\varepsilon_0}\dfrac{q}{r^2}$.
III ✗ — the strong nuclear force is short-range, effective only up to a few femtometres, and dies away far faster than any inverse square.
IV ✗ — a bar magnet is a dipole; its field falls off as $\dfrac1{r^3}$, not $\dfrac1{r^2}$. (An isolated magnetic pole, which would give an inverse square, does not exist.)
Two of the four. Option (b).
Q.57 [Physics]
While pouring water slowly from a jug, a general observation is that a water layer usually flows along the side of the jug. Which property of water among the following is responsible for this phenomenon?
Water clings to the lip of the jug and runs down its outer wall because the adhesive forces between water and the solid surface, together with the cohesive forces within the liquid that keep the stream intact, hold the film to the wall. Both are manifestations of surface tension — the same property that produces capillary rise and the meniscus.
Vapour pressure (b) governs evaporation, compressibility (c) the response to pressure, and viscosity (d) the resistance to flow — none of them explains a film sticking to a solid surface.
Q.58 [Physics]
A fish is at a depth $d$ in water of refractive index $4/3$. If a transparent slab of refractive index $3/2$ and thickness $d/2$ is placed on the surface of water, then which one of the following is the apparent depth of the fish observed by an observer in air?
$\text{apparent depth}=\sum\dfrac{t_i}{\mu_i}.$
Water layer: $\dfrac{d}{4/3}=\dfrac{3d}{4}$
Slab: $\dfrac{d/2}{3/2}=\dfrac{d}{3}$
Total $=\dfrac{3d}{4}+\dfrac{d}{3}=\dfrac{9d+4d}{12}=\dfrac{13d}{12}.$ Option (c).
The answer exceeds $d$ because the slab adds real thickness above the water — the fish is now deeper below the topmost surface than it was.
Q.59 [Physics]
A particle of mass $m$ moves along $x$-direction under the force $F(x)=F_0\left(1-\dfrac{x}{L}\right)$ for $0\le x\le L$. If the particle starts from rest at $x=0$, then what is the speed $v$ of the particle at $x=L$?
$W=\displaystyle\int_0^{L}F_0\left(1-\frac{x}{L}\right)dx=F_0\left[x-\frac{x^2}{2L}\right]_0^{L}=F_0\left(L-\frac L2\right)=\frac{F_0L}{2}.$
Starting from rest, $W=\tfrac12mv^2$:
$\tfrac12mv^2=\dfrac{F_0L}{2}\Rightarrow v=\sqrt{\dfrac{F_0L}{m}}.$ Option (b).
Geometrically the work is the area under the $F$–$x$ line: a triangle of base $L$ and height $F_0$, i.e. $\tfrac12F_0L$ — the same answer without any calculus.
Q.60 [Physics]
A narrow tunnel passes through the centre of a planet of radius R and uniform mass density $\rho$. A particle is released into the tunnel. What is the angular frequency $\omega$ of oscillation of the particle equal to? (Symbols carry their usual meaning)
$M_r=\dfrac43\pi r^3\rho\ \Rightarrow\ F=-\dfrac{GmM_r}{r^2}=-\dfrac{4}{3}\pi G\rho m\,r.$
The force is proportional to the displacement and directed towards the centre — simple harmonic motion with
$m\omega^2=\dfrac43\pi G\rho m\ \Rightarrow\ \omega=\sqrt{\dfrac{4\pi G\rho}{3}}.$ Option (a).
Equivalently $\omega=\sqrt{g/R}$, so for the Earth the period would be about 84 minutes — the same as that of a satellite skimming the surface.
Q.61 [Physics]
On a rainy day, rain drops fall vertically with speed $v$. An observer is moving towards east with speed $v$, while another observer moves towards north with the same speed $v$. What is the angle between apparent rain directions observed by them?
Apparent velocity $=\vec v_{\text{rain}}-\vec v_{\text{observer}}$:
Eastward observer: $(0,0,-v)-(v,0,0)=(-v,0,-v)$
Northward observer: $(0,0,-v)-(0,v,0)=(0,-v,-v)$
Angle between them:
$\cos\theta=\dfrac{(-v)(0)+(0)(-v)+(-v)(-v)}{(v\sqrt2)(v\sqrt2)}=\dfrac{v^2}{2v^2}=\dfrac12\Rightarrow\theta=60^\circ.$ Option (d).
The tempting wrong answer is $90^\circ$ — the angle between the two observers' own directions. The apparent-rain vectors both tilt downwards, which closes the angle between them to $60^\circ$.
Q.62 [Physics]
What is the minimum horizontal speed given to the bob of a simple pendulum of length 50 cm so that it describes a complete circle? (Take $g=10$ m/s$^2$)
Applying energy conservation between the bottom and the top (height $2L$):
$\tfrac12mv^2=\tfrac12mv_{\text{top}}^2+mg(2L)\Rightarrow v^2=gL+4gL=5gL.$
$v=\sqrt{5gL}=\sqrt{5\times10\times0\cdot5}=\sqrt{25}=5$ m/s. Option (a).
Remember the contrast: for a rod (which can push as well as pull) the requirement falls to $v=\sqrt{4gL}$.
Q.63 [Physics]
Two conducting wires made of the same material have lengths L and $1\cdot2$ L. If the volume of the longer wire is half that of the shorter wire, then what is the electric resistance of the longer wire in comparison with the shorter wire?
$R=\dfrac{\rho \ell}{A}=\dfrac{\rho \ell^2}{V}.$
Shorter wire: $R_1=\dfrac{\rho L^2}{V}$.
Longer wire: $\ell=1\cdot2L$ and volume $=V/2$, so $R_2=\dfrac{\rho(1\cdot2L)^2}{V/2}=\dfrac{2\times1\cdot44\,\rho L^2}{V}=2\cdot88\,R_1.$
$R_2$ is $2\cdot88$ times $R_1$, i.e. larger by $1\cdot88\,R_1=188\%$. Option (c).
Option (a) is the trap for those who report the ratio $288\%$ instead of the increase.
Q.64 [Physics]
A biconvex lens is made of a material of refractive index 2 such that the ratio of the radii of curvature of its two faces is $1:2$. A point source in air is placed on the principal axis of the lens at a distance $u$ from the lens. Which one of the following is correct if the image is formed exactly at the same distance as that of the point source? (where R is the radius of curvature of the first face)
Step 2 — the focal length. For a biconvex lens with first radius $+R$ and second radius $-2R$, the lens maker's formula gives
$\dfrac1f=(\mu-1)\left(\dfrac{1}{R_1}-\dfrac{1}{R_2}\right)=(2-1)\left(\dfrac1R+\dfrac1{2R}\right)=\dfrac{3}{2R}\Rightarrow f=\dfrac{2R}{3}.$
Step 3 — combine. $u=2f=\dfrac{4R}{3}$, i.e. $3u=4R$. Option (d).
The sign convention on $R_2$ is the whole game: for a biconvex lens the second surface has a negative radius, which turns the subtraction into an addition.
Q.65 [Physics]
In a carrom game, a striker of mass 15 g hits a coin of mass 5 g head on and the coin moves with a speed of $0\cdot36$ m/s. If the time of contact between the striker and the coin is 3 milliseconds, then what is the average force applied by the striker on the coin?
$F_{\text{avg}}=\dfrac{\Delta p}{\Delta t}=\dfrac{m_{\text{coin}}\,v}{\Delta t}.$
$m=5\text{ g}=0\cdot005$ kg, $v=0\cdot36$ m/s, $\Delta t=3$ ms $=0\cdot003$ s.
$F=\dfrac{0\cdot005\times0\cdot36}{0\cdot003}=\dfrac{0\cdot0018}{0\cdot003}=0\cdot60$ N. Option (b).
The striker's mass of 15 g is a decoy — the force on the coin depends only on the coin's change of momentum. (By Newton's third law the coin pushes back on the striker with the same 0·60 N.)
Q.66 [Physics]
A hollow prism is filled with water of refractive index $1\cdot34$ and white light is incident on the prism. The white light is assumed to have wavelengths ranging from 4020 Å to 6700 Å. What is the corresponding wavelength range in water?
$\lambda_{\text{medium}}=\dfrac{\lambda_{\text{air}}}{\mu}.$
$\dfrac{4020}{1\cdot34}=3000$ Å and $\dfrac{6700}{1\cdot34}=5000$ Å.
So the range becomes 3000 Å to 5000 Å. Option (a).
Option (d) multiplies instead of dividing. A useful check: wavelength must decrease in a denser medium, so any option larger than the original range is wrong on sight.
Q.67 [Physics]
A heating filament and an ideal resistor of fixed value are connected in series with a DC voltage source. After some time, the filament has reached its operating point so that the current in the circuit is steady. Which one of the following is correct?
• total circuit resistance increases → option (c) is wrong;
• the steady current $I=\dfrac{E}{R+r}$ therefore decreases → option (a) is wrong;
• the voltage across the fixed resistor, $V=IR$, falls with the current → option (b) is correct.
Option (d) cannot be settled at all: $P_{\text{fil}}=\dfrac{E^2r}{(R+r)^2}$ rises with $r$ only while $r
This is why an incandescent bulb draws a large surge of current at switch-on and settles to a smaller steady current.
