UPSC CSE Prelims Paper 2 Practice Test - 1 - UPSC MCQ

• If M1 persons can do a piece of work in D1 days and M2 persons can do same piece of work in D2 days, then M1*D1= M2 * D2.

•  

  Let the original number of men in the group be 'x'. (M1)

•  

  After 6 men left, the size of group be (x-6) men. (M2)

Now using the above formula, we get

⇒ x * 18 = (x-6) * 20

⇒ 18x = 20x -120

⇒ 120= 20x-18x

⇒ 120 = 2x

⇒ x=60

Therefore, the original number of men in the group is 60 men.

• Since pipe B is faster than pipe A and thus, the tank will be emptied.

• Part of the tank to be emptied = 2/5

• Part emptied by (A+B) in 1 minute= (1/6 - 1/10) = 1/15.

Therefore,

⇒ 1/15 : 2/5 :: 1: x

⇒ 2/5 * 15 = 6 minutes

Formula: A and B together can do a work in x days, B and C together in y days, while C and A together in z days. If they all work together, the work will be completed in: (2xyz)/( xy+yz+zx)

In the above given problem 'x' = 8 days, 'y' = 6 days and 'z' = 10 days.

Substituting the values x, y and z in the formula, If they all work together, the work will be completed in : (2 * 8 * 6 * 10)/((8*6)+(6*10)+(10*8))

⇒ 960/(48+60+80) = 960/188 = 240/47 days

The passage emphasizes the need for both immediate humanitarian aid and long-term solutions to tackle the root causes of hunger, such as conflict and climate shocks. Therefore, the most logical and rational inference is that while humanitarian aid is crucial, it alone is not enough to solve the problem of global hunger.

Formula: If M1 persons can do a piece of work in D1 days for h1 hours and M2 persons can do the same piece of work in D2 days for h2 hours,

then: M1D1h1 = M2D2h2.

In the above given problem M1=15 men, D1=20 days, h1=8 hours, M2=20 men, D2= 12 days. Substituting the above values in the formula, we get

⇒ 15 * 20 * 8 = 20 * 12 * h2;

⇒ 2400 = 240 * h2; h2 = 10 hours

Therefore, 10 hrs a day should 20 men take to complete the same work in 12 days.

From the given data, we can get

• A's one day work = 1/24,

• B's one day work = 1/9 and

• Cs one day work = 1/12.

Since, B and C start the work and left after 3 days;

• the work done by B and C is = 3 *((1/9) +(1/12)) = 7/12.

• Therefore, remaining work = 1- 7/12 =5/12.

• Time taken by A to complete the remaining work = 24 * 5/12 =10 days.

If A can do a work in 'x' days and A + B can do the same work in 'y' days, then the number of days required to complete the work if B works alone is given by the formula: ( x * y)/(x-y).

Aman alone takes 5 days (i.e x) to complete a piece of work and along with his son he can complete same of piece of work in 3 days(i.e y).

Therefore, his son alone takes ( x * y)/(x-y) days to complete the same piece of work.

By substituting the given values in formula, his so will take (5 * 3)/(5-3) = 15/2 = 7.5 days.

The focus of the passage is on bringing out how disasters unevenly impact the rich and poor. Hence C is the correct answer.

• Tank filled in one hour when the taps A and B are open = (1/12)+(1/15)= 9/60= 3/20.

• Tank filled in one hour when the taps A and C are open = (1/12) + (1/20) = 8/60 = 2/15

• Therefore, part of the tank filled in two hours = (3/20) + (2/15) = 17/60.

• Part filled in 6 hours = ( 17/60) * 3 = 51/60

• Remaining part = 9/60 = 3/20

After 6 hours Now it is (A+B)' s turn

• Time taken by the A+B to fill 3/20 part = 1 hour

• Therefore, total time taken = 6+1 = 7 hours

• Let, the time is taken by pipe A = x

• Then, time is taken by pipe B = x/3

• By substituting these values, we get: 1/x + 3/x = 1/32 x = 128 minutes

Daily Earning of A+B+C = Rs 300

1. Daily Earning of A and C together = A + C = Rs 188 ... (1)

2. Daily Earning of B and C together = B + C = Rs 152 ... (2)

Adding (1) and (2) we get A+B+2C = 188 + 152 = Rs 340

Therefore, Daily earning of C = 340 - 300 = Rs 40.

