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GATE 2021 : Toppers Weekly Quiz 8 (App update required to attempt this test)

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Question 1

The analytic function

has singularities at

Question 2

The principal argument of the complex number

Question 3

Let matrix and matrix B can be written as B = A⁸ – 5A⁷ + 7A⁶ – 3A⁵ + A⁴ – 5A³ + 8A² – 2A +1 then which of the following option represents matrix B?

Question 4

The value of

is…..

Question 5

The partial differential equation

Question 6

People were prohibited ______ their vehicles near the entrance of the main administrative building.

Question 7

Given that N is a 4 digit positive integer and we plan to plant exactly N trees in a memorial park. How many distinct values of N are possible such that each row of trees planted has as many trees as the number of columns?

Question 8

Select the word that is most SIMILAR in meaning to the bold word in capital letters
VAPID

Question 9

Choose the correct alternative that will continue the same pattern and replace the question mark in the given series.

3, 15, ?, 63, 99, 143

Question 10

If the sum of n positive integers k₁, k₂, k₃....., k_n is an even number, then number of odd integers involved in the expression is:

Question 11Multiple Correct Options

Consider a differential equation:

having boundary condition as y = 4 at x = 1. If solution of the differential equation is y = Ae^Be^–Bx, where A and B are constants. Then choose the correct option(s):

Question 12

Three riflemen takes one shot each at the same target. The probability of the first riflemen hitting the target is 0.4, the probability of the second rifleman hitting the target is 0.5 and the probability of the third riflemen hitting the target is 0.8. Find the probability that exactly two of them hit the target?

Question 13

Let C be the boundary of the region in the first quadrant bounded by Y=1–x²_, x=0 and y = 0, oriented counter-clockwise.

Question 14Multiple Correct Options

Let

. Then which of the following statement is/are correct with respect to u², where max. and min. denotes maximum and minimum values of the function u²?

Question 15Multiple Correct Options

If the determinant

. Then which of the following statement is/are correct?

Question 16

After the inauguration of the new building, the Head of the Department (HoD) collated faculty preferences for office space. P wanted a room adjacent to the lab. Q wanted to be close to the lift. R wanted a view of the playground and S wanted a corner office.

Assuming the everyone was satisfied, which among the following shows a possible allocation?

Question 17

An oil tank can be filled by pipe X in 5 hours and pipe Y in 4 hours, each pump working on its own. When the oil tank is full and the drainage hole is open, the oil is drained in 20 hours. If initially the tank was empty and someone started the two pumps together but left the drainage hole open, how many hours will it tak for the tank to be filled? (Assume that the rate of drainage is independent of the head)

Question 18

An electronic safe has a key which is made up of 5 digits (not necessarily distinct). It is also known that the first digit is three times the last digit. The third digit is 3 less than the second digit and fourth digit is 4 more than the second digit. Also there are 3 pairs of digits which add up to give 11. The sum of the 5 digit number which can open the electronic lock of the safe is _______.

Question 19

In a cricket match, five batsmen A, B, C, D and E scored an average of 36 runs. D scored 5 more than E; E scored 8 fewer than A; B scored as many as D and E combined; and B and C scored 107 between them. The runs scored by E are______

Question 20

A man can row 100 km upstream and 144 km downstream in 18 hours. He can also row 140 km upstream and 180 km downstream in 24 hours. The rate of current is ________ km/hr.

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ESE & GATE EE General

May 25ESE & GATE EE