Q.68 [Physics]
Two astronauts X and Y float in deep space far from external forces. Initially, they are at rest relative to one another. X throws a tool towards Y. Consider the two astronauts and the tool as one system. Which one of the following statements is correct?
Internal forces — X's push on the tool, the tool's push back on X, the tool's impact on Y — cannot move the centre of mass, however violently the individual parts move.
Option (d). After the throw, X recoils one way and the tool travels the other in exactly the proportion that keeps the centre of mass where it was.
Q.69 [Physics]
A uniform rope hangs symmetrically over a smooth pulley. One end of the rope is given a slight mass, making that side slightly heavier. Which one of the following is correct?
(c) is wrong. The rope has mass, so the tension varies along it: each element must support the weight of the rope below it as well as provide its share of the acceleration. Uniform tension holds only for a massless rope.
(d) is wrong. Mass is transferred from the rising side to the falling side, so the centre of mass descends.
Q.70 [Physics]
An insulating container contains 250 g of water at 20°C. Steam at 100°C is passed through it, heating it up to 25°C. During this process, part of the steam also gets condensed, raising the mass of water to 252 g. If the specific heat of water is 1 Cal g$^{-1}$ °C$^{-1}$, then what is the value of the latent heat of steam?
Heat gained by the original 250 g of water, from 20°C to 25°C:
$Q_{\text{gain}}=250\times1\times(25-20)=1250$ Cal.
Heat lost by the $252-250=2$ g of steam that condensed — first condensation at 100°C, then cooling of that condensate from 100°C to 25°C:
$Q_{\text{lost}}=2L+2\times1\times(100-25)=2L+150.$
Equating: $2L+150=1250\Rightarrow2L=1100\Rightarrow L=550$ Cal/g. Option (c).
Forgetting the second term — the cooling of the condensed water — gives $L=625$, which is not on offer; that omission is the commonest error in calorimetry problems of this shape.
Note: some circulated keys mark (d) 560 Cal/g. The balance above closes exactly on 550, and the accepted textbook value for the latent heat of steam is about 540 Cal/g, so 550 is both the computed and the physically sensible figure.
Q.71 [Physics]
Three parallel glass slabs of refractive indices $1\cdot5$, $\sqrt3$ and $1\cdot5$ respectively have widths 2 mm, 1 mm and 4 mm. The combination is in air. Light is incident at the first slab at an angle of incidence $\pi/3$. What is the angle with respect to the normal at which the light will emerge from the final surface?
$\mu_{\text{air}}\sin\theta_{\text{air}}=\mu_1\sin\theta_1=\mu_2\sin\theta_2=\mu_3\sin\theta_3=\mu_{\text{air}}\sin\theta_{\text{out}}.$
Since the first and last media are both air, $\sin\theta_{\text{out}}=\sin\theta_{\text{in}}$, so the ray emerges at $\dfrac\pi3$ — parallel to the original direction, merely displaced sideways. Option (c).
The refractive indices and the three widths are all decoys: they fix the lateral shift, not the emergent angle.
Q.72 [Physics]
Consider three wires X, Y and Z of the same length such that the ratio of their conductivities is $1:2:3$. Further, the cross-sectional area of wire Z is twice that of Y and the resistance of X is equal to the resistance of Z. What is the ratio of the resistance of Y to that of X?
Write $\sigma_X:\sigma_Y:\sigma_Z=1:2:3$ and $A_Z=2A_Y$.
$R_X=\dfrac{\ell}{A_X},\qquad R_Y=\dfrac{\ell}{2A_Y},\qquad R_Z=\dfrac{\ell}{3(2A_Y)}=\dfrac{\ell}{6A_Y}.$
The condition $R_X=R_Z$ gives $\dfrac{\ell}{A_X}=\dfrac{\ell}{6A_Y}\Rightarrow A_X=6A_Y$, hence $R_X=\dfrac{\ell}{6A_Y}$.
$\dfrac{R_Y}{R_X}=\dfrac{\ell/(2A_Y)}{\ell/(6A_Y)}=3.$ So $R_Y:R_X=3:1$. Option (b).
Q.73 [Physics]
Two point charges of 4 C and 16 C are kept at a distance of $0\cdot15$ m. A third point charge of 1 C is kept between them such that the potential energy of the system is minimum. What is the magnitude of the electric field at the 1 C charge?
The same result the long way. With the 1 C charge at distance $x$ from the 4 C charge,
$U=k\left[\dfrac{4}{x}+\dfrac{16}{d-x}+\dfrac{64}{d}\right],\qquad \dfrac{dU}{dx}=k\left[-\dfrac{4}{x^2}+\dfrac{16}{(d-x)^2}\right]=0$
$\Rightarrow(d-x)^2=4x^2\Rightarrow d-x=2x\Rightarrow x=\dfrac d3=0\cdot05\text{ m}.$
There the two fields are $\dfrac{k(4)}{(0\cdot05)^2}=1600k$ and $\dfrac{k(16)}{(0\cdot10)^2}=1600k$ — equal in magnitude and opposite in direction, so they cancel exactly.
Q.74 [Physics]
Consider the following statements in respect of sound waves :
I. The speed of sound waves decreases with an increase in temperature if the atmospheric pressure remains the same.
II. The speed of sound waves increases with increasing humidity if the atmospheric pressure remains the same.
III. The speed of sound waves is not affected by a change in atmospheric pressure, provided the temperature is kept constant.
Which of the statements given above are correct ?
I is false. The second form shows $v\propto\sqrt T$ — speed increases with temperature, by roughly $0\cdot61$ m/s per °C near room temperature.
II is true. Water vapour ($M=18$) is lighter than the average of dry air ($M\approx29$), so moist air is less dense and sound travels faster through it.
III is true. At constant temperature, raising the pressure raises the density in the same proportion, so $P/\rho$ — and hence $v$ — is unchanged.
Answer (b).
Q.75 [Physics]
Statement-I : Marine animals remain alive in winter and move near the bottom of lakes despite frozen water on the surface.
Statement-II : The density of water is maximum at 4°C and water at the bottom of lakes remains warm in winter.
Which one of the following is correct in respect of the above statements ?
Water shows anomalous expansion: on cooling it contracts down to 4°C and then expands below that temperature. The densest water, at 4°C, therefore sinks to the bottom, while colder water — and finally ice at 0°C — floats on top.
The ice sheet then acts as an insulator, so the lower layers stay at about 4°C through the winter and aquatic life survives there.
Option (a). Had water behaved like ordinary liquids, lakes would freeze from the bottom upwards and the life in them would not survive.
Q.76 [Chemistry]
Consider the following statements regarding oxidation numbers :
I. The oxidation number of oxygen in peroxides and superoxides is assigned as $-1$ and $-1/2$ respectively.
II. In all its compounds, fluorine has an oxidation number of $-1$.
III. In a reduction half-reaction, the oxidation number of the reductant decreases.
Which of the statements given above are correct ?
II is true. Fluorine is the most electronegative element, so it is always $-1$ in its compounds and never positive.
III is false — and this is the point of the item. In a reduction half-reaction it is the oxidant that is reduced and whose oxidation number falls. The reductant is the species that is oxidised, so its oxidation number rises.
Answer (a). The mnemonic: OIL RIG — Oxidation Is Loss, Reduction Is Gain (of electrons); the reducing agent gives electrons away and is itself oxidised.
Q.77 [Chemistry]
Consider the following statements regarding the properties of hydrogen and water :
I. Tritium, the isotope of hydrogen, is radioactive and emits low energy alpha particles.
II. In the gas phase, the structure of water is linear.
III. The basic principle of a hydrogen economy is the transportation and storage of energy in the form of liquid or gaseous molecular hydrogen.
Which of the statements given above are not correct ?
I is not correct. Tritium is indeed radioactive, but it is a beta emitter of low energy, not an alpha emitter. (An alpha particle is a helium nucleus; a hydrogen isotope has nothing to emit one from.)
II is not correct. Water is bent, with a bond angle of about $104\cdot5^\circ$, in the gas phase as much as in the liquid. The two lone pairs on oxygen push the O–H bonds together.
III is correct — this is the standard NCERT definition of the hydrogen economy.
So the ones that are not correct are I and II. Option (a).
Q.78 [Chemistry]
Consider the following statements regarding nitrogen :
I. Nitrogen contains a triple bond.
II. Nitrogen is a triatomic gas.
III. Forces acting between nitrogen molecules are weak van der Waals forces.
Which of the statements given above are correct ?
II is false. Nitrogen is diatomic (N₂), not triatomic. Ozone (O₃) is the familiar triatomic gaseous element.
III is true. Between the molecules there are only weak London dispersion forces, which is why nitrogen is a gas at room temperature and boils at $-196$°C.
Answer (c). Note how I and III together explain the two faces of nitrogen: very strong bonding within the molecule, very weak forces between molecules.
Q.79 [Chemistry]
In a dry test tube, 2 mL of HCl ($0\cdot1$ N) is taken. To this, 4 mL of NaOH ($0\cdot1$ N) is added. The solution is stirred well, followed by the addition of 2 drops of phenolphthalein. What will be the colour of the solution?
