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Correct answer: B
The ratio $36:84$ simplifies to $3:7$. So $42:X = 3:7$, giving $X = \frac{42\times 7}{3} = 98$.
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Correct answer: A
Let original cost $=C$. Cost price $=0.9C$, selling price $=1.08C$. Profit $=1.08C-0.9C=0.18C$. Profit% $=\frac{0.18C}{0.9C}\times100 = 20\%$ profit.
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Correct answer: D
$SI=\frac{PRT}{100}$. (A)$=\frac{6600\times5\times2}{100}=660$; (B)$=\frac{200\times6\times5}{100}=60$; (C)$=\frac{840\times5\times4}{100}=168$; (D)$=\frac{5000\times12\times2}{100}=1200$. Decreasing order: $1200(D),660(A),168(C),60(B)$ = (D),(A),(C),(B).
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Correct answer: B
Radius $r=\frac{14}{2}=7$ cm. The four quarter-circles inside the square together make one full circle: area $=\pi r^2=\frac{22}{7}\times7^2=154$ cm$^2$. Square area $=14^2=196$ cm$^2$. Shaded region $=196-154=42$ cm$^2$.
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Correct answer: C
$d=\sqrt{(-1-(-5))^2+(3-7)^2}=\sqrt{4^2+(-4)^2}=\sqrt{16+16}=\sqrt{32}=4\sqrt{2}$ units.
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Correct answer: C
Mode = value with highest frequency = 29 (frequency 28). For median, $N=100$, so average of 50th and 51st values. Cumulative frequencies: 20→6, 25→26, 28→50, 29→78. The 50th value is 28 and 51st is 29, so median $=\frac{28+29}{2}=28.5$. Then $3(29)-2(28.5)=87-57=30$.
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Correct answer: C
(A) Numbers $>4$ are {5,6}: $P=\frac{2}{6}=\frac{1}{3}$ ✓. (B) Numbers $\geq4$ are {4,5,6}: $P=\frac{3}{6}=\frac{1}{2}\neq\frac{1}{3}$ ✗. (C) Numbers $\leq3$ are {1,2,3}: $P=\frac{3}{6}=\frac{1}{2}$ ✓. (D) Numbers $\leq6$: all outcomes, $P=1$ ✓. Correct: (A),(C),(D).
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Correct answer: C
(A) $^8P_3-{}^{10}C_3=336-120=216$ → (III). (B) $^8P_5=8\times7\times6\times5\times4=6720$ → (IV). (C) $^nP_4=360 \Rightarrow n(n-1)(n-2)(n-3)=360=6\cdot5\cdot4\cdot3 \Rightarrow n=6$ → (I). (D) $^nC_2=210 \Rightarrow \frac{n(n-1)}{2}=210 \Rightarrow n(n-1)=420=21\times20 \Rightarrow n=21$ → (II). So (A)-III, (B)-IV, (C)-I, (D)-II.
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Correct answer: C
Let son's age $=S$, father's $=F$. $F=2S+4$. After 10 years: $F+10=(S+10)+30 \Rightarrow F=S+30$. So $2S+4=S+30 \Rightarrow S=26$, and $F=26+30=56$ years.
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Correct answer: A
If angles at distances $a$ and $b$ are complementary, height $h=\sqrt{ab}$. Here $h=\sqrt{5\times20}=\sqrt{100}=10$ m.
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Correct answer: B
$r=\frac{21}{2}=10.5$ cm → (A) ✓. Volume $=\pi r^2 h=\frac{22}{7}\times10.5^2\times28=9702$ cm$^3 \neq 12936$ → (B) ✗. CSA $=2\pi r h=2\times\frac{22}{7}\times10.5\times28=1848$ cm$^2$ → (C) ✓. TSA $=2\pi r(r+h)=2\times\frac{22}{7}\times10.5\times38.5=2541$ cm$^2$ → (D) ✓. Correct: (A),(C),(D).
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Correct answer: C
Together rate $=\frac{1}{24}$, P's rate $=\frac{1}{32}$, so Q's rate $=\frac{1}{24}-\frac{1}{32}=\frac{4-3}{96}=\frac{1}{96}$. Work in 8 days together $=\frac{8}{24}=\frac{1}{3}$. Remaining $=\frac{2}{3}$. Time for Q $=\frac{2/3}{1/96}=\frac{2}{3}\times96=64$ days.
