General Aptitude

Question 1
The world is going through the worst pandemic in the past hundred years. The air travel industry is facing a crisis, as the resulting quarantine requirement for travelers led to weak demand.
In relation to the first sentence above, what does the second sentence do?
A
Restates an idea from the first sentence.
B
Second sentence entirely contradicts the first sentence.
C
The two statements are unrelated.
D
States an effect of the first sentence.
GATE ME 2021 SET-2      Verbal Ability
Question 1 Explanation: 
First option is wrong because second sentence does not contradict the first sentence. Third option is wrong because two sentences are related. Fourth option is wrong because the second sentence does not repeat the first one.
Hence second option is correct which shows the result of the cause.
Question 2
Consider a square sheet of side 1 unit. The sheet is first folded along the main diagonal. This is followed by a fold along its line of symmetry. The resulting folded shape is again folded along its line of symmetry. The area of each face of the final folded shape, in square units, equal to _____
A
\frac{1}{4}
B
\frac{1}{8}
C
\frac{1}{16}
D
\frac{1}{32}
GATE ME 2021 SET-2      Numerical Ability
Question 2 Explanation: 


Area=\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2}=\frac{1}{8}
Question 3


The ratio of the area of the inscribed circle to the area of the circumscribed circle of an equilateral triangle is
A
\frac{1}{8}
B
\frac{1}{6}
C
\frac{1}{4}
D
\frac{1}{2}
GATE ME 2021 SET-2      Numerical Ability
Question 3 Explanation: 


\begin{aligned} \sin 30^{\circ} &=\frac{r}{R} \\ \text { Area ratio } &=\frac{\pi r^{2}}{\pi R^{2}}=\sin ^{2} 30=\frac{1}{4} \end{aligned}
Question 4
A box contains 15 blue balls and 45 black balls. If 2 balls are selected randomly, without replacement, the probability of an outcome in which the first selected is a blue ball and the second selected is a black ball, is ____
A
\frac{3}{16}
B
\frac{45}{236}
C
\frac{1}{4}
D
\frac{3}{4}
GATE ME 2021 SET-2      Numerical Ability
Question 4 Explanation: 
The probability of first ball is blue and second ball is black is given as,
P=\frac{15}{60} \times \frac{45}{59}=\frac{45}{236}
Question 5
Given below are two statements 1 and 2, and two conclusions I and II.

Statement 1: All entrepreneurs are wealthy.
Statement 2: All wealthy are risk seekers.

Conclusion I: All risk seekers are wealthy.
Conclusion II: Only some entrepreneurs are risk seekers.

Based on the above statements and conclusions, which one of the following options is CORRECT?
A
Only conclusion I is correct
B
Only conclusion II is correct
C
Neither conclusion I nor II is correct
D
Both conclusions I and II are correct
GATE ME 2021 SET-2      Verbal Ability
Question 5 Explanation: 
Possible cases are:

Conclusion-I is incorrect becaue some risk seeker are wealthy.
Conclusion-II is also incorrect because all the entrepreneurs are risk seeker as well as wealthy
Question 6
The front door of Mr. X's house faces East. Mr. X leaves the house, walking 50 m straight from the back door that is situated directly opposite to the front door. He then turns to his right, walks for another 50 m and stops. The direction of the point Mr. X is now located at with respect to the starting point is ____
A
South-East
B
North-East
C
West
D
North-West
GATE ME 2021 SET-2      Numerical Ability
Question 6 Explanation: 


Question 7
If \oplus \div \odot =2;\;\oplus \div \triangle =3;\;\odot +\triangle =5;\;\triangle \times \otimes =10,
Then, the value of ( \otimes - \oplus)^2 is
A
0
B
1
C
4
D
16
GATE ME 2021 SET-2      Numerical Ability
Question 7 Explanation: 
\begin{aligned} \frac{\oplus}{\odot}&=2, \frac{\oplus}{\Delta}=3 \\ \therefore \qquad\frac{\Delta}{\odot}&=\frac{2}{3} &\ldots(1)\\ \odot+\Delta&=5 &\ldots(2)\\ \text{From (1) and (2)}\\ \Delta&=2, \odot=3\\ \text{and}\\ \oplus &=6,2 \times \otimes=10 \\ \otimes &=5 \\ \Rightarrow \quad(\otimes-\oplus)^{2}&=(5-6)^{2} =1 \end{aligned}
Question 8
A digital watch X beeps every 30 seconds while watch Y beeps every 32 seconds. They beeped together at 10 AM. The immediate next time that they will beep together is ____
A
10.08 AM
B
10.42 AM
C
11.00 AM
D
10.00 PM
GATE ME 2021 SET-2      Numerical Ability
Question 8 Explanation: 
LCM of (30 and 32) is 480
480 seconds = 8 minutes
Hence, time will be 10.08 pm
Question 9
Consider the following sentences:

(i) The number of candidates who appear for the GATE examination is staggering.
(ii) A number of candidates from my class are appearing for the GATE examination.
(iii) The number of candidates who appear for the GATE examination are staggering.
(iv) A number of candidates from my class is appearing for the GATE examination.

Which of the above sentences are grammatically CORRECT?
A
(i) and (ii)
B
(i) and (iii)
C
(ii) and (iii)
D
(ii) and (iv)
GATE ME 2021 SET-2      Verbal Ability
Question 9 Explanation: 
"The number of" is singular and it takes singular verb. "A number of " is plural and it takes plural verb.
Question 10
Five persons P, Q, R, S and T are to be seated in a row, all facing the same direction, but not necessarily in the same order. P and T cannot be seated at either end of the row. P should not be seated adjacent to S. R is to be seated at the second position from the left end of the row. The number of distinct seating arrangements possible is:
A
2
B
3
C
4
D
5
GATE ME 2021 SET-2      Numerical Ability
Question 10 Explanation: 
The possible distinct arrangement are
S R P T A, A R P T S, S R T P A
Hence, number of distinct sitting arrangement. = 3


There are 10 questions to complete.

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