HCl: $2\text{ mL}\times0\cdot1\text{ N}=0\cdot2$ meq
NaOH: $4\text{ mL}\times0\cdot1\text{ N}=0\cdot4$ meq
The acid neutralises only $0\cdot2$ meq of the base, leaving $0\cdot2$ meq of NaOH in excess, so the final solution is basic.
Phenolphthalein is colourless in acid and neutral solution and turns pink in basic solution. Option (c).
(Option (d) blue belongs to litmus, not phenolphthalein — a deliberate mix-up of indicators.)
Q.80 [Chemistry]
Consider the following statements :
I. Zinc metal, when treated with both HCl (aq.) and NaOH (aq.) separately, produces molecular hydrogen.
II. An aqueous copper sulphate solution cannot be kept in a zinc vessel.
III. Lemon, tamarind and tomato are natural sources of citric acid, oxalic acid and tartaric acid, respectively.
Which of the statements given above are correct ?
$\mathrm{Zn}+2\mathrm{HCl}\rightarrow\mathrm{ZnCl_2}+\mathrm{H_2}$
$\mathrm{Zn}+2\mathrm{NaOH}\rightarrow\mathrm{Na_2ZnO_2}+\mathrm{H_2}$
II is true. Zinc is above copper in the reactivity series, so it displaces copper from the solution — $\mathrm{Zn}+\mathrm{CuSO_4}\rightarrow\mathrm{ZnSO_4}+\mathrm{Cu}$ — and the vessel is eaten away.
III is false. The last two are swapped: tamarind is the natural source of tartaric acid and tomato of oxalic acid. Only lemon → citric acid is right.
Answer (a).
Q.81 [Chemistry]
Consider the following statements :
I. A solution of iodine in ethanol known as 'tincture of iodine' is a heterogeneous mixture.
II. A suspension is a heterogeneous mixture and its particles scatter a beam of light passing through it, making its path visible.
III. A colloidal solution, although it appears homogeneous, is a heterogeneous mixture.
Which of the statements given above are correct ?
II is true. Suspension particles are larger than 100 nm, big enough to be seen and to scatter light.
III is true. A colloid looks uniform to the eye but is heterogeneous on the microscopic scale — which is exactly why it shows the Tyndall effect.
Answer (b). The three-way classification by particle size — solution (<1 nm), colloid (1–100 nm), suspension (>100 nm) — settles all three statements at once.
Q.82 [Chemistry]
Consider the following statements :
I. A 30% solution of hydrogen peroxide is marketed as '10 volume' H₂O₂.
II. In the compound copper sulphate pentahydrate, all the five water molecules are hydrogen bonded.
Which of the statements given above is/are correct ?
II is false. In $\mathrm{CuSO_4\cdot5H_2O}$, four water molecules are coordinated to the Cu²⁺ ion through dative bonds; only the fifth is held by hydrogen bonding, linking the sulphate ion to two of the coordinated waters.
Answer (d). It is the fifth water that is hardest to drive off, and its loss is what turns the blue crystal white.
Q.83 [Chemistry]
Consider the following statements :
I. The leaves of nettle, a herbaceous plant, cause painful stings when touched accidentally because of the secretion of formic acid.
II. When gypsum is heated at 100°C, it forms calcium carbonate hemihydrate, called Plaster of Paris.
III. When moistened with water, anhydrous copper sulphate forms a green-coloured copper sulphate dihydrate.
Which of the statements given above is/are correct ?
II is false. Heating gypsum to about 100°C gives calcium sulphate hemihydrate, $\mathrm{CaSO_4\cdot\tfrac12H_2O}$, not calcium carbonate.
III is false on two counts. Anhydrous copper sulphate takes up water to form the pentahydrate, and the colour produced is blue, not green. This is the standard laboratory test for the presence of water.
Answer (a).
Q.84 [Chemistry]
Consider the following pairs :
| Chemical Reaction | Type of Chemical Reaction | |
|---|---|---|
| I. | Fe(s) + CuSO₄ (aq.) → FeSO₄ (aq.) + Cu(s) | Displacement reaction |
| II. | Na₂SO₄ (aq.) + BaCl₂ (aq.) → BaSO₄(s) + 2NaCl (aq.) | Double displacement reaction |
| III. | Fe₂O₃(s) + 3CO(g) → 2Fe(s) + 3CO₂(g) | Redox reaction |
| IV. | 2KClO₃(s) → 2KCl(s) + 3O₂(g) | Thermal decomposition reaction |
II ✓ — the two compounds exchange partners and an insoluble barium sulphate precipitates: a double displacement (specifically a precipitation reaction).
III ✓ — Fe₂O₃ is reduced to Fe while CO is oxidised to CO₂, so it is a redox reaction. This is the reaction in the blast furnace.
IV ✓ — a single compound breaks into simpler products on heating: thermal decomposition.
All four match. Option (d).
Q.85 [Chemistry]
What are the approximate percentages by mass of nitrogen and hydrogen respectively in urea?
Nitrogen: $2\times14=28$, so $\dfrac{28}{60}\times100=46\cdot7\%\approx47\%$.
Hydrogen: $4\times1=4$, so $\dfrac{4}{60}\times100=6\cdot7\%\approx7\%$.
Option (d). Urea's high nitrogen content is precisely why it is the most widely used nitrogenous fertiliser in India.
Q.86 [Chemistry]
Coconut oil upon hydrolysis with potassium hydroxide gives :
The alkali here is potassium hydroxide, so the products are glycerol and the potassium salts of the fatty acids — that is, soft soap. Option (d).
Traps in the options: (b) names sodium instead of potassium, and (c) says glycol (a two-carbon diol) instead of glycerol (a three-carbon triol).
Q.87 [Chemistry]
Consider the following statements regarding hydrogen bonds :
I. Hydrogen bonds can only form when hydrogen is bonded to oxygen, nitrogen or fluorine.
II. Hydrogen bonds are intramolecular only.
III. The strength of hydrogen bond decreases with a decrease in the electronegativity of the two bonded atoms.
Which of the statements given above is/are not correct ?
I is correct as the standard rule: a hydrogen bond requires hydrogen to be attached to one of the three small, highly electronegative atoms — F, O or N.
II is not correct. Hydrogen bonds are of two kinds: intermolecular (between molecules — as in water, which is why it boils at 100°C) and intramolecular (within one molecule — as in o-nitrophenol). Saying 'intramolecular only' is plainly wrong.
III is correct. The bond is essentially electrostatic, so less electronegative partners mean a weaker bond: the strength runs H–F > H–O > H–N.
Answer (b).
Q.88 [Chemistry]
Ionic compounds have high melting and boiling points. This is due to :
(b) describes molecular solids such as iodine, which melt easily; (c) describes metals; (d) is the opposite of the truth — high lattice energy is exactly what causes the high melting point.
The same lattice energy explains why ionic solids are hard and brittle, and why they conduct only when molten or dissolved, once the ions are free to move.
Q.89 [Chemistry]
Which of the following statements is/are correct in respect of Portland cement ?
I. Adding more water (higher water-cement ratio) accelerates the initial setting time of cement.
II. The addition of a small percentage of gypsum gives the desired retardation.
III. Gypsum is added during manufacturing to accelerate the setting time of cement.
Select the answer using the code given below :
II is true. About 2–3 per cent gypsum is added to the clinker to retard setting; without it the tricalcium aluminate would cause 'flash set' within minutes, leaving no time to place and work the concrete.
III is false. It states the opposite of II — gypsum retards, it does not accelerate.
Answer (d). Note that II and III contradict each other, so at most one of them can be right — a useful way to narrow the options immediately.
Q.90 [Chemistry]
Consider the following pairs :
| Example of Colloid | Type of Colloid | |
|---|---|---|
| I. | Cloud | Aerosol |
| II. | Mud | Sol |
| III. | Milk | Emulsion |
| IV. | Rubber | Foam |
I ✓ Cloud — liquid droplets dispersed in a gas, which is an aerosol (fog and mist belong here too).
II ✓ Mud — solid particles dispersed in a liquid, which is a sol.
III ✓ Milk — liquid fat dispersed in liquid water, which is an emulsion.
IV ✓ Rubber — taken as foam rubber, this is gas dispersed in a solid, which the NCERT table lists as a solid foam.
All four match. Option (d).
Worth noting: the fourth pair only works if 'rubber' is read as foam rubber, the example NCERT actually prints for the gas-in-solid entry. Vulcanised rubber on its own would be a solid sol, and a candidate who marked (c) Three on that reading has a defensible case.
Q.91 [Biology]
Consider the following statements in relation to respiration in animals :
I. Glucose breaks down into pyruvate in the cytoplasm of all cells in both aerobic and anaerobic conditions.
II. The energy released during anaerobic respiration is greater than the energy released in aerobic respiration.
III. Carbon dioxide is released only in aerobic respiration.
Which of the statements given above is/are correct ?
II is false. Aerobic respiration yields far more energy: about 36–38 ATP per glucose against just 2 ATP from anaerobic breakdown, because only the aerobic route runs the Krebs cycle and the electron transport chain.
