GS: Hindi / English · Language questions stay in their original language.
150 questions · 150 marks · 2 hours 30 minutes
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Correct answer: (A) California
California's legislature became the first in the United States to vote to outlaw discrimination on the ground of caste.
Correct answer: (C) Bhutan
Bhutan has announced the eradication of rubella; a small population and intensive vaccination let it reach the target early.
Correct answer: (A) General Dalbir Singh Suhag
The United States conferred the ‘Legion of Merit’ on General Dalbir Singh Suhag, a former Chief of the Indian Army Staff.
Correct answer: (C) Bringing Indian heritage back to India
The purpose of the ‘India Pride Project’ is to trace Indian idols and heritage objects that were stolen and taken abroad, and bring them back to India.
Correct answer: (D) More than one of the above
Of these only the Andes is a young fold mountain. The Aravallis and the Appalachians are both very old, worn-down fold mountains, so more than one of the options is not a young fold mountain.
Correct answer: (C) Alps region
The snow line lies lower where it is colder. The Alps are far from the equator in the temperate zone, so their snow line is lower than that of the Himalaya or of equatorial mountains.
Correct answer: (B) Malwa Plateau
Running west to east across India, the Tropic of Cancer passes through the largest part of the Malwa Plateau.
Correct answer: (C) Tamil Nadu
Thorn forests grow in dry areas of low rainfall—the rain-shadow tracts of Karnataka and Andhra Pradesh are such. Tamil Nadu has mainly dry deciduous forest.
Correct answer: (C) Meghalaya
Laterite soil forms where rainfall is heavy and the ground alternately dries and soaks. Of the States given only Meghalaya is like that; Uttar Pradesh and Bihar have alluvial soil.
Correct answer: (C) Brazil
With the African Union joining, the membership of the G20 grew, and Brazil hosted that first enlarged summit, which was called the G21.
Correct answer: (C) Hygrometer
The instrument for measuring the moisture in the air is the hygrometer. A hydrometer measures the relative density of a liquid.
Correct answer: (A) Western Disturbance
The low-pressure system coming in from the direction of the Mediterranean is called a western disturbance. It brings the winter rain of north-west India, which the wheat crop profits by.
Correct answer: (E) None of the above
The Santhal rebellion of 1855–56 was led by Sidhu and Kanhu Murmu. All three names given belong to later peasant movements.
Correct answer: (A) Gandhi-Irwin Pact
The Gandhi–Irwin Pact was signed on 5 March 1931, after which the Civil Disobedience Movement was called off and Gandhiji agreed to attend the Second Round Table Conference.
Correct answer: (B) 1928
The Bihar Youth League was formed in 1928 and drew the province's young people into the national movement.
Correct answer: (A) Bepin Behari Varma
The Salt Satyagraha at Champaran on 6 April 1930 was led by Bepin Behari Varma.
Correct answer: (A) 24 September 1932
The Poona Pact was signed on 24 September 1932 between Gandhiji and Dr Ambedkar, agreeing on reserved seats in place of separate electorates.
Correct answer: (B) Babu Kunwar Singh
The 1857 revolt in Bihar was led by Babu Kunwar Singh of Jagdishpur.
Correct answer: (E) None of the above
The Champaran question was raised at the Lucknow session of the Congress in 1916, where Raj Kumar Shukla pressed Gandhiji to come. All three sessions given are wrong.
Correct answer: (C) Hasrat Mohani
The slogan ‘Inquilab Zindabad’ was given by the poet and freedom fighter Hasrat Mohani, and was later made famous by Bhagat Singh and his companions.
Correct answer: (C) 28%
After a 20% discount 80% is left, and after a further 10% on that, 90% of it—so 0·8 × 0·9 = 0·72. The customer pays 72%, which makes the single equivalent discount 28%.
Correct answer: (A) 537920
A rise of 2·5% an hour means multiplying by 1·025. After two hours the count = 512000 × 1·025 × 1·025 = 537920.
Correct answer: (A) ₹62,500
Falling 20% a year leaves the value 0·8 times what it was. In two years that is 0·8 × 0·8 = 0·64 times, so the purchase price = 40000 ÷ 0·64 = ₹62,500.
Correct answer: (D) More than one of the above
Equal diagonals do not have to make a rectangle—an isosceles trapezium has them too—so (II) is not necessarily true. In the same way diagonals cutting at right angles do not guarantee a rhombus unless they also bisect each other, so (III) fails as well. Two statements being so, the answer is ‘more than one’.
Correct answer: (B) 1680 cm²
The difference of the parallel sides is 78 − 52 = 26 cm, so a triangle of sides 26, 28 and 30 forms, whose height is the height of the trapezium. That triangle's area works out to 336 cm², so the height = 2 × 336 ÷ 26. Then the area = ½ × (78 + 52) × height = 1680 cm².
Correct answer: (A) 30
108 cubic metres = 1,08,000 litres. At 60 litres a minute it takes 1,08,000 ÷ 60 = 1800 minutes, that is 30 hours.
Correct answer: (B) becomes four times
The surface area depends on the product of two sides, so doubling every side makes it 2 × 2 = 4 times.
