GATE - APTITUDE 2022 GG

 1) Inhaling the smoke from a burning _________ could _________ you quickly.

(A) tire / tier

(B) tire / tyre

(C) tyre / tire

(D) tyre / tier

Solution :

• Inhaling smoke from a burning tyre (rubber covering of a wheel) is harmful.

• The verb tire means to cause fatigue or exhaustion, which fits the context of the sentence ("could tire you quickly").

  

Solution :

For the sphere to fit:

• The diameter of the sphere must equal the side length of the cube.

• Side length of the cube=Diameter of the sphere=2r

• Now volume = (2r)³ = 8 r³

3) Pipes P and Q can fill a storage tank in full with water in 10 and 6 minutes,

respectively. Pipe R draws the water out from the storage tank at a rate of 34

litres per minute. P, Q and R operate at a constant rate.

If it takes one hour to completely empty a full storage tank with all the pipes

operating simultaneously, what is the capacity of the storage tank (in litres)?

(A) 26.8

(B) 60.0

(C) 120.0

(D) 127.5

Solution : Let the capacity of the storage tank be C litres.

Pipe P fills the tank in 10 minutes, so its filling rate is C/10 litres per minute.

Pipe Q fills the tank in 6 minutes, so its filling rate is C/6 litres per minute.

Pipe R empties the tank at a rate of 34 litres per minute.

When all three pipes are operating simultaneously, the tank is emptied in 1 hour (60 minutes).

The combined filling rate of P and Q is (C/10 + C/6) litres per minute.

The net rate of change of water in the tank when all three pipes are operating is

(C/10 + C/6 - 34) litres per minute.

Since the tank is emptied in 60 minutes, the net rate of change must be negative, and the total amount emptied is equal to the capacity of the tank, C.

So, we have:

60 × (C/10 + C/6 - 34) = -C

Dividing by 60:

C/10 + C/6 - 34 = -C/60

Multiplying by 60 to eliminate fractions:

6C + 10C - 2040 = -C

16C - 2040 = -C

17C = 2040

C = 2040 / 17

C = 120

4) Six persons P, Q, R, S, T and U are sitting around a circular table facing the

center not necessarily in the same order. Consider the following statements:

• P sits next to S and T.

• Q sits diametrically opposite to P.

• The shortest distance between S and R is equal to the shortest distance

between T and U.

Based on the above statements, Q is a neighbor of

(A) U and S

(B) R and T

(C) R and U

(D) P and S

Solution :

• P is between S and T.

• Q is directly opposite P.

• R is opposite S, and U is opposite T.

• Thus, Q is neighbors are R and U.

Solution : We will encounter 2 doors while go from P to Q.

6) Rice, a versatile and inexpensive source of carbohydrate, is a critical component

of diet worldwide. Climate change, causing extreme weather, poses a threat to

sustained availability of rice. Scientists are working on developing Green Super

Rice (GSR), which is resilient under extreme weather conditions yet gives higher

yields sustainably.

Which one of the following is the CORRECT logical inference based on the

information given in the above passage?

(A) GSR is an alternative to regular rice, but it grows only in an extreme weather

(B) GSR may be used in future in response to adverse effects of climate change

(C) GSR grows in an extreme weather, but the quantity of produce is lesser than

regular rice

(D) Regular rice will continue to provide good yields even in extreme weather

Solution : GSR is being developed to address the challenges posed by climate change.

7) A game consists of spinning an arrow around a stationary disk as shown below.

When the arrow comes to rest, there are eight equally likely outcomes. It could

come to rest in any one of the sectors numbered 1, 2, 3, 4, 5, 6, 7 or 8 as shown.

Two such disks are used in a game where their arrows are independently spun.

What is the probability that the sum of the numbers on the resulting sectors upon

spinning the two disks is equal to 8 after the arrows come to rest?

(A)1/16

(B)5/64

(C)3/32

(D)7/64

Solution : Each disk has 8 outcomes, so the total number of outcomes for two disks is: 8×8=64

Favorable Outcomes (Sum = 8):

We need pairs (x,y) such that x+y=8, where x and y are numbers from 1 to 8.

The pairs that satisfy this condition are:

(1,7),(2,6),(3,5),(4,4),(5,3),(6,2),(7,1)

These are 7 pairs.

The probability is the ratio of favorable outcomes to total outcomes = 7/64

8) Consider the following inequalities.

(i)3𝑝 − 𝑞 < 4

(ii)3𝑞 − 𝑝 < 12

Which one of the following expressions below satisfies the above two

inequalities?

(A) 𝑝 + 𝑞 < 8

(B) 𝑝 + 𝑞 = 8

(C) 8 ≤ 𝑝 + 𝑞 < 16

(D) 𝑝 + 𝑞 ≥ 16

Solution :

3𝑝 − 𝑞 < 4

3𝑞 − 𝑝 < 12

So, 2q+2p < 16

then , p+q < 8

9) Given below are three statements and four conclusions drawn based on the

statements.

Statement 1: Some engineers are writers.

Statement 2: No writer is an actor.

Statement 3: All actors are engineers.

Conclusion I: Some writers are engineers.

Conclusion II: All engineers are actors.

Conclusion III: No actor is a writer.

Conclusion IV: Some actors are writers.

Which one of the following options can be logically inferred?

(A) Only conclusion I is correct

(B) Only conclusion II and conclusion III are correct

(C) Only conclusion I and conclusion III are correct

(D) Either conclusion III or conclusion IV is correct

Solution :

Some writers are engineers.

• This can be inferred from Statement 1 ("Some engineers are writers"), as it means there is at least some overlap between engineers and writers. Conclusion I is correct.

No actor is a writer.

• This follows from Statement 2 ("No writer is an actor") because no writer can be an actor. Conclusion III is correct.

10)

Solution :

• In option C, the pieces align correctly to form a square. The edges and corners match perfectly without leaving any gaps or overlaps.

• The round cutout aligns near the center when the pieces are arranged correctly.