III is true for animals, which is what the stem asks about. In animal muscle, the anaerobic route converts pyruvate to lactic acid and releases no carbon dioxide; CO₂ appears only in the mitochondrial (aerobic) pathway. (In yeast, by contrast, anaerobic respiration gives ethanol and CO₂ — but yeast is not an animal.)
Answer (c).
Note: some circulated keys mark (a) I only, reading statement III against the yeast pathway. The stem's restriction to animals is the deciding clue — without it the phrase 'in relation to respiration in animals' would serve no purpose.
Q.92 [Biology]
In humans, the exit of partially digested food from the stomach into the small intestine is regulated by which one of the following structures/processes ?
The pyloric sphincter, a ring of muscle at the lower end of the stomach, opens and closes to release chyme into the duodenum a little at a time. This measured release is what allows the intestine to neutralise the acid and digest the food properly.
Peristalsis (a) is the wave of contraction that moves food along the whole alimentary canal but does not regulate passage at a junction; the villi (d) are for absorption, not control.
The same principle operates at the other end of the oesophagus, where the cardiac sphincter guards the entry into the stomach.
Q.93 [Biology]
Which of the following cells form components of complex permanent tissue in plants ?
I. Companion cells
II. Sieve tubes
III. Tracheids
IV. Vessels
Select the answer using the code given below :
Complex permanent tissue is made of more than one type of cell working as a unit; in plants there are two such tissues, both of them conducting tissues:
Xylem — tracheids, vessels, xylem parenchyma and xylem fibres.
Phloem — sieve tubes, companion cells, phloem parenchyma and phloem fibres.
Companion cells and sieve tubes belong to the phloem; tracheids and vessels to the xylem. All four therefore qualify.
(Simple permanent tissue, by contrast, is made of one cell type only — parenchyma, collenchyma or sclerenchyma.)
Q.94 [Biology]
Which one of the following is not a part of the hindbrain of human beings ?
The hindbrain has three parts — the medulla oblongata, the pons and the cerebellum.
The corpus callosum is a thick band of nerve fibres in the forebrain that connects the two cerebral hemispheres and lets them exchange information.
Worth holding on to: the medulla controls involuntary actions such as breathing, heartbeat, blood pressure and vomiting; the cerebellum handles posture, balance and the precision of voluntary movement; the pons relays signals between the cerebellum and the rest of the brain.
Q.95 [Biology]
Which of the following organisms show external fertilization ?
I. Pigeon
II. Frog
III. Fish
IV. Lizard
Select the answer using the code given below :
External fertilization — gametes meeting outside the body, in water — is the rule in frogs and most fish. It needs a watery medium, so it is confined to aquatic and amphibious animals, and is compensated for by producing very large numbers of eggs.
Pigeon and lizard are amniotes that fertilise internally and lay shelled eggs on land; internal fertilization is precisely the adaptation that freed vertebrates from dependence on water for reproduction.
Q.96 [Biology]
Which one of the following plant groups is characterized by having a haploid plant body ?
In bryophytes — mosses and liverworts — the conspicuous, long-lived plant body is the gametophyte, which is haploid (n). The diploid sporophyte is small, short-lived and remains attached to and dependent on the gametophyte.
In pteridophytes, gymnosperms and angiosperms the position is reversed: the dominant plant body is the diploid sporophyte, and the gametophyte is reduced (in flowering plants, to a few cells inside the flower).
Bryophytes are also called the 'amphibians of the plant kingdom' because they still need water for the sperm to swim to the egg.
Q.97 [Biology]
A flower typically is composed of :
These are the four whorls of a typical flower, from outside inwards:
Calyx (sepals) → Corolla (petals) → Androecium (stamens, the male whorl) → Gynoecium (carpels, the female whorl).
The other options plant intruders from elsewhere: stomata are pores on leaves, the cotyledon is part of the seed, the cambium is a meristem in the stem, and the root cap protects the root tip. None of them is a floral part.
Q.98 [Biology]
Which one of the following organelles is found in both prokaryotic and eukaryotic cells ?
The defining feature of a prokaryotic cell is the absence of a true nucleus and of membrane-bound organelles. Ribosomes have no membrane, so they are the one structure common to both kinds of cell.
They differ in size — 70S in prokaryotes, 80S in the eukaryotic cytoplasm — and that difference is what several antibiotics exploit, attacking bacterial ribosomes while leaving human ones alone.
The nucleus, mitochondria and Golgi complex are all membrane-bound and therefore exclusively eukaryotic. (Mitochondria and chloroplasts do carry their own 70S ribosomes — the evidence behind the endosymbiotic theory.)
Q.99 [Biology]
Which one of the following is not a connective tissue in the human body ?
Animal tissues fall into four groups — epithelial, connective, muscular and nervous. Cardiac muscle belongs to the muscular group: involuntary, striated, and found only in the wall of the heart.
Cartilage, bone and blood are all connective tissues, defined by cells scattered in an abundant extracellular matrix — solid and rigid in bone, firm but flexible in cartilage, and liquid (plasma) in blood.
Blood is the option most often doubted: it counts as connective tissue because it too consists of cells suspended in a matrix, and because it connects the body's parts by transporting materials between them.
Q.100 [Biology]
Which one of the following is not a characteristic of an insect-pollinated plant ?
Light, small, smooth and dry pollen produced in enormous quantity is the mark of a wind-pollinated (anemophilous) plant, which must let the wind carry it far — as in grasses and cereals.
Insect-pollinated (entomophilous) flowers advertise and reward instead: they are brightly coloured and scented, they secrete nectar, and their pollen is sticky or spiny so that it clings to the visiting insect's body.
Wind-pollinated flowers, having no need to attract anything, are typically small, dull and scentless, with long exposed stamens and feathery stigmas.
Q.101 [Geography]
Consider the following States :
I. Tripura
II. Chhattisgarh
III. Assam
IV. Odisha
How many of the States given above have jute mills ?
India has about 70 jute mills, the great majority of them in West Bengal, along a narrow belt on the banks of the Hugli. Beyond Bengal, mills are located in Bihar, Uttar Pradesh, Assam, Odisha, Andhra Pradesh, Tripura and Chhattisgarh — a list that covers all four States named here.
The industry clusters on the Hugli because the Ganga–Brahmaputra delta grows the raw jute, the river supplies cheap water transport and water for processing, Kolkata provides banking, insurance and a port for export, and the surrounding States supply abundant labour.
Q.102 [Geography]
Which one of the following is classified under the physical processes of weathering ?
Weathering has three families: physical (mechanical), chemical and biological.
Physical processes break rock apart without changing its chemistry — unloading and expansion, frost action, thermal expansion and contraction, salt weathering, and water pressure in joints and pores.
Oxidation, carbonation, hydration and solution are all chemical processes: they alter the minerals themselves. Oxidation rusts iron-bearing minerals; carbonation dissolves limestone and gives us karst caves; hydration makes minerals absorb water and swell.
Answer (a).
Q.103 [Geography]
Consider the following statements :
I. The Steppes of Eurasia are temperate grasslands.
II. The Pampas of South America are classified as tropical grasslands.
Which of the statements given above is/are correct ?
I is true. The Steppes of Eurasia are the classic temperate grassland, lying in the continental interior of the mid-latitudes.
II is false. The Pampas of Argentina and Uruguay are also temperate grassland, not tropical.
The regional names are worth fixing: temperate grasslands are the Steppes (Eurasia), Prairies (North America), Pampas (South America), Veld (South Africa), Downs (Australia) and Canterbury (New Zealand). Tropical grasslands are the Savanna (Africa), Llanos and Campos (South America).
Q.104 [Geography]
Consider the following statements regarding the slash-and-burn agricultural practices in India :
I. This practice is a primitive subsistence farming.
II. This practice is known as Jhum in the North Eastern Hill region.
III. When soil fertility decreases, farmers shift to a fresh patch of land.
Which of the statements given above is/are correct ?
Slash-and-burn, or shifting cultivation, is a form of primitive subsistence farming practised on small patches with primitive tools and family labour, dependent on the monsoon and the natural fertility of the soil.
A patch of forest is cleared and burnt, the ash enriching the soil; when fertility falls after two or three seasons the family moves to a fresh patch and lets the old one recover under forest.
It carries a different name in nearly every region: Jhum in the North Eastern states, Podu in Andhra Pradesh and Odisha, Bewar or Penda in Madhya Pradesh, Kumari in the Western Ghats and Milpa in Mexico and Central America.
Q.105 [Geography]
Consider the following statements regarding western disturbances in the Indian climate :
I. These are shallow cyclonic depressions.
II. They originate over the Caspian Sea and travel to India.
Which of the statements given above is/are correct ?
I is true. Western disturbances are shallow extra-tropical cyclonic depressions that arrive in winter from the west and north-west.
II is false. They originate over the Mediterranean Sea and are steered into the subcontinent by the westerly jet stream. (They do cross Iran and Afghanistan on the way, which is the source of the confusion.)
Their importance is out of all proportion to their size: the winter rain they bring — mahawat — is critical for the standing rabi crop, especially wheat in Punjab, Haryana and western Uttar Pradesh, and they supply the snowfall that feeds the Himalayan rivers through the summer.