Correct answer: (B) 30–40
The total frequency is 78, so the median falls at the 39th value. The cumulative frequencies are 3, 11, 27, 57—39 first falls inside 57, so the median class is 30–40.
Correct answer: (C) 2
Multiplying both sides by 7 gives 2^(3x−1) + 10 = 42, that is 2^(3x−1) = 32 = 2⁵. Equating the indices, 3x − 1 = 5, so x = 2.
Correct answer: (A) 18 km/hr
Take the speed in still water as v. Downstream the speed is (v + 2) and upstream (v − 2), and the distance is the same both ways: 4(v + 2) = 5(v − 2). Solving gives v = 18 km/hr.
Correct answer: (B) √2
sin θ + cos θ can be written as √2 sin(θ + 45°). The greatest value of a sine is 1, so the maximum is √2.
Correct answer: (C) 4
The slope of the first line = (8 − 6)/(4 + 2) = 1/3. For the lines to be perpendicular the second slope must be −3: (24 − 12)/(x − 8) = −3, so x − 8 = −4 and x = 4.
Correct answer: (D) More than one of the above
Putting tan 45° = 1 gives |(m − ½)/(1 + m/2)| = 1, which has two solutions—m = 3 and m = −1/3. Both appear among the options, so the answer is ‘more than one’.
Correct answer: (B) 1
The line through (h, 0) and (0, k) has the intercept form x/h + y/k = 1. Since (a, b) lies on it, a/h + b/k = 1.
Correct answer: (B) x sin α + y cos α = p
The perpendicular makes an angle α with the y-axis, so (90° − α) with the x-axis. Putting ω = 90° − α in the normal form x cos ω + y sin ω = p gives x sin α + y cos α = p.
Correct answer: (C) −10/3, 5/2
Putting y = 0 gives 3x = −10, so the x-intercept is −10/3. Putting x = 0 gives −4y = −10, so the y-intercept is 5/2.
Correct answer: (C) 720 km
Raising the speed by 6 cuts the time by 4 hours and lowering it by 6 adds 6 hours. The two conditions give 3t − 2s = 12 and s − t = 6, from which t = 24 hours and s = 30 km/hr. So the distance = 30 × 24 = 720 km.
Correct answer: (A) ₹78,000; ₹72,000; ₹66,000
Each year a third of the principal, ₹60,000, has to be repaid, along with 10% interest on what is still owed. The first year: interest on 1,80,000 is ₹18,000 → ₹78,000; the second: on the remaining 1,20,000, ₹12,000 → ₹72,000; the third: on 60,000, ₹6,000 → ₹66,000.
Correct answer: (A) 0
Cosine does not change with the sign, so cos(−1710°) = cos(1710°). Taking 1440° (four full turns) off 1710° leaves 270°, and cos 270° = 0.
Correct answer: (C) √6
The mean = 75 ÷ 5 = 15. The deviations are −4, −1, 0, 2, 3 and their squares add to 30. The variance = 30 ÷ 5 = 6, so the standard deviation is √6.
Correct answer: (B) 2π cm
One full turn of the tip covers 2π × 1·5 = 3π cm. Forty minutes is two-thirds of an hour, so the distance = (2/3) × 3π = 2π cm.
Correct answer: (C) 27
aⁿ − bⁿ is always divisible by (a − b). Here 41 − 14 = 27, so 41ⁿ − 14ⁿ is a multiple of 27 for every positive integer n.
Correct answer: (C) 3/4
Of 52 cards 13 are diamonds, so 39 are not. The probability = 39/52 = 3/4.
Correct answer: (B) ₹4,400; ₹3,300; ₹1,760
Their work in an hour is 1/6, 1/8 and 1/15. Taking 120 as the common denominator the work is in the ratio 20 : 15 : 8, which adds to 43. 9460 ÷ 43 = 220, so the shares are ₹4,400, ₹3,300 and ₹1,760.
Correct answer: (C) 6
Take the smaller number as b; then the square of the larger is 26b + 3 and (26b + 3) + b² = 410. Solving gives b = 11, and the larger number's square is 289, that is 17. The difference = 17 − 11 = 6.
Correct answer: (B) −10
By the remainder theorem put x = −1: (−1) − 10 − 2 + 3 = −10.
Correct answer: (C) ₹41,750
This is an arithmetic progression of common difference ₹1,500. The sum of twelve months = 12a + 1500 × 66 = 6,00,000, so 12a = 5,01,000 and a = ₹41,750.
Correct answer: (A) 9, 10, 11
Take the three numbers as n, n+1, n+2: n² + (n+1)(n+2) = 191, that is 2n² + 3n − 189 = 0, giving n = 9. The numbers are 9, 10 and 11.
Correct answer: (B) isosceles
Work out the distances—AB² = a²/3 + a² = 4a²/3 and BC² is 4a²/3 too, but AC² = 4a². Two sides are equal and the third different, and AB² + BC² ≠ AC², so the triangle is isosceles, neither equilateral nor right-angled.
Correct answer: (A) b²
Write the first line as x sin θ + y cos θ = b sin 2θ; the perpendicular from the origin is p = b sin 2θ. From the second, q = b cos 2θ. So p² + q² = b²(sin²2θ + cos²2θ) = b².