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Correct answer: B
Downstream speed $=\frac{10}{0.5}=20$ km/h. Upstream speed $=\frac{10}{40/60}=\frac{10}{2/3}=15$ km/h. Speed of stream $=\frac{20-15}{2}=2.5$ km/h.
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Correct answer: D
$37^2=1369$. The units digit is $9$ (since $7^2=49$ ends in 9).
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Correct answer: B
AP: $a=23$, $d=-2$, last term $=5$. $5=23+(n-1)(-2) \Rightarrow -18=-2(n-1) \Rightarrow n-1=9 \Rightarrow n=10$ rows.
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Correct answer: C
First letters H,K,N,Q,T increase by 3 each ✓; last letters Q,N,K,H,E decrease by 3 each ✓. The numbers should follow doubling: $4,10,20,40,80$ (each roughly double the previous: $4\to10,10\to20,20\to40,40\to80$). The given term Q43H breaks the pattern (should be 40, giving Q40H). Hence Q43H does not fit.
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Correct answer: C
Option 3 is explicitly described as containing the embedded quadrilateral shape (the key figure) together with an additional triangle, forming an envelope-like pattern. The other options do not contain the complete quadrilateral. Hence Option 3 contains the given figure as its part.
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Correct answer: A
From 5 a.m. (day 1) to 10 p.m. on the 4th day, the faulty clock shows $3\times24 + 17 = 89$ hours. Since the clock loses 16 min in 24 h, it runs at $\frac{1424}{1440}$ of true rate; so $1424$ clock-minutes correspond to $1440$ true minutes. True time elapsed $=89\times\frac{1440}{1424}\approx90$ hours. Adding 90 hours to 5 a.m. = 3 days (72 h) + 18 h $=$ 5 a.m. + 18 h $=$ 11 p.m.
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Correct answer: C
Days from 1 July to 1 November: July (31) + August (31) + September (30) + October (31) $=123$ days. $123 \bmod 7 = 4$ (since $119=17\times7$). Sunday $+4$ days $=$ Thursday.
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Correct answer: B
Across each row the hatching increases progressively while the dividing lines (here both diagonals forming an X) are retained. Row 3 has the X-divided rectangle with hatching growing from none → one triangle → more. The missing figure keeps the X (both diagonals) and adds further hatching, matching Option 2 (both diagonals with the left triangle and part of the top hatched).
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Correct answer: B
U # C: U is daughter of C. C - D: C is wife of D, so D is U's father. D + H: D is brother of H, so H is a male sibling of U's father. H + T: H is brother of T. Therefore H is the brother of U's father → H is U's uncle.
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Correct answer: B
A right-side mirror laterally inverts left and right. In fig(x) the black triangle is at the bottom-right and the ball is top-left; in the mirror image the black triangle moves to the bottom-left and other elements flip accordingly, keeping the same sizes. Option 2 is the correctly laterally-inverted image.
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Correct answer: D
ALPHABET reversed letter-by-letter gives TEBAHPLA, so the code simply reverses the word. Reversing DECIPHER: D-E-C-I-P-H-E-R → R-E-H-P-I-C-E-D = REHPICED.
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Correct answer: D
Milk, Water and Oil are liquids, whereas Sugar is a solid. Hence Sugar is the odd one out.
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Correct answer: A
Start at (0,0). North 20 → (0,20). Left (West) 50 → (-50,20). Right (North) 40 → (-50,60). Right (East) 50 → (0,60). Distance from start $=\sqrt{0^2+60^2}=60$ m.
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Correct answer: C
Position from right $=$ Total $-$ position from left $+1 = 30-17+1 = 14$.
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Correct answer: B
Differences are 3, 5, 7, 9 (consecutive odd numbers), so next difference is 11. $30+11=41$.
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Correct answer: A
Each column is an AP: column 3 is 14, 21, ? with common difference 7, so $?=21+7=28$. (Also column 1: +3; column 2: +5; column 3: +7.)
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Correct answer: C
W=4, V=5. 'W immediately behind T' means T is just ahead → T=3. One person between V(5) and Z means Z=7 or Z=3; since T=3, Z=7. Y is behind both U and W(4), so Y>4; positions 5,7 are taken by V,Z, so Y=6. Remaining positions 1,2 go to U and X (with X ahead of Y, satisfied). Thus Y is sixth must be true.