Q.106 [Geography]
Consider the following statements regarding earthquake waves :
I. P-waves are similar to sound waves.
II. S-waves can travel through gaseous, liquid and solid materials.
III. The zone between 105° and 145° from the epicentre is identified as the shadow zone for both P- and S-waves.
Which of the statements given above are correct ?
I is true. P-waves are longitudinal — the particles vibrate along the direction of travel, exactly as in a sound wave. They are also the fastest, which is why they arrive first (P for primary).
II is false. S-waves are transverse and travel only through solids. Their failure to cross the outer core is the central evidence that the outer core is liquid.
III is true. Beyond 105° no direct S-wave arrives, and between 105° and 145° no direct P-wave arrives either, so that band is the shadow zone for both waves. Past 145° P-waves reappear.
The shadow zone for S-waves alone is much wider — the whole region beyond 105°, covering about 40 per cent of the Earth's surface.
Q.107 [Geography]
Consider the following statements :
I. At the equator, the Coriolis force is zero and here the winds blow perpendicular to the isobars.
II. The Coriolis force is directly proportional to the angle of latitude.
III. The Coriolis force and the resultant wind do not blow parallel to the isobars at higher latitudes.
Which of the statements given above are correct ?
I is true. The Coriolis effect vanishes at the equator, so the pressure gradient force acts alone and the wind crosses the isobars at right angles. This is also why tropical cyclones cannot form within about 5° of the equator — there is no deflection to set the system spinning.
II is true. The Coriolis force is directly proportional to the angle of latitude: zero at the equator, maximum at the poles.
III is false. The opposite holds. Away from the equator, where the Coriolis force is appreciable, it comes into balance with the pressure gradient force and the resultant wind blows parallel to the isobars — this is the geostrophic wind.
Note: some circulated keys mark (a) I, II and III. The geostrophic balance is stated explicitly in the standard text — 'the pressure gradient force is balanced by the Coriolis force and the resultant wind blows parallel to the isobar' — which is what makes statement III untenable.
Q.108 [Geography]
The Hawaiian volcanoes are the most famous examples of :
The Hawaiian volcanoes — Mauna Loa and Kilauea above all — are built almost entirely of basaltic lava, which is very fluid. It flows far before solidifying, so the cone that grows is broad and gently sloping, like a warrior's shield laid on the ground.
They are the largest volcanoes on Earth by volume and generally erupt quietly; explosive eruptions occur only when water gets into the vent.
By contrast, composite volcanoes (Fujiyama, Vesuvius) are built of viscous, silica-rich lava and ash in alternating layers and erupt violently; a caldera is the collapsed hollow left after a very large eruption; and flood basalt provinces, such as the Deccan Traps, are vast lava plateaus rather than cones.
Q.109 [Geography]
The temperate forests in the Nilgiris, Anaimalai and Palani hills are called :
Sholas are the stunted, evergreen montane temperate forests that survive in the sheltered folds and valleys of the Western Ghats above about 1,500 m, set in a natural mosaic with rolling grassland. The Nilgiri, Anaimalai and Palani hills carry the classic examples.
The distractors are all real but different: Myristica swamps are freshwater swamp forests of the Western Ghats lowlands; Devarakadu (deva-kadu) are the sacred groves of Kodagu in Karnataka, protected by community custom.
Q.110 [Geography]
Consider the following statements with regard to igneous rocks :
I. These rocks cannot be changed into metamorphic rocks.
II. When molten material is cooled slowly at great depths, mineral grains tend to be very small.
III. These rocks are known as primary rocks.
Which of the statements given above is/are correct ?
I is false. Igneous rocks change into metamorphic rocks readily under heat and pressure — granite becomes gneiss, basalt becomes amphibolite. The rock cycle allows any rock type to turn into any other.
II is false. It reverses the rule. Slow cooling at depth gives crystals time to grow, producing coarse-grained intrusive rocks such as granite; rapid cooling at the surface gives fine-grained extrusive rocks such as basalt, or glassy ones such as obsidian.
III is true. Igneous rocks are called primary rocks because they form directly from the solidification of magma or lava, and sedimentary and metamorphic rocks are ultimately derived from them.
The name itself is the clue: Latin ignis, fire.
Q.111 [Geography]
Consider the following statements :
I. The Prime Meridian is the same as the International Date Line.
II. West of the International Date Line is always a day later than east of the line.
III. The Earth turns 15° of longitude in an hour.
Which of the statements given above is/are correct ?
I is false. The Prime Meridian is 0° longitude, through Greenwich; the International Date Line follows roughly the 180° meridian, on the opposite side of the globe — and deviates from it to keep island groups and countries on one side.
II is true. Crossing the line westward you advance the calendar by a day, so the western side is a day ahead of the eastern side.
III is true. The Earth turns 360° in 24 hours, i.e. 15° per hour, or 1° in four minutes — the arithmetic behind every longitude-and-time calculation.
That same figure is why India's standard meridian at 82°30′ E puts IST 5 hours 30 minutes ahead of GMT.
Q.112 [Geography]
The Earth's equatorial region bulges outward, but the Earth flattens slightly towards the polar regions due to the :
The Earth's spin on its axis throws material outwards most strongly where the rotational speed is greatest — at the equator — and not at all at the poles, where the rotational velocity is zero. The result is an oblate spheroid: bulging at the equator, flattened at the poles.
The equatorial radius is about 6,378 km against a polar radius of about 6,357 km — a difference of some 21 km.
Option (c) confuses rotation (spin on the axis) with revolution (orbit round the Sun); option (d) inverts cause and effect, since $g$ is in fact smaller at the equator, partly because of this very bulge.
Q.113 [Geography]
In the southern hemisphere, trade winds blow from :
Trade winds blow from the subtropical high-pressure belts towards the equatorial low. In the southern hemisphere the Coriolis force deflects moving air to the left, so a southward-moving wind is turned to become a south-easterly, blowing towards the north-west.
In the northern hemisphere the deflection is to the right and the trades blow from the north-east.
Remember the naming convention: a wind is always named for the direction it comes from. Where the two trade-wind systems converge lies the ITCZ, and the belt of calms there is the doldrums.
Q.114 [Geography]
Consider the following statements regarding the structure of the atmosphere :
I. The average height of the troposphere is higher nearer the poles than at the equator.
II. The mesosphere contains the ozone layer.
III. Radio waves transmitted from the Earth are reflected to the Earth by the ionosphere.
IV. In the mesosphere, temperature decreases with an increase in altitude.
Which of the statements given above are correct ?
I is false. The troposphere is thickest over the equator — about 18 km — and thinnest over the poles, about 8 km, because strong convection at the equator pushes the tropopause upwards.
II is false. The ozone layer lies in the stratosphere, at roughly 15–35 km. Its absorption of ultraviolet radiation is what makes the stratosphere warm with height.
III is true. The ionosphere, from about 80 km upwards, contains electrically charged particles that reflect radio waves and make long-distance radio communication possible.
IV is true. In the mesosphere the temperature falls with altitude, reaching about $-100$°C at the mesopause — the coldest part of the atmosphere. It is also where most meteors burn up.
Q.115 [Geography]
Consider the following oceanic currents :
I. Oyashio
II. Canaries
III. Labrador
IV. Kuroshio
V. Benguela
VI. Alaska
VII. Humboldt
How many of the above are Pacific Ocean currents ?
Pacific Ocean: Oyashio (cold, off Kamchatka and northern Japan), Kuroshio (warm, off Japan), Alaska (warm, in the Gulf of Alaska) and Humboldt or Peru (cold, off the western coast of South America) — four in all.
Atlantic Ocean: Canaries (cold, off north-west Africa), Labrador (cold, off eastern Canada) and Benguela (cold, off south-west Africa).
Two of these carry wider importance: the meeting of the warm Kuroshio and the cold Oyashio makes the north-west Pacific one of the world's great fishing grounds, and the Humboldt is the current whose weakening is bound up with the El Niño phenomenon.
Q.116 [Geography]
Consider the following :
I. Abrasion
II. Attrition
III. Hydraulic action
IV. Solution
Which of the above are the main types of river erosion ?
A river erodes its bed and banks in four distinct ways:
Hydraulic action — the sheer force of moving water prising material out of cracks in the bed and banks.
Abrasion (corrasion) — the load carried by the river being scraped and hurled against the bed, the process that drills potholes.
Attrition — the load particles knocking against one another and being worn smaller and rounder; this wears the load, not the bed.
Solution (corrosion) — soluble minerals, especially in limestone, being dissolved by the water.
All four are standard, so the answer is 'all of the above'.
Q.117 [Geography]
A prolonged period of inadequate rainfall marked with mal-distribution of the same over time and space is known as :
The definition given — a long spell of inadequate rainfall, badly distributed in time and space — is the definition of meteorological drought. It is the first stage, defined purely by the rainfall record.
The others follow from it and are defined by their effects:
Agricultural (soil moisture) drought — soil moisture falls too low to sustain crops and cattle;
Hydrological drought — surface and sub-surface water levels fall below the normal, drying rivers, tanks and wells;
Ecological drought — the productivity of a natural ecosystem fails and ecological stress and damage follow.
