UPSC 2016 Prelims Questions with Answers

Marked price Rs.770 with a 10% cash discount gives a selling price of 770 × 0.9 = Rs.693. This selling price still yields a 10% gain, so cost price = 693 ÷ 1.1 = Rs.630.

0.16. The target radius is 0.5 m because diameter is 1 m. The red region radius is 0.20 m. Probability of hitting the red region, assuming uniform landing over the target, is area(red)/area(target) = pi(0.20)^2 / pi(0.50)^2 = 0.04/0.25 = 0.16.

150 m. The apples are placed in a straight line at equal intervals from the bucket. The runner must return to the bucket after each apple, so the total distance is twice the sum of the six apple distances. With distances 5, 8, 11, 14, 17 and 20 m, total = 2 x (5+10+15+20+25+30) = 2 x 75 = 150 m.

Rs. 12,000. Current total monthly income of 5 persons = 5 x 10,000 = Rs. 50,000. One person's annual income increases by Rs. 1,20,000, i.e. monthly increase = Rs. 10,000. New monthly family income = Rs. 60,000. New average = 60,000/5 = Rs. 12,000.

Z. Convert each statement to a full-work time. W does 25% in 30 days, so full work takes 120 days. X does 1/4 in 10 days, so full work takes 40 days. Y does 40% in 40 days, so full work takes 100 days. Z does 1/3 in 13 days, so full work takes 39 days. Z finishes first.

7. A and B walk in opposite directions at 2 and 3 rounds per hour, so their relative speed is 5 rounds per hour. They meet every 1/5 hour = 12 minutes. After 8:00 a.m. and before 9:30 a.m., the meetings occur at 8:12, 8:24, 8:36, 8:48, 9:00, 9:12 and 9:24. That is 7 times.

12. Total students = 60. Girls are twice boys, so boys = 20 and girls = 40. Kamal is 17th from the top, so 16 students are ahead of him. Of these, 9 are girls; hence 7 are boys. Including Kamal, boys up to his rank = 8. Boys after him = 20 - 8 = 12.

Overhead tank volume = π × 2² × 7 = 28π ≈ 88 m³. Underground tank volume = 5.5 × 4 × 6 = 132 m³. After filling the overhead tank, the underground tank still holds 132 − 88 = 44 m³, i.e. 44/132 = 1/3 of its capacity.

6. Form 4-digit numbers using 1,2,3,4 once each. Apply the restrictions: 2 and 3 must not be adjacent; 1 must not be immediately followed by 3; 4 must not be last; and 1 must not be first. Checking the 24 possible permutations after these filters leaves 6 valid numbers. Hence 6 numbers can be formed.

3 only. The passage stresses that the world food-supply issue is linked to the capability to maintain a sustained supply of food amid changing demand and weak supply arrangements. It does not make a sharp decline in area under food production the central reason. Population pressure is part of the larger background, but the question asks what mainly gives worldwide supply its importance; the passage's direct emphasis is on limitations in sustained supply. Hence only statement 3 is the best answer.

The passage identifies the demand-supply balance as the core of world agriculture and stresses price-affordability by the poor in the developing world as central to food security. Hence balancing demand and supply of food (1) and increasing the purchasing power of the poor (3) help reduce hunger and starvation; imports and changing consumption patterns are not cited as solutions.

The passage states it in its opening line: historically, the biggest challenge to world agriculture has been to achieve a balance between demand for and supply of food. The other options are not stated.

The passage says food production, marketing and prices - especially price-affordability by the poor - have become global issues needing global solutions. So improving price affordability (2) and regulating the conditions of marketing (3) are the fundamental solutions mentioned; agro-based industries and universal food subsidy are not discussed.

The passage links warming to increased microbial activity, which in turn releases carbon trapped in soil. The most logical corollary is therefore that increasing green cover (a warming-linked change) could trigger the release of carbon trapped in soil.

The statement says comparisons between underdeveloped and industrialised countries are difficult because part of the output in underdeveloped countries is produced outside commercial channels. The author implies that this non-commercialized sector in underdeveloped countries makes national income comparisons particularly difficult.

