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GATE 2019: Topper's Mathematics Quiz 3 (App update required to attempt this test)

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Question 1

is a circle

and

then

Question 2

Consider the integral given as,

, what is the value of variance?

Question 3

Let

be the solution of the differential equation

with initial conditions

and

Then the value of

is_________.

Question 4

Find the value of

Question 5

Given function f(z) = z⁴ is

Question 6

Find integration of complex function

around

Question 7

Let

and

. Then

has infinitely many solutions if trace (M) is ……………………..

Question 8

Two players, A and B, alternately keep rolling a fair dice. The person to get a six first wins the game. Given that player A starts the game, the probability that A wins the game is

Question 9

For a complex number z, find the value of

Question 10

The difference between local maximum and local minimum value of

Question 11

The value of the integral is equal to

Question 12

The eigen values of the matrix given below are

Question 13

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

Question 14

Consider the following equations
3x – y – z + 2w = 0
3x + y – z – 2w = 0
12x + 3y – 4z – 6w = 0
The system of equations will be

Question 15

The maximum value of “a” such that the matrix

has three linearly independent real eigenvectos is

Question 16

The smaller angle (in degrees) between the planes x + y + z =1 and 2x – y + 2z = 0 is ________

Question 17

The matrix

has det A. = 100 and trace A=14
The value of

Question 18

Let f(z) = $Description: Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE EC 10-Mar\GATE-ECE-2015-Paper-2_files\image101.png$ . If f(z ₁) = f(z₂) for all z₁≠ z₂, a = 2, b = 4 