Q.118 [Geography]
Which group of landlocked states shares a boundary with Madhya Pradesh ?
Madhya Pradesh borders five States: Rajasthan, Uttar Pradesh, Chhattisgarh, Maharashtra and Gujarat. Jharkhand is not among them, which rules out options (b) and (c).
The question then applies a second filter — the group must consist of landlocked States. Maharashtra and Gujarat both have coastlines on the Arabian Sea, so they drop out, leaving Rajasthan, Uttar Pradesh and Chhattisgarh.
Note: some circulated keys mark (a), which is simply the list of all five neighbours. That reading treats 'landlocked' as describing Madhya Pradesh rather than the group being asked for — and if the word carried no filtering force, the item would collapse into a plain 'which States border MP' question with two different correct-looking options.
Q.119 [Geography]
Consider the following statements regarding the nature of rocks :
I. Rocks are aggregates of one or more minerals.
II. Granite is softer than soapstone.
III. Gabbro is black and quartzite can be milky white.
IV. Sedimentary rocks are related to foliation.
Which of the statements given above are not correct ?
I is correct — a rock is by definition an aggregate of one or more minerals, and need not have a definite chemical composition.
II is not correct. It is the other way round: soapstone (talc) is the softest mineral known, at 1 on the Mohs scale, while granite is hard. Soapstone can be scratched with a fingernail.
III is correct — rocks differ in colour as well as hardness, and gabbro being black while quartzite is milky white is the standard textbook illustration.
IV is not correct. Foliation — the banded, layered alignment of minerals — is a feature of metamorphic rocks such as slate, schist and gneiss, produced by directed pressure. Sedimentary rocks show bedding or stratification, which is a different thing.
Note: some circulated keys mark (b) I and III. Both of those statements are standard textbook material, so that key cannot stand.
Q.120 [Geography]
The 'Agricultural Population Density' is referred to as the ratio of the :
The measure asks how many people who depend on farming are supported by each unit of land that can actually be cultivated — so the numerator must be the agricultural population, not the total population, and the denominator the net cultivable land.
It is distinct from two neighbouring measures: arithmetic density (total population ÷ total land area) and physiological density (total population ÷ net cultivable land, which is option (a)).
Agricultural population density is the more telling figure for a country like India, where a large share of the population still depends directly on the land, because it measures the real pressure of people on the cultivable soil.
Q.121 [History]
The annual session of the Indian National Congress in December 1929 was held in :
The December 1929 session, presided over by Jawaharlal Nehru on the banks of the Ravi, adopted the resolution of Purna Swaraj — complete independence — as the Congress goal, and called for 26 January 1930 to be observed as Independence Day.
The other sessions named: Surat 1907 (the split between Moderates and Extremists), Amritsar 1919 (after the Jallianwala Bagh massacre) and Tripuri 1939 (the Subhas Chandra Bose episode).
The date chosen in 1930 is the reason the Constitution was brought into force on 26 January twenty years later.
Q.122 [History]
Shortughai, a Harappan trading post in Afghanistan, was important for the Harappans for the possible supply of :
Shortughai, on the Oxus in north-eastern Afghanistan, was the most distant Harappan settlement and sat close to the Badakhshan mines — the ancient world's only significant source of lapis lazuli, the deep blue stone prized for beads and ornaments.
Option (b) can be dismissed on principle: the Harappan civilisation belongs to the Bronze Age and knew no iron.
Conch shell came from the coast, at Nageshwar and Balakot; copper from the Khetri mines of Rajasthan and from Oman; carnelian from Lothal and Gujarat; steatite from south Rajasthan and north Gujarat.
Q.123 [History]
Which of the following statements are correct regarding the demands of the protest movement known as Luddism (1811 – 17) ?
I. A minimum wage for workers.
II. The right to form trade unions so that they could legally present their demands.
III. The use of machinery for efficient labour-saving production.
Select the answer using the code given below :
The Luddites, led by the mythical 'General Ned Ludd', were skilled English textile workers who smashed the new machines between 1811 and 1817.
Their demands were for a minimum wage, control over the employment of women and children, work for those thrown out of jobs by the machines, and the right to form trade unions to press these demands lawfully. So I and II are correct.
III is false — and is the exact opposite of what they stood for. The Luddites opposed the introduction of labour-saving machinery, because it destroyed their livelihoods.
Their name survives in the modern word 'luddite' for anyone hostile to new technology.
Q.124 [History]
Consider the following statements regarding the Industrial Revolution in Britain :
I. At the beginning of industrialization, coal and iron ore were plentifully available in Britain.
II. The blast furnace came into use at the beginning of the 18th century.
III. Britain was lucky in possessing excellent coking coal and high-grade iron ore in the same basins.
Which of the statements given above are correct ?
I ✓ Britain's coal and iron ore reserves were abundant and near the surface — the raw material base without which the revolution could not have begun.
II ✓ The coke-fired blast furnace was brought into use by Abraham Darby at Coalbrookdale in 1709, at the very start of the 18th century. It freed iron smelting from its dependence on charcoal and therefore on the dwindling forests.
III ✓ Coking coal and high-grade iron ore occurring in the same basins meant that neither had to be hauled far — a decisive advantage in an age of costly land transport, and the reason Britain's iron industry grew where it did.
Later refinements followed: Henry Cort's puddling furnace and rolling mill in the 1780s, and Bessemer's converter in 1856.
Q.125 [History]
Which one of the following inscriptions records the history of a guild of silk weavers ?
The Mandasor (Mandsaur, Madhya Pradesh) stone inscription of the Gupta period, dated to the mid-fifth century CE, records that a guild of silk weavers migrated from Lata (in Gujarat) to Dashapura and there built and later repaired a temple of the Sun.
It is a prize source for economic history: it shows craft guilds moving as organised bodies, changing occupation, and acting as collective patrons of religion.
The others: the Hathigumpha inscription near Bhubaneswar is the record of the Kalinga king Kharavela; Kudumiyamalai in Tamil Nadu carries an early inscription on music; and the Udayagiri cave inscriptions belong to the reign of Chandragupta II.
Q.126 [History]
Match List I with List II :
| List I (Event) | List II (Year) |
|---|---|
| I. Passing of the Age of Consent Bill | A. 1893 |
| II. Establishment of the Arya Samaj | B. 1883 |
| III. Death of Dayanand Saraswati | C. 1875 |
| IV. Foundation of the Nagari Pracharini Sabha | D. 1891 |
I — Age of Consent Bill, 1891 (D). Pushed through after the Phulmoni Dasi case, it raised the age of consent for girls from ten to twelve and provoked fierce opposition from orthodox opinion, with Tilak among its critics.
II — Arya Samaj, 1875 (C). Founded at Bombay by Dayanand Saraswati, with the call 'Back to the Vedas' and a programme against idolatry, caste rigidity and untouchability.
III — Death of Dayanand Saraswati, 1883 (B).
IV — Nagari Pracharini Sabha, 1893 (A). Founded at Banaras to promote Hindi in the Devanagari script.
The chronology itself — 1875, 1883, 1891, 1893 — is enough to fix the answer once the founding and the death are placed.
Q.127 [History]
Consider the following statements with regard to the types of land listed in the Amarakosha :
I. Devamatrika refers to land watered by rain.
II. Aprahata refers to fallow land.
III. Pankila refers to highly fertile land.
Which of the statements given above is/are correct ?
The Amarakosha, the fifth-century Sanskrit lexicon of Amarasimha, lists categories of land in careful detail — evidence of how closely land was classified in early India.
I ✓ Devamatrika — literally 'having the gods as mother', i.e. land watered by rain rather than by irrigation.
II ✓ Aprahata — fallow land, left uncultivated.
III ✗ Pankila means muddy land. The word for fertile land is urvara.
The rest of the list runs: ushara (barren), maru (desert), shadvala (grassy), jalaprayah (watery), kachchaha (land close to water), sharkara (strewn with pebbles) and sharkaravati (sandy).
Q.128 [Polity and Governance]
Consider the following statements regarding the role of political parties in modern democracies :
I. In most democracies, elections are fought mainly among the candidates put up by political parties.
II. Political parties put forward different policies and programmes and the voters choose from them.
III. Political parties shape public opinion.
Which of the statements given above are correct ?
Each statement names one of the standard functions of political parties in a democracy:
I ✓ Parties contest elections; in most democracies candidates are selected and put up by parties rather than standing independently.
II ✓ Parties put forward different policies and programmes, reducing a mass of opinions to a few broad positions from which voters can choose.
III ✓ Parties shape public opinion by raising and highlighting issues, and through the pressure groups and movements attached to them.
Their other functions are making laws, forming and running governments, playing the part of the opposition, and giving people access to government machinery and welfare schemes.
Note: some circulated keys mark (b) II and III only. Statement I is a standard textbook proposition and there is nothing in it to fault.
Q.129 [History]
Consider the following statements with regard to the Lahore Session :
I. The Congress decided to observe Independence Day on 26 January 1930.
II. It was decided to hoist the National Flag and sing patriotic songs at different venues.
III. Gandhiji suggested that the event be held synchronously in all the places.
Which of the statements given above are correct ?