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Correct answer: C
The four pieces are complementary jigsaw cut-outs: piece (A)'s arrowhead notch fits piece (D)'s L-foot protrusion, and piece (B)'s V-notch is filled by piece (C)'s slanted trapezoid, with all four interlocking to tile a complete square. Hence all four pieces (A),(B),(C),(D) are required.
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Correct answer: A
COVAXIN, developed by Bharat Biotech with ICMR, was India's first indigenous (wholly home-developed) COVID-19 vaccine. Covishield was manufactured in India but based on the Oxford-AstraZeneca technology; Sputnik-V and Moderna are foreign.
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Correct answer: A
Kinematics is the branch of mechanics that describes the motion of objects (displacement, velocity, acceleration) without reference to the forces causing it.
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Correct answer: D
Chloroform (CHCl3) is industrially produced by the chlorination of methane (CH4), which is a gas. Among the options, methane is the gas used.
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Correct answer: C
Rishabhnath (Adinath) is regarded as the first of the 24 Tirthankaras in Jainism. Mahavira was the 24th and last.
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Correct answer: A
The Ilbari (Mamluk) dynasty, founded by Qutb-ud-din Aibak and continued by Iltutmish and Balban, is commonly called the Slave Dynasty of the Delhi Sultanate.
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Correct answer: D
The slogan was given by Bal Gangadhar Tilak, who launched the Home Rule Movement (1916). Hence it is associated with the Home Rule Movement.
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Correct answer: A
Chandrayaan-3 was launched from the Satish Dhawan Space Centre (SDSC SHAR), Sriharikota, on 14 July 2023 — not from the Vikram Sarabhai Space Centre. Statements B (4th country to soft-land), C (lander Vikram, rover Pragyan) and D (first near the lunar South Pole) are correct. Hence A is incorrect.
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Correct answer: A
The IUCN Red List of Threatened Species is the global inventory of the conservation status of species, cataloguing those threatened with the risk of extinction.
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Correct answer: B
Shakespeare → The Tempest (II); Lewis Carroll → Through the Looking Glass (III); E M Forster → A Passage to India (IV); Bernard Shaw → The Man of Destiny (I). So (A)-II, (B)-III, (C)-IV, (D)-I.
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Correct answer: B
Calcium is essential for bone formation (A), blood clotting (B) and muscle contraction/function (C). Blood formation (haematopoiesis) requires iron, not calcium, so (D) is incorrect. Hence (A),(B),(C) only.
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Correct answer: D
Economic Liberalization (1991) → Right to Information Act (2005) → Mars Orbiter Mission (2013) → Swachh Bharat Abhiyaan (2014). Order: (D),(C),(B),(A).
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Correct answer: D
Establishment of UN (1945) → Fall of Berlin Wall (1989) → Apartheid ends in South Africa (1994) → Adoption of SDGs (2015). Order: (D),(A),(B),(C).
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Correct answer: B
The Coco Channel (Coco Strait) separates the North Andaman Islands (India) from the Coco Islands belonging to Myanmar. (Preparis Strait lies further north between Coco Islands and Preparis Island.)
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Correct answer: C
Article 9 states that a person who voluntarily acquires the citizenship of a foreign State shall not be a citizen of India. Hence it deals with persons voluntarily acquiring foreign citizenship.
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Correct answer: D
The GST Compensation Fund (financed by the GST compensation cess) was created to compensate States for any loss of revenue arising from the implementation of GST for the first five years.
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Correct answer: A
(A) Clouds are classified by appearance and height ✓. (B) Cirrus are high feathery ice-crystal clouds ✓. (D) Altocumulus are mid-level heap-like clouds with flat bases and rounded tops ✓. (C) is incorrect because nimbostratus clouds produce continuous (steady), not sporadic, rain. Hence (A),(B),(D) only.
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Correct answer: C
Aizawl is the capital of Mizoram. (Shillong–Meghalaya, Kohima–Nagaland, Agartala–Tripura.)
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Correct answer: C
Japan → Yen (II); Russia → Ruble (III); China → Yuan (IV); Norway → Krone (I). So (A)-II, (B)-III, (C)-IV, (D)-I.
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Correct answer: C
The Gandikota Gorge ('Grand Canyon of India') in Andhra Pradesh is carved by the Penna (Pennar) River.
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Correct answer: B
India's National Emblem is adapted from the Lion Capital of Ashoka, which was erected at Sarnath. Hence King Ashoka, situated at Sarnath.
Original question paper source: National Testing Agency (NTA), CUET (UG) 2025. Reproduced for educational use. Answers & explanations by UniDrill.