After cattle domestication made drinking milk advantageous, lactose tolerance evolved independently - a genetic change driven by a lasting change in food habits. The passage thus implies that a permanent change in the food habits of a community can bring about a genetic change in its members.

The passage says a meat-and-dairy-centred diet, which is spreading through the developing world, will take a greater toll on the world's resources. The inference is that our increasing demand for foods sourced from animals puts a greater burden on our natural resources.

110. Numbers from 100 to 300 that begin with 2 are 200 to 299: 100 numbers. Numbers that end with 2 between 100 and 300 are 102, 112, ..., 292: 20 numbers. The overlap, numbers from 200 to 299 ending in 2, has 10 numbers. Total = 100 + 20 - 10 = 110.

R + S is divisible by 10. Since R and S are both divisible by 5, R-S is divisible by 5, R x S is divisible by 25, and R^2 + S^2 is divisible by 5. But R + S need not be divisible by 10: for example, 5 + 10 = 15, which is not divisible by 10.

Split FRACTION into two equal halves: FRAC and TION. The code writes each half in reverse order, as shown by the examples (SYSTEM → SYS + MET and NEARER → AEN + RER). Reversing both halves gives CARF + NOIT = CARFNOIT.

10 days. Ram and Shyam together complete 60% in 4 days, so their combined rate = 15% per day. Shyam alone completes the remaining 40% in 8 days, so Shyam's rate = 5% per day. Therefore Ram's rate = 15% - 5% = 10% per day. Ram alone would complete the whole job in 100/10 = 10 days.

The big cube is cut into 4 × 4 × 4 = 64 small cubes. Small cubes with exactly one painted face are the centre pieces of each face: on a 4×4 face, the inner 2×2 block = 4 cubes per face, and there are 6 faces → 4 × 6 = 24 cubes.

Net north-south movement = 12 km north - 15 km south = 3 km south. Net east-west movement = 15 km east - 19 km west = 4 km west. The person is therefore 3 km south and 4 km west of the start, at a distance of sqrt(3^2 + 4^2) = 5 km.

25 m. The trunk breaks at C, 12 m above the ground. The broken top touches the ground at D, 5 m away from the base A. Triangle ACD is right-angled with AC=12 and AD=5, so the broken part CD = sqrt(12^2+5^2)=13 m. Original height = AC + CD = 12 + 13 = 25 m.

C wears the tie. B and A wear the sweater and jacket. Ribeiro does not wear black, and neither B nor Ribeiro wears a white sweater. Testing the constraints: A is Kumar wearing the white sweater, B is Singh wearing the black jacket, and C is Ribeiro wearing the blue tie. Hence A wore the sweater.

The consistent assignment is A = Kumar (white sweater), B = Singh (black jacket) and C = Ribeiro (blue tie): Ribeiro avoids black, Singh avoids white, and Kumar avoids a jacket. Since C wears the tie and Ribeiro cannot wear black, the tie is blue.

Kumar cannot wear a jacket and C wears the tie, so C must be Kumar; Ribeiro is therefore not C. B cannot wear a white sweater, and Singh avoids white, leaving Ribeiro with the blue tie. Hence C's surname is Ribeiro.

9. He is on the 1st step. After climbing 4 more steps, he reaches the 5th step. If the 5th step is exactly the middle step, the ladder has equal steps above and below it: 4 below and 4 above. Total steps = 4 + 1 + 4 = 9.

12 : 11. Let the basic pays be B1 and B2. Total emoluments are equal. First person gets 65% allowance, so total = 1.65B1. Second person gets 80% allowance, so total = 1.80B2. Therefore 1.65B1 = 1.80B2, giving B1:B2 = 1.80:1.65 = 180:165 = 12:11.

1 year. Three years ago, total age of 5 members = 80. Today those 5 members together are older by 5 x 3 = 15 years, so their total is 95. The present average of the 6-member family is the same as the old average, 80/5 = 16. Present total for 6 members = 6 x 16 = 96. Baby's age = 96 - 95 = 1 year.

400 sq m. For a rectangle with length x and breadth y, x + y = 40. Area xy is maximum when x = y = 20 by AM-GM or by symmetry. Maximum area = 20 x 20 = 400 sq m.

