Time Left - 45:00 mins

GATE 2021: Topper's Weekly Quiz-7 (App update required to attempt this test)

Attempt now to get your rank among 262 students!

Question 1

Mohan walks 119 m in the east direction from a street and turned to his left and walked 120 m. Now he came back to his starting point following the shortest way. Now he goes 169 m in the north direction and took a left turn and walked 80 m and turned right and walked 30. How much total distance has he covered and right now which direction he is facing now?

Question 2

The ratio of the present ages of Prannoy Roy and Radhika Roy is 4 : 3. 8 years ago, the ratio of ages of Prannoy Roy and Radhika Roy was 6 : 3. 15 years hence, what will be the age of Radhika Roy?

Question 3

What will be the value of the following equation if ‘÷’ means ‘addition’, ‘+’ means ‘subtraction’, ‘-‘means ‘multiplication’ and ‘×’ means ‘division’?

54 × 6 – 7 ÷ 8 + 2 = ?

Question 4

The solution curve of the differential equation

passes through the point (1,0). Then among the points given below, the curve also passes through:

Question 5

The contour

given below is on the complex plane

where

The value of the integral is __________.

Question 6

Select the word which means the same as the group of words given.

Too unimportant to consider

Question 7

Identify the best way to improve the underlined part of the given sentence. If there is no improvement required, select ‘no Improvement’.

I couldn’t hear we singing because of the noise.

Question 8

Which number will replace the question mark (?) in the following series?

14, 18, 32, 50, ?

Question 9

All queens and kings are removed from a deck of playing cards. Ace will be considered as 1 and jack will be considered as 0. You took out 4 cards. The probability that all cards will be in order (order is - 1234,0123,2345,6789….) from the same deck is M. What is (M x 10⁵ )?

Question 10

Find the Laplace transform of the function f(t) given as

Question 11

The value of integral

, where C is the square with vertices at ±i, 2 ±i is ………………….

Question 12

Two alloys A and B contain gold and copper in the ratios of 2 : 3 and 3 : 7 by mass, respectively. Equal masses of alloys A and B are melted to make an alloy C. The ratio of gold to copper in alloy C is __________.

Question 13

Let

and

be independent normal random variables with zero mean and unit variance. The probability that

is the smallest among the four is ___________.

Question 14

Consider matrix

and vector

The number of distinct real values of

for which the equation

has infinitely many solution is ___________.

Question 15

Let M be a real

matrix. Consider the following statements:
S1:

has 4 linearly independent eigenvectors.
S2:

has 4 distinct eigenvalues.
S3:

is non-singular (invertible).
Which one among the following is TRUE?

Question 16

If the number 715?423 is divisible by 3 (? denotes the missing digit in the thousandths place), then the smallest whole number in the place of ? is _______.

Question 17

What is the value of

Question 18

Leila aspires to buy a car worth Rs. 10,00,000 after 5 years. What is the minimum amount in Rupees that she should deposit now in a bank which offers 10% annual rate of interest, if the interest was compounded annually?