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# Gate 2021 : Toppers Weekly Quiz 4 (App update required to attempt this test)

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Question 1

The determinant of matrix A is 5 and the determinant of matrix B is 40. The determinant of matrix AB is ________.

Question 2

Consider the matrix , if the inverse of matrix is  then value of λ2 - λ1 is _______.

Question 3

The price of sugar is decreased by 20%, then find the % change in the consumption, so that the expense only increases by 10%?

Question 4

Shahid says that his age is 4 years more than thrice the age of his daughter. Meera says that her age is 7 years more than the average age of Shahid and his daughter. What is the average age of all the three, two years from now if the difference between the age of Shahid and that of Meera is 7 years?

Question 5

A can paint a house in 55 days and B can do it in 66 days. Along with C, they did the job in 12 days only. Then, C alone can do the job in how many days?

Question 6

Select the most appropriate idiom (in the context) to fill in the sentence.

To be a successful lawyer, one must know how to _______________________.

Question 7

The values of function 𝑓(x) at 5 discrete poets are given below:

using Trapezoial rule with step size or 0.1, the value or is_______

Question 8

Select the most appropriate meaning of the idiom underlined in the sentence.

I am going to stay at home because I am feeling under the weather today.

Question 9

If eigen value a matrix A is , then the eigen value of is

Question 10

The directional derivative of at in the direction of line PQ, where , is _____.

Question 11

Sandy and Mandy do (8/13)th part of a work and the rest of the work was completed by Andy. If Sandy, Mandy and Andy take the same work for Rs 2600, then what is the share (in Rs) of Andy?

Question 12

Consider an ant crawling along the curve (x-2)2 + y2 = 4, where x and y are in meters. The ant starts at the point (4, 0) and moves counter-clockwise with a speed of 1.57 meters per second. The time taken by the ant to reach the point (2, 2) is (in seconds) ________

Question 13

Find the value of limit

Question 14

A mixture contains 80% acid and rest water. Part of the mixture that should be removed and replaced by the same amount of water to make the ratio of acid and water 4 : 3 is

Question 15

A sum placed on compound interest double itself in 3 years. In how many years it will become 4 times of itself?

Question 16

The solution of the ordinary differential equation given below, with initial condition y (2) = 3, is

Question 17

P is an orthogonal matrix and A is a periodic matrix with period 4 and Q=PAPT. If PT Q2003P is equal to Aa, then the value of ‘a’ is _________.

Question 18

20 men or 24 women can complete a piece of work in 24 days. If 30 men and 12 women undertake the work, then they can complete the same work in:

Question 19

A loan of Rs. 12 lakhs were taken from bank with simple interest for as many years as the rate of interest. After loan period is over, Rs. 432000 was paid as an interest. What was the rate of interest?

Question 20

If the function
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