GS: Hindi / English · Language questions stay in their original language.
150 questions · 150 marks · 2 hours 30 minutes
Choose one option per question.
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Correct answer: (B) Vinegar
Vinegar is a true solution of an acid in water, so it is not a colloid. Blood and smoke are both colloids.
Correct answer: (D) More than one of the above
Manganese is used in making batteries, in the matchbox industry and in photography alike, so the answer is ‘more than one’.
Correct answer: (D) More than one of the above
The balance of the body is kept by the cerebellum and the inner part of the ear together, so the answer is ‘more than one’.
Correct answer: (C) Energy is released and stored in the form of ATP
The energy released in respiration is stored as ATP, which the cell spends as it needs.
Correct answer: (A) Sir William Jones
The Asiatic Society of Bengal was founded in 1784 by Sir William Jones.
Correct answer: (C) Irrigation
In India water is used most for irrigation—the greater part of all consumption goes to farming.
Correct answer: (B) 1934
The Congress Socialist Party was formed at Patna in 1934; Jayaprakash Narayan and Acharya Narendra Dev were among its founders.
Correct answer: (B) 336
The ratio is 14 : 25, so the difference is 11 parts: 11 parts = 264, that is one part = 24. The smaller number = 14 × 24 = 336.
Correct answer: (C) Copper
Ghatshila in Jharkhand is famous for the production of copper.
Correct answer: (A) Baku-Azerbaijan
The UN Climate Change Conference 2024 (COP29) was set for Baku in Azerbaijan in November 2024.
Correct answer: (C) Kali
The Kali river makes the boundary between India and Nepal; in Uttarakhand it is also called the Sharda.
Correct answer: (C) Parallel
Street lamps are connected in parallel, so that if one goes out the rest keep burning and each gets the full voltage.
Correct answer: (A) France
France became the first country in the world to write the right to abortion into its Constitution.
Correct answer: (E) None of the above
Dr Sadanand Date, known for his part in the 26/11 Mumbai attacks, was made Director General of the National Investigation Agency (NIA) in March 2024—not of the CRPF, the ED or the BSF. So none of the options is correct.
Correct answer: (C) 10√2 meters
The longest pole will equal the diagonal of the room: √(8² + 6² + 10²) = √200 = 10√2 metres.
Correct answer: (C) Calcutta Public Library in March 1836
The National Library of India begins its journey with the Calcutta Public Library, opened in March 1836.
Correct answer: (C) Diffusion of auxins towards the shady side of the shoot
When light falls on a shoot the auxin spreads to the shady side, where the cells then grow longer—so the stem appears to bend towards the light.
Correct answer: (E) None of the above
The four airmen chosen for Gaganyaan are Prashanth Balakrishnan Nair, Ajit Krishnan, Angad Pratap and Shubhanshu Shukla. All three names given are from that list, so ‘None of the above’ is the right answer.
Correct answer: (A) ₹425
Take Subramaniam's amount as S, so Naidu's is S + 125. From S + (S + 125) = 975, 2S = 850, that is S = ₹425.
Correct answer: (C) Cricket ‘Bat’
By the Peshawar High Court's ruling of January 2024, Imran Khan's Pakistan Tehreek-e-Insaf got back its electoral symbol, the cricket ‘bat’.
Correct answer: (B) 4
196 = 2² × 7², so the sum of the exponents = 2 + 2 = 4.
Correct answer: (C) −3/7
1/α + 1/β = (α + β)/(αβ). Here α + β = −3/4 and αβ = 7/4, so the value is (−3/4) ÷ (7/4) = −3/7.
Correct answer: (C) 0
From 11(a + 10d) = 7(a + 6d), 11a + 110d = 7a + 42d, that is 4a + 68d = 0 and a + 17d = 0. The 18th term is itself a + 17d, so it is 0.
Correct answer: (B) 3x = 2y
Setting the two distances equal: (x − 5)² + (y − 1)² = (x + 1)² + (y − 5)². Simplifying gives 12x = 8y, that is 3x = 2y.
Correct answer: (A) 45°
When the shadow equals the height, tan θ = 1, so the sun's altitude is 45°.
Correct answer: (E) None of these
Take the radii as 3 and 4 and the heights as 2 and 3. The cylinder's volume is π × 9 × 2 = 18π and the cone's (1/3) × π × 16 × 3 = 16π. The ratio is 18 : 16 = 9 : 8, which is not among the options (they give 8 : 9).
