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GATE 2021: Topper's Weekly Quiz-4 (App update required to attempt this test)

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Question 1

In a family, there are total consumption of 35 kg wheat and 12 kg of sugar every month. If the price of sugar is  more than that of wheat. And if he spends total Rs. 765 on the wheat and sugar every month. If the price of sugar in increased by %. Find the percentage of reduction on the wheat consumption so the expenditure remains the same.

Question 2

Direction: A statement with one blank is given below. Choose the set of words from the given options which can be used to fill the given blank.

Despite almost ubiquitous scepticism, the electoral bonds have prevailed and, that too, almost solely _________________ rhetorical claims of “transparency of political funding system,” “clean money,” and “donor’s anonymity.”

i. with the backing of the ruling government’s

ii. based on the endorsement derived from the political party at power’s

iii. backed by the political party at power’s

Question 3

Which letter—cluster will replace the question mark (?) in the following series?

HQCF, MVHK, JSEH, OXJM, ?

Question 4

Three different positions of the same dice are shown. Which symbol will be on the face opposite to the one having ‘*’?


Question 5

In the following diagram, the triangle represents 'Dentists‘, the circle represents 'Professors' and the rectangle represents ‘Doctors’. The numbers in different segments show the number of persons.


How many professors are dentists but not doctors?

Question 6

A, B and C can complete a work in 20, 25 and 45 days respectively. They started the work together and A left 4 days before the completion of the work and B left 3 days before the completion of work. Find the total no. of days for the work to be completed.

Question 7

is

Question 8

The Laplace transform of a function is given by 

Question 9

Matrix B = has a eigen vectors as . Find the corresponding eigen values for the given eigen vectors.

Question 10

A dice is rolled once, If odd number comes then the probability that it is prime is

Question 11

The value of the function  is _________.

Question 12

From the solution to the initial value problem:. If y(1) =1 then pick the closest estimate of y(2).

Question 13

Manali invested certain amount in three different schemes A, B and C at the rate of interest 10% p.a., 15% p.a., 18% p.a. respectively. If total interest at the end of one year was Rs. 3720 and the amount invested in scheme A was 150% of the amount invested in scheme B and 220% of the amount invested in scheme C. What was the amount invested in Scheme B?

Question 14

The table shows the production of different types of cars (in thousands).

The total production of type B cars in 2015 and type D cars 2016 is what percent less than the total production of type E cars in five years?

Question 15

In a class, the average weight of five students increased by 3 kg when a new student comes in place of one of them weighing 41 kg. Find the weight of the new student.

Question 16

Pointing to a man, Pallavi said, “he is married to my cousin’s mother Natasha". How is Natasha related to Pallavi?

Question 17

Find the Solution of the differential equation y``+4y`+13y=0, y (0) = 0; y`(0) =1

Question 18

For a continuous random variable X having the pdf f(x) given by

. what will be the median of the random variable X .

Question 19

The formula of density of a gas is defined by , where  density,  mass,  Volume. Find the percentage change in density if the mass is increased by 35% and volume is decreased by 20%.

Question 20

The ratio of present ages of Vijay and Prashant is 8 : 9. The ratio of their ages before 6 years was 13 : 15. Find the ratio of their ages of 12 years from now.
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Sep 19ESE & GATE EC