• Work done by A in one day = 1/6.

• Work done by B in one day = 1/8

• Work done by C in one day = 1/3 - (1/6+1/8) = 1/3 -7/24 = (8-7)/24 = 1/24.

A's wage : B's wage : C's wage = 1/6 : 1/8 : 1/24 = 4: 3: 1

Therefore, C's share = (1/8) * 3200 = Rs 400.

• Work done by A in one day = 1/20. o B's 1 day's work (1/12 - 1/20) = (2/60)= 1/30.

• B's half day work = (1/30)/2 = 1/60

• A and B 's one day work (if B work for half day) = (1/20 + 1/60) = (4/60)= 1/15

• Therefore, total number of days to complete the work = 15 days.

Options B and C are wrong because they are not the key focus of the passage. The passage tells us about the increasing risk of vector borne diseases as a result of climate change and the efforts undertaken by scientists to deal with such threat which doesn't necessarily lead to the inference that the world is ill prepared, even though it might be the case. Hence option A is correct.

(A+B)'s 1 day' s work = (1/11 + 1/20 ) = 31/220

(A+C)'s 1 day's work = ( 1/11 + 1/55) = 6/55

Work done in 2 days by them= ( 31/220 + 6/55) = 55/220 = %.

Therefore, Whole work will be done in 8 days

9×360 children = 18×72 men = 12×162 women

⇒ 45 children = 18 men

= 27 women

⇒ 5 children = 2 men = 3 women

Now, 4 men + 12 women + 10 children

= 4 men + 8 men + 4 men

= 16 men

∵ 18 men can complete the work in 72 days.

∴ 16 men can complete the work in =18×72/16 = 81 days

Let 1 man's 1 day work be x and 1 woman's 1 day work be y. then

4x+6 y= 1/8 ••• (1)

3x+7y = 1/10 •••(2)

Multiplying (1) by 3, (2) by 4 and subtracting, we get

10 y = (4/10- 3/8)

= (16-15)/40 = 1/40

⇒ y = 1/400

1 woman's 1 day work = 1/400

10 women's 1 day work = (1/400*10) = 1/40

Hence 10 women can finish the work in 40 days

Let B's 1 day work =x.

Then , A's 1 day's work=2x

X+2x=1/12

⇒ 3x=1/12

⇒ x=1/36.

B's 1 day work=1/36.

Hence B alone can finish the work in 36 days.

• Part filled in 1 min. = 3/7.

• Remaining part = (1- 3/7)= 4/7

• Let the required time be x min.

• Therefore, 3/7: 4/7:: 1: x

  ⇒ 3x/7 = (4/7*1)

  ⇒ x= 4/3 min.

All the three are issues that can be addressed or mitigated by increasing focus on adaptation. Hence all three are correct. Thus, D is the correct answer.

The Average speed= (Total Distance/Total Time taken)

Time taken to cover first 12 km= (Distance/Speed)= (12/3)= 4 hours

Time taken to cover second 12 km= 12/4= 3 hours

Time taken to cover last 12 km= 12/ 6= 2 hours

Hence, total time taken for whole journey= (4+3+2) hours= 9 hours

Therefore, the average speed of whole journey= (Total distance/total time)

Average speed of man= (36/9)= 4 km/hr

Given condition:

Speed of the boat in still water = 6 km/hr.

Speed of boat in downstream = 3 * speed of boat in upstream.

Let the speed of the current be 'x' km/hr.

Therefore, speed of the boat in upstream (i.e against the current) = (6-x) km/hr.