13 km. The movement from O to A is 5 km in the north-east direction and then from A to B is 12 km in the north-west direction. North-east and north-west directions are perpendicular to each other. Therefore OB = sqrt(5^2 + 12^2) = sqrt(169) = 13 km.

The passage shows that agriculture plus forestry and land-use change account for a large share of greenhouse gas emissions. Since land use is a major emissions source, the imperative inference is that we must modify our land use practices to mitigate climate change; it does not call for banning mechanised farming or claim no technological solutions exist.

The statement presents politics and economics as mutually shaping each other rather than one dominating the other — it is about the interrelationship of Politics and Economics.

The passage argues that nature made man's wants greater than his individual powers, so that no one can supply his own wants without the aid of society. The natural conclusion is that diverse natural wants forced man towards a social system.

Statement 1 fails because of the word only: the passage does not say abolition of manual scavenging would fully solve urban sanitation problems. Statement 2 is supported - the passage urges promoting pour-flush toilets and ending dry latrines, which requires greater awareness of safe sanitation practices in urban areas.

The passage notes that banking has been restructured to serve the middle and upper-middle class, and that a new agenda is needed to serve the common man. The essentially implied message is the need to promote financial inclusion.

The passage explains that water and biodiversity are interdependent: the hydrological cycle decides how biodiversity functions, and vegetation and soil drive the movement of water. So biodiversity sustains nature's ability to recycle water.

The passage says climate adaptation may be rendered ineffective if policies are not designed in the context of other development concerns, illustrating with a food-security strategy that bundles coordinated measures. The inference is that climate adaptation should be examined in tandem with other economic development options.

The passage says crony capitalism kills transparency and competition, harming free enterprise and opportunity, and that it is a major issue to be tackled. The needed response is greater transparency in the functioning of the government and promoting financial inclusion - the opposite of opaque, discretionary favouritism.

Each of the five questions has 2 choices (T/F), so the number of distinct answer sequences is 2⁵ = 32. For no two candidates to have identical sequences, the maximum number of candidates is 32.

4 cm. The rectangular tin area = 12 x 8 = 96 sq cm. A closed cube has surface area 6a^2. So 6a^2 = 96, giving a^2 = 16 and a = 4 cm.

4. Each one-way journey takes 42 hours. A train starts daily from each end at 6 AM. At any time, trains that started in the previous 42 hours are still on the route. For a daily service, two departures per day are needed, one from each end. Since the route occupancy spans nearly two days, the minimum fleet needed is 4 trains.

10%. Let the third number Z = 100. Then X = 80 and Y = 72. Percentage by which Y is less than X = (80 - 72)/80 x 100 = 8/80 x 100 = 10%.

The arrangement is fixed for most boxes: A at the extreme right (orange, tennis), C fifth from right (green, cricket) with B beside it (volleyball), the golf ball in the violet box with the hockey box between golf and volleyball. The football box is the only remaining slot, but both blue and yellow remain unassigned to it, so the colour of the football box cannot be determined.

Working through the constraints: D holds the football, E holds the golf ball in the violet box, F holds the hockey ball, and the hockey box cannot be blue or yellow, so it must be indigo. Hence F is painted indigo; the other statements are not forced.

The golf ball is in the violet box and is not in D. The hockey box sits between the golf and volleyball boxes, and A, B and C are fixed as tennis, volleyball and cricket respectively. Only E can hold the golf ball. Hence E contains the golf ball.

80%. Let male employees be m and female employees be f. Overall average = 5000, male average = 5200, female average = 4200. By alligation, m:f = (5000-4200):(5200-5000) = 800:200 = 4:1. Therefore males are 4/5 = 80% of employees.

Statement 1 means A is at least as old as B, and B is older than C, so A must be older than C. The statements do not force A to be strictly older than B, or fix the relation between B/D or D/C.

12. 18 very tall boys are three-fourths of all boys, so total boys = 18 x 4/3 = 24. Boys are two-thirds of the total class, so total students = 24 x 3/2 = 36. Girls = 36 - 24 = 12.