Correct answer: (E) None of these
In an isosceles right triangle the hypotenuse = side × √2 = 4√2 × √2 = 8 cm, which is not among the options.
Correct answer: (D) 12100, 2100
Under compound interest the amount = 10000 × 1·1 × 1·1 = ₹12,100, so the interest = 12100 − 10000 = ₹2,100.
Correct answer: (E) None of these
There are 3 × 3 = 9 pairs in all. Those with xy < 9 are (1,1), (1,4), (2,1), (2,4) and (3,1)—five of them. So the probability is 5/9, which is not among the options.
Correct answer: (A) 5 : 4
For 2x² − 5x + 4 = 0 the sum of the roots is 5/2 and the product 4/2 = 2. The ratio = (5/2) : 2 = 5 : 4.
Correct answer: (B) 3AB² = 4AD²
In an equilateral triangle AD = (√3/2) × AB, so AD² = (3/4)AB², that is 4AD² = 3AB²—written here as ‘3AB² = 4AD²’.
Correct answer: (A) 44
Put 2πr − r = 37: r(44/7 − 1) = 37, that is r × 37/7 = 37 and r = 7. The circumference = 2 × (22/7) × 7 = 44 cm.
Correct answer: (D) 0
The right angle is at C, so A + B = 90°, and cos 90° = 0.
Correct answer: (D) 1/12
A sum of 10 comes in three ways—(4,6), (5,5) and (6,4). Out of 36 outcomes the probability = 3/36 = 1/12.
Correct answer: (B) P³
Of P, P² and P³ the highest power is P³, and it is divisible by the other two, so the LCM is P³.
Correct answer: (C) 25π cm²
The circle inscribed in a square has a diameter equal to the square's side, so the radius is 5 cm and the area = π × 25 = 25π cm².
Correct answer: (B) 132/7
The area of the sector = (60/360) × π × 6² = 6π = 6 × 22/7 = 132/7 cm².
Correct answer: (A) an even integer
(n + 1)² − 1 = n² + 2n = n(n + 2). When n is even both n and n + 2 are even and one of them is a multiple of 4, so the product is divisible by 8.
Correct answer: (A) 6 cm
The chord of the larger circle touches the smaller one, so the perpendicular from the centre to it is 4 cm. Half the chord = √(25 − 16) = 3, so the whole chord is 6 cm.
Correct answer: (A) −10
Putting x = 2 gives 4 + 6 + k = 0, so k = −10.
Correct answer: (C) 16 : 81
The areas of similar triangles are in the square of the ratio of their sides: 4² : 9² = 16 : 81.
Correct answer: (B) 2a = b
The line through A(1, 2) and B(0, 0) has slope 2, so at C(a, b), b/a = 2, that is 2a = b.
Correct answer: (E) None of these
A 5% share of ₹100 pays ₹5 of dividend, so ₹65 needs 13 shares. Thirteen shares for ₹1,430 makes the market price 1430 ÷ 13 = ₹110, which is not among the options.
Correct answer: (A) 14 : 11
Set the perimeters equal: 2πr = 4a, so a = πr/2. The ratio of the areas = πr² : π²r²/4 = 4 : π = 4 : 22/7 = 14 : 11.
Correct answer: (B) 5¹⁰
32 = 2⁵, so m = 2 and n = 5. Then (n)^(mn) = 5^(2 × 5) = 5¹⁰.
Correct answer: (D) x² + 5x + 6
The zeroes are −2 and −3, so the polynomial is (x + 2)(x + 3) = x² + 5x + 6.
Correct answer: (B) 5
The mean of the first n natural numbers is (n + 1)/2. Setting that equal to 3n/5 gives 5(n + 1) = 6n, so n = 5.
Correct answer: (C) 1 : 8
Cut at half the height, the smaller cone stays similar to the whole and every measure of it is halved. Volume goes as the cube of the measures, so the ratio is 1 : 8.
Correct answer: (E) None of these
An 8% dividend of ₹2,840 means 8% of the nominal value = 2840, so the nominal value = 2840 ÷ 0·08 = ₹35,500—which is not among the options.
Correct answer: (A) 0
cos(45° − θ) = sin(90° − 45° + θ) = sin(45° + θ). The two terms are equal, so their difference is 0.