GATE 2021 : Toppers Weekly Quiz 3 for ESE & GATE EE Exams

Question 1

The average weight of P, Q and R is 47 kg. If the average weight of P and Q be 32.5 kg and that of Q and R be 48.5 kg, then what is the weight of Q (in kgs)?

Question 2

A bucket is filled liquid 3 part water and 5 part alcohol. How much of mixture drawn of and replaced with water so that mixture may be half water and half alcohol.

Question 3

Out of 5 women and 4 men a committee of three members is to be formed in such a way that at least one member is a women. In how many different ways can it be done?

Question 4

Direction: Study the following bar graph carefully and answer the questions that follow.
The graph given below represent the number of users of two broadband services X and Y across 5 cities A, B, C, D and E.

The number of users of brand X in city B is what percent of the number of brand Y in city E?

Question 5

Direction: Read the data carefully and answer the following questions:

Bar chart given below shows the number of citizens living in cities A and B in different years (2016, 2017, 2018 and 2019).

If the number of males in city A in 2016 is 30 more than the females, then find the total citizens of city A in 2019 is what percent more or less than the number of females in 2016?

Question 6

Given that

and

, the value of A³ is

Question 7

Consider the matrix A =

. The condition on m for which the eigen values of matrix are of opposite sign ___.

Question 8

What are the eigenvalues of the following 2 x 2matrix

?

Question 9

The trace and determinant of a 2 × 2 matrix are known to be –2 and –35 respectively. Its eigenvalues are

Question 10

If

then

is

Question 11

The directional directive of 4x²y + z³ at (1, 2, 1) in the direction of

is

Question 12

The curl of vector field

(x, y, z) = x²

+ 2z

– y

is:

Question 13

The solution of the differential equation

is

Question 14

Which of the following is an integrating factor of [xdy – ydx] =

Question 15

The solution of differential equation

is

Question 16

The modulus of the complex number $Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE EC-ME-17-Mar\GATE-ME-2010_files\image016.png$ is

Question 17

If the cube given below is turned twice to the right, then what will be the hidden numbers ?

Question 18

A cube is made by folding the given sheet. In the cube so formed, which of the following pairs of letters will be on opposite sides?

Question 19

In a certain code language, if the word PLATINUM is coded as AIUPLTNM, then how is the word ADVENTURE coded?

Question 20

Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(S) from the statements.

Statements:
I. Some Keyboards are laptops.
II. Some keyboards are not black.

Conclusions:
I. Some laptops are black.
II. No black is a laptop.