The Lahore Session of December 1929 adopted Purna Swaraj as the goal and resolved that 26 January 1930 would be observed as Independence Day.
The programme for the day was deliberately simple and uniform: the national flag was to be hoisted, the pledge of independence read out, and patriotic songs sung at meetings across the country.
Gandhiji asked that the meetings be held at the same hour everywhere, so that the whole country would be seen to act as one — a piece of symbolic choreography that made a scattered set of local gatherings into a single national event.
The Civil Disobedience Movement followed within weeks, with the Dandi March beginning on 12 March 1930.
Q.130 [History]
Consider the following statements :
I. The Kailasanatha temple of Kanchi is the earliest Pallava temple hewn from solid rock.
II. The Vaikuntha Perumal temple at Kanchi is a rare Pallava temple dedicated to Lord Vishnu.
Which of the statements given above is/are correct ?
I is false. The Kailasanatha temple at Kanchipuram, built under Rajasimha (Narasimhavarman II) in the early eighth century, is a structural temple — built up from dressed stone blocks — not one hewn from living rock. The earliest Pallava rock-cut work is the cave temple series of Mahendravarman I, and the famous monolithic rathas are at Mamallapuram.
II is true. The Vaikuntha Perumal temple at Kanchi, built under Nandivarman II, is dedicated to Vishnu — unusual among Pallava temples, most of which are Shaivite. Its sculpted panels also record Pallava dynastic history.
The Pallava building sequence is worth carrying: rock-cut caves (Mahendravarman) → monolithic rathas (Narasimhavarman I) → structural temples (Rajasimha and Nandivarman).
Q.131 [Polity and Governance]
Consider the following pairs with reference to the Constitution of India :
| Part | Subject | |
|---|---|---|
| I. | Part V | The Union |
| II. | Part X | The Scheduled and Tribal Areas |
| III. | Part XII | Relations between the Union and the States |
| IV. | Part XIV | Amendment of the Constitution |
I ✓ Part V — The Union (Articles 52–151): the President, Parliament, the Supreme Court, the CAG.
II ✓ Part X — The Scheduled and Tribal Areas (Articles 244–244A).
III ✗ Relations between the Union and the States is Part XI (Articles 245–263). Part XII deals with Finance, Property, Contracts and Suits.
IV ✗ Amendment of the Constitution is Part XX (Article 368). Part XIV covers Services under the Union and the States, including the UPSC and the State Public Service Commissions.
So only two pairs match.
Q.132 [International Relations]
With reference to the Panchsheel, which of the following is/are correct ?
I. Mutual respect for territorial integrity and sovereignty
II. Mutual non-interference
III. Collective security against non-aggression
IV. Peaceful co-existence
Select the answer using the code given below :
The Panchsheel — the Five Principles of Peaceful Coexistence, set out in the India–China agreement on Tibet of 29 April 1954 — are:
1. Mutual respect for each other's territorial integrity and sovereignty ✓ (I)
2. Mutual non-aggression
3. Mutual non-interference in each other's internal affairs ✓ (II)
4. Equality and mutual benefit
5. Peaceful co-existence ✓ (IV)
III is wrong because it substitutes 'collective security' for the actual principle of mutual non-aggression. Collective security is an alliance idea that belongs to the opposite tradition — precisely what the non-aligned framework of Panchsheel was set against.
Q.133 [Polity and Governance]
Consider the following statements related to national integration :
I. The expression of regional issues is not a part of democratic politics.
II. Nation-building is an ongoing process.
III. Regional imbalance is associated with India's development experience.
IV. Regions together form the nation.
Which of the statements given above are correct ?
I is false. The expression of regional aspirations is a normal and legitimate part of democratic politics, not a threat to it. India's experience has been that regional demands accommodated through democratic negotiation — the linguistic reorganisation of States, the creation of new States — have strengthened the union rather than weakened it.
II is true. Nation-building has no terminal point; it is continuously renewed.
III is true. Uneven development between and within regions has been a persistent feature of India's development experience, and a recurring source of political demand.
IV is true. The nation is made up of its regions; regional identity and national identity are not in competition.
Q.134 [International Relations]
Consider the following statements regarding UN reforms :
I. India demands an expanded Security Council.
II. India does not support an increase in non-permanent members.
III. The majority of the UN General Assembly members are from developing countries.
Which of the statements given above is/are correct ?
I is true. India has pressed for an expanded and more representative Security Council, and seeks a permanent seat for itself — a body designed for the world of 1945 no longer reflects the world that exists.
II is false. India supports expansion in both categories — permanent and non-permanent — so that developing countries and under-represented regions, Africa and Latin America among them, gain a voice.
III is true. Developing countries are a clear majority of the 193 members of the General Assembly, which is why the Assembly's agenda is so heavily shaped by development questions.
India has served as a non-permanent member eight times, most recently in 2021–22, and works through the G4 (with Brazil, Germany and Japan) to press for reform.
Q.135 [Polity and Governance]
Which one of the following Five-Year Plan documents was titled as 'Towards Faster and More Inclusive Growth' ?
The Eleventh Five-Year Plan (2007–12) carried the approach-paper title 'Towards Faster and More Inclusive Growth', and inclusiveness was its organising idea: growth that reached the poor, the farm sector, the disadvantaged castes and communities and the lagging regions.
For reference: the Eighth (1992–97) came after the 1991 reforms and set out management of the transition to a market economy; the Ninth (1997–2002) had 'growth with social justice and equality'; the Tenth (2002–07) aimed at doubling per capita income in ten years; and the Twelfth (2012–17), the last of the series, was titled 'Faster, More Inclusive and Sustainable Growth'.
The Planning Commission was replaced by NITI Aayog in 2015 and the Five-Year Plans ended with the Twelfth.
Q.136 [Polity and Governance]
Consider the following statements regarding the PESA Act, 1996 :
I. Gram Sabhas have the power to declare Scheduled Areas.
II. Gram Sabhas have the powers related to the management of community resources.
III. The PESA applies to all States except areas under the Fifth Schedule.
Which of the statements given above is/are not correct ?
I is not correct. Scheduled Areas are declared by the President under Paragraph 6 of the Fifth Schedule, not by Gram Sabhas.
II is correct. Under PESA the Gram Sabha is empowered over community resources — minor forest produce, minor water bodies, minor minerals, land alienation, village markets, money-lending and the local plans — and must be consulted before land acquisition and rehabilitation.
III is not correct. It inverts the Act's scope. PESA — the Provisions of the Panchayats (Extension to the Scheduled Areas) Act, 1996 — was enacted precisely to extend Part IX of the Constitution to the Fifth Schedule areas, which Article 243M had excluded. It applies to ten States with Fifth Schedule areas.
Q.137 [Polity and Governance]
Which one of the following is neither a constitutional nor a statutory body ?
NITI Aayog was created on 1 January 2015 by an executive resolution of the Union Cabinet, replacing the Planning Commission. It owes its existence neither to the Constitution nor to an Act of Parliament, which makes it an executive (non-statutory, non-constitutional) body.
The others all have a firm legal basis:
Finance Commission — constitutional, Article 280.
Union Public Service Commission — constitutional, Article 315.
National Green Tribunal — statutory, set up under the NGT Act, 2010.
The Planning Commission it replaced was likewise an executive body, so the change of name did not change its legal standing.
Q.138 [Polity and Governance]
Which one of the following committees recommended constitutional recognition for local bodies ?
The Thungon Committee (1988), appointed by the Congress party's sub-committee on politics and constituted under the National Front, recommended that panchayati raj bodies be given constitutional recognition, together with a fixed five-year term, provision for elections within six months of supersession, reservation for SCs, STs and women, and a District Collector as the chief executive officer of the zila parishad.
These recommendations fed directly into the 73rd and 74th Constitutional Amendments of 1992, which finally gave local bodies constitutional status.
The other committees in this lineage are Balwant Rai Mehta (1957), which proposed the three-tier structure, Ashok Mehta (1977), which proposed a two-tier structure, G.V.K. Rao (1985) and L.M. Singhvi (1986), which also urged constitutional status.
Q.139 [Polity and Governance]
The anti-defection provisions were incorporated in the Constitution through which one of the following Constitutional Amendments ?
The 52nd Constitutional Amendment Act, 1985, passed in the first year of Rajiv Gandhi's government, inserted the Tenth Schedule and amended Articles 101, 102, 190 and 191 to disqualify legislators for defection.
A member is disqualified for voluntarily giving up party membership or for voting against the party whip. The original provision protecting a 'split' by one-third of a party was deleted by the 91st Amendment (2003), which now allows only a merger backed by two-thirds of the members.
For reference: the 61st Amendment (1989) lowered the voting age from 21 to 18.
Q.140 [International Relations]
Consider the following statements regarding the Neighbourhood First Policy :
I. India provides high-impact community development projects to Afghanistan.
II. Bhutan is India's key maritime neighbour and vital partner in Vision MAHASAGAR.
III. India launched Operation Brahma to provide relief following an earthquake in Myanmar.
Which of the statements given above are correct ?
I is true. India has long run High Impact Community Development Projects (HICDPs) in Afghanistan — small, quickly delivered works in education, health, water and sanitation spread across its provinces.
