General Aptitude

 Question 1
In an equilateral triangle PQR, side PQ is divided into four equal parts, side QR is divided into six equal parts and side PR is divided into eight equals parts. The length of each subdivided part in cm is an integer. The minimum area of the triangle PQR possible, in $cm^2$, is
 A 18 B 24 C $48 \sqrt{3}$ D $144 \sqrt{3}$
GATE CE 2021 SET-2      Numerical Ability
Question 1 Explanation:

For $\left(\frac{a}{4}, \frac{a}{6}, \frac{a}{8}\right)$ to be integer, a must be LCM of 4, 6 and 8. So a = 24
$\text { Area }=\frac{\sqrt{3}}{4} a^{2}=\frac{\sqrt{3}}{4} \times 24^{2}=144 \sqrt{3}$
 Question 2

In the figure shown above, PQRS is a square. The shaded portion is formed by the intersection of sectors of circles with radius equal to the side of the square and centers at S and Q.
The probability that any point picked randomly within the square falls in the shaded area is __________
 A $4-\frac{\pi}{2}$ B $\frac{1}{2}$ C $\frac{\pi}{2}-1$ D $\frac{\pi}{4}$
GATE CE 2021 SET-2      Numerical Ability
Question 2 Explanation:
\begin{aligned} \text { Probability } &=\frac{f A}{T A} \\ f A &=\left(\frac{\pi r^{2}}{4}-\frac{r^{2}}{2}\right) \times 2 \\ \frac{f A}{T A} &=\frac{\left(\frac{\pi r^{2}}{4}-\frac{r^{2}}{2}\right) \times 2}{r^{2}}=\left(\frac{\pi}{2}-1\right) \end{aligned}
 Question 3
1.Some football players play cricket.
2.All cricket players play hockey.
Among the options given below, the statement that logically follows from the two statements 1 and 2 above, is :
 A No football player plays hockey B Some football players play hockey C All football players play hockey D All hockey players play football
GATE CE 2021 SET-2      Verbal Ability
Question 3 Explanation:

 Question 4
The author said, "Musicians rehearse before their concerts. Actors rehearse their roles before the opening of a new play. On the other hand, I find it strange that many public speakers think they can just walk onto the stage and start speaking. In my opinion, it is no less important for public speaker to rehearse their talks."
Based on the above passage., which one of the following is TRUE?
 A The author is of the opinion that rehearsing is important for musicians, actors and public speakers B The author is of the opinion that rehearsing is less important for public speakers than for musicians and actors C The author is of the opinion that rehearsing is more important only for musicians than public speakers D The author is of the opinion that rehearsal is more important for actors than musicians
GATE CE 2021 SET-2      Verbal Ability
Question 4 Explanation:
The last sentence of the passage decides the answer with the key words "No Less Important".
 Question 5
On a planar field, you travelled 3 units East from a point O. Next you travelled 4 units South to arrive at point P. Then you travelled from P in the North-East direction such that you arrive at a point that is 6 units East of point O. Next, you travelled in the North-West direction, so that you arrive at point Q that is 8 units North of point P.
The distance of point Q to point O, in the same units, should be _____________
 A 3 B 4 C 5 D 6
GATE CE 2021 SET-2      Numerical Ability
Question 5 Explanation:

$O Q=\sqrt{3^{2}+4^{2}}=5$
 Question 6
Four persons P, Q, R and S are to be seated in a row. R should not be seated at the second position from the left end of the row. The number of distinct seating arrangements possible is:
 A 6 B 9 C 18 D 24
GATE CE 2021 SET-2      Numerical Ability
Question 6 Explanation:
Number of arrangements $=3 \times 3 !=18$
 Question 7
$\oplus$ and $\odot$ are two operators on numbers p and q such that $p \odot q=p-q$, and $p \oplus q=p \times q$
Then, $(9 \odot(6 \oplus 7)) \odot(7 \oplus(6 \odot 5))=$
 A 40 B -26 C -33 D -40
GATE CE 2021 SET-2      Numerical Ability
Question 7 Explanation:
\begin{aligned} [9-(6 \times 7)]-[7 \times 1] &=-33-7 \\ &=-40 \end{aligned}
 Question 8
Two identical cube shaped dice each with faces numbered 1 to 6 are rolled simultaneously. The probability that an even number is rolled out on each dice is:
 A $\frac{1}{36}$ B $\frac{1}{12}$ C $\frac{1}{8}$ D $\frac{1}{4}$
GATE CE 2021 SET-2      Numerical Ability
Question 8 Explanation:
Probability of getting even number on a dice$=\frac{3}{6}=\frac{1}{2}$
$\therefore$Two dice are rolled simultaneously,
Hence required probability $=\frac{1}{2} \times \frac{1}{2}=\frac{1}{4}$
 Question 9

The mirror image of the above text about X-axis is

 A A B B C C D D
GATE CE 2021 SET-2      Numerical Ability
 Question 10
i. Arun and Aparna are here.
ii. Arun and Aparna is here.
iii. Arun's families is here.
iv. Arun's family is here.

Which of the above sentences are grammatically CORRECT?
 A (i) and (ii) B (i) and (iv) C (ii) and (iv) D (iii) and (iv)
GATE CE 2021 SET-2      Verbal Ability
Question 10 Explanation:
Two subject joined with 'and' become plural and hence plural verb is there in first statement, in fourth sentence the subject is family which is singular and takes singular verb.

There are 10 questions to complete.

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