Speed of the boat in downstream (i.e in the direction of current) = (6+x) km/hr

Now, substituting values in given condition, we get

⇒ (6+x) = 3 * (6-x)

⇒ 6+x = 18-3x

⇒ 4x=12

⇒ x=3 km/hr 

Thus, speed of the current = 3 km/hr.

• As per the given information, the velocity of the stream is 4 km/hr.

• The speed of the boat in still water is 10 km/hr.

• Therefore, speed of boat in downstream = (10+4)= 14km/hr

• The speed of boat in upstream = (10-4) = 6 km/hr.

• Let the distance between A and B be 'x'. As C is the distance between B and C is x/2.

• Total time taken to reach is 26 hours.

Therefore,

x/14 + (x/2)/6 = 26

⇒ x/14 + x/12 = 26

⇒ (7x+6x)/84 = 26

⇒ 13 x /84 = 26

⇒ x/84 = 2

⇒ x = 168.

The distance between A and B is 168 km.

Let the distance between Tina's house and school be 'x' km.

Therefore, time to cover the distance from her house to school = (Distance/ speed) = (x/3) hours.

Similarly, time to cover the distance from her school to house = (x/2) hours.

It is given that total time taken for whole journey= 5 hours.

Thus, (x/3 + x/2)= 5

⇒ ((2x+3x)/6)= 5

⇒ (5x/6) = 5

⇒ 5x=30 or x=6

Thus, distance between her house and school is 6 km

Correct answer- option C

a) Most inventions are too trivial to qualify for patent protection.

• Incorrect: The passage does not indicate that most inventions are trivial; it merely outlines criteria for what qualifies as patentable.

b) Patent filings are often irrelevant to the actual technological advancements made.

• Incorrect: This option contradicts the passage, which states that patent filings are a measure of the spread of science and technology.

c) Patent protection incentivizes innovation and is essential for technological progress.

• Correct Answer: This option directly aligns with the passage, as it highlights the importance of patent protection in fostering innovation and technological growth.

d) Patent protection is only beneficial for large corporations, not individual inventors.

• Incorrect: The passage does not limit the benefits of patent protection to large corporations, thus making this option misleading.

It is given that: Speed in still water = 8 km/hr

Speed of the stream = 4 km/hr

Speed of upstream = (8-4) = 4 km/hr

Speed of downstream = (8+4) = 12 km/hr

Total time = 1.5 hrs

Let x is the distance.

Then substituting the values, we get

x/12 + x/4 = 3/2

x = 4.5 km

Let the speed of the train be 's' m/s.

Let the length of the train be 'x' meters.

Relative speed of train and the first person who is moving at the speed of 5 m/s in opposite direction = (s+5) m/s.

Therefore, total distance travelled (i.e length of train) 'x'= Relative speed X time

x = (s+5) * 6 …. ( Eq 1)

Relative speed of train and the second person who is moving at the speed of 10 m/s in opposite direction = (s+10) m/s

Therefore, total distance travelled (i.e length of train) 'x' = Relative speed X time

x = (s+10) * 5 …. (Eq 2)

Since length of the train is same in both the cases, if we equate the equation 1 and equation 2 we get

⇒ (s+5) * 6 = (s+10) * 5

⇒ 6s+30= 5s+50

⇒ 6s - 5s = 50 - 30

⇒ s = 20 m/s (i.e speed of the train)

Now, putting the value of speed of the train in equation 1 (we can put the value equation 2 as well) we get

Length of the train 'x' = (20+5) * 6

• x = 25 * 6

• x= 150

Therefore, length of the train is 150 meters.

Average speed = 2xy/(x+y) km/hr

= (2*70*55)/ (70+55) km/hr

= (2*70*55)/125 km/hr

= 308/5 km/hr

= 61.6 km/hr

Speed = (45*5/18)m/sec = 25/2 m/sec.

Required time =(171+229)/(25/2) sec.

= (400*2/25)sec. =32 sec.

The passage focuses on bringing out the lack of sustainable practices in Indian agriculture which are creating several issues. All the examples given above are examples of measures undertaken to boost productivity at the expense of sustainability. Hence A is the correct answer.