II is false on the plainest ground: Bhutan is landlocked and cannot be a maritime neighbour. MAHASAGAR — Mutual and Holistic Advancement for Security and Growth Across Regions — is India's maritime vision for the Indian Ocean, announced in 2025 as the successor to SAGAR; its partners are the island and littoral states.
III is true. Operation Brahma was India's relief mission after the earthquake that struck Myanmar in March 2025, sending search-and-rescue teams, a field hospital and relief material within hours.
Answer (b).
Q.141 [Defence]
India has engaged in an agreement to supply BrahMos missiles to which of the following countries ?
I. Indonesia
II. Philippines
III. Singapore
IV. Vietnam
Select the correct answer using the code given below :
Philippines — the first foreign buyer, with a contract of about USUS$375 million signed in January 2022 for shore-based anti-ship batteries; the first delivery was made in April 2024.
Vietnam — an agreement has been signed, confirmed officially in May 2026.
Indonesia — a procurement agreement was entered into in March 2026.
Singapore has no such agreement, which is what makes III wrong.
BrahMos is a joint India–Russia venture (Brahmaputra + Moskva), so exports are cleared only to countries friendly to both partners. It has become the flagship of India's defence-export push.
Q.142 [Current Affairs]
Ramanujan Fellowship is an initiative of the Department of Science & Technology, Government of India. It was launched under the :
The Ramanujan Fellowship is meant to bring back brilliant scientists and engineers of Indian origin working abroad, offering them a research position in an Indian institution. It is administered by the ANRF, which operates under the Department of Science and Technology.
ANRF was set up under the ANRF Act, 2023 and subsumed the earlier Science and Engineering Research Board (SERB), taking over its fellowship and grant programmes. It is chaired ex officio by the Prime Minister, with the Union Ministers of Science and Technology and of Education as vice-presidents.
The other options are separate initiatives: the National Quantum Mission (2023) and the National Supercomputing Mission (2015) are mission-mode programmes, not fellowship vehicles.
Q.143 [Current Affairs]
Which of the following countries is not a member of the International Big Cat Alliance ?
The International Big Cat Alliance (IBCA) was launched by India in April 2023 on the 50th anniversary of Project Tiger, and became a full treaty-based intergovernmental organisation in 2025 with its headquarters in India. It covers the seven big cats — tiger, lion, leopard, snow leopard, cheetah, jaguar and puma.
Somalia and Sri Lanka are among its member countries, and Saudi Arabia joined in May 2026 as its 26th member. France is not a member.
India has committed ₹150 crore to the Alliance for 2023–28. A handful of states — Kazakhstan, Namibia, Thailand, Ecuador and Vietnam — hold observer status rather than membership.
Q.144 [Current Affairs]
Consider the following statements regarding the 'Green Nobel' :
I. It is given every alternate year.
II. In 2026, six winners were chosen and one of the winners is from Asia.
III. All the winners of 2026 are women.
Which of the statements given above is/are correct ?
The 'Green Nobel' is the Goldman Environmental Prize, instituted in 1989 and given to grassroots environmental activists.
I is false. It is awarded annually, not every other year — to six winners, one from each of the six inhabited continental regions (Africa, Asia, Europe, Islands and Island Nations, North America, and South and Central America).
II is true. Six winners were chosen in 2026, and the Asia prize went to Borim Kim of South Korea for the continent's first successful youth-led climate litigation.
III is true. The 2026 cohort was the first all-women line-up in the prize's history.
Each winner receives USUS$200,000. The Indian recipients over the years include Medha Patkar (1992), Rashida Bee and Champa Devi Shukla (2004), Ramesh Agrawal (2014) and Prafulla Samantara (2017).
Q.145 [Current Affairs]
Which two countries signed a US$2·6 billion uranium supply agreement in March 2026 ?
The agreement was announced during the visit of Canadian Prime Minister Mark Carney to India on 2 March 2026. Under it the Saskatchewan-based company Cameco will supply about 22 million pounds (roughly 9·9 million kg) of uranium concentrate to India between 2027 and 2035.
It was one of ten commercial agreements signed during the visit, together worth about US$5·5 billion, and the two sides also opened negotiations on a Comprehensive Economic Partnership Agreement.
The deal marks the repair of relations after the rupture of 2023. India's ability to buy uranium on the open market at all rests on the 2008 NSG waiver that followed the India–US civil nuclear agreement.
Q.146 [Defence]
Consider the following statements regarding Exercise DUSTLIK-2026 :
I. It is a joint military exercise between India and UAE.
II. Its aim is to foster military cooperation and enhance combined capabilities to execute joint operations in semi-mountainous terrain.
Which of the statements given above is/are correct ?
I is false. DUSTLIK is the annual joint military exercise between India and Uzbekistan, not the UAE. The name is Uzbek for 'friendship', and the exercise has been held alternately in the two countries since 2019.
II is true. Its stated aim is to build military cooperation and joint capability for operations in semi-urban and semi-mountainous terrain under a UN mandate, with a focus on counter-terrorism.
India's exercise with the UAE is Desert Cyclone (army) and Desert Eagle (air force) — a distinction worth holding, since exercise names are a standing favourite in this paper.
Q.147 [Defence]
Which of the following statements about 'Vayu Shakti-2026' is/are correct ?
I. The Vayu Shakti-2026 exercise took place in Jaisalmer, Rajasthan.
II. Advanced fighter aircraft of the Indian Air Force, including Rafale, HAL Tejas and Mirage 2000 carried out strikes.
III. Boeing Apache and Boeing Chinook helicopters participated in this exercise.
Select the answer using the code given below :
Exercise Vayu Shakti-2026 was the Indian Air Force's firepower demonstration held on 27 February 2026 at the Pokhran firing range in Jaisalmer district, Rajasthan, with the President of India as chief guest.
Over 130 aircraft took part. The fighter fleet included Rafale, the indigenous Tejas, Su-30MKI, Mirage-2000, MiG-29, Jaguar and Hawk; transport aircraft included the C-17, C-130J and C-295; and the helicopters included the Apache and Chinook, along with the LCH Prachand, ALH Dhruv Mk-IV, Mi-17 and Chetak.
The exercise is held roughly once every three years and demonstrates the IAF's ability to deliver precise strikes by day and by night.
Q.148 [Defence]
Which of the following statements related to water governance is/are correct ?
I. River Basin Management (RBM) is a Central Sector Scheme under the Ministry of Jal Shakti, Government of India.
II. The major objectives of the RBM Scheme focus on promoting the use of water for domestic use.
III. The Brahmaputra Board is one of the key implementing agencies of the RBM.
Select the answer using the code given below :
I is true. River Basin Management is a Central Sector Scheme of the Department of Water Resources, River Development and Ganga Rejuvenation under the Ministry of Jal Shakti.
II is false. The scheme's objectives are integrated planning, sustainable use and protection of surface and groundwater at the river-basin level — basin master plans, surveys and investigations, and the planning of multipurpose projects. Domestic water supply is not its focus; that belongs to the Jal Jeevan Mission.
III is true. The scheme is implemented through three organisations: the Brahmaputra Board, the Central Water Commission and the National Water Development Agency.
The Brahmaputra Board's remit — flood control, erosion management and drainage in the North Eastern region — makes it central to the scheme's work in the Brahmaputra and Barak basins.
Q.149 [Current Affairs]
Which of the following statements regarding the Khelo India Tribal Games is/are correct ?
I. The inaugural edition of the Khelo India Tribal Games was organized in two States - Jharkhand and Odisha.
II. 'Morveer' was the official mascot of these games.
III. The Khelo India Tribal Games are part of the Khelo India Scheme.
Select the answer using the code given below :
I is false. The inaugural Khelo India Tribal Games were held in a single State — Chhattisgarh — from 25 March to 3 April 2026, across venues at Raipur, Jagdalpur and Surguja. Karnataka topped the medal tally.
II is true. The mascot was 'Morveer', from the Chhattisgarhi mor (mine, our own) and veer (brave) — a name chosen to carry the pride and identity of tribal communities.
III is true. The Games are a new vertical of the Khelo India Scheme, which already runs the Youth Games, University Games, Winter Games and Para Games.
They are India's first national multi-sport event devoted specifically to tribal athletes, and include indigenous tribal sports alongside the standard disciplines.
Q.150 [Defence]
Consider the following statements :
I. Over 60% of defence equipment sourced by the Armed Forces of India is now produced domestically.
II. The Indian defence focus is on scale, resilience and indigenous capability.
Which of the statements given above is/are correct ?
I is true. The share of domestically produced equipment in India's defence procurement has crossed 65 per cent, reversing the position of a decade ago when roughly the same proportion was imported.
II is true. Scale, resilience and indigenous capability are the declared thrust of policy, pursued through the positive indigenisation lists that bar the import of named items, the earmarking of a large share of the capital procurement budget for domestic industry, 74 per cent FDI through the automatic route, the two defence industrial corridors in Uttar Pradesh and Tamil Nadu, and the iDEX scheme for start-ups.
Defence exports have grown in step, from about ₹700 crore in 2013-14 to well over ₹21,000 crore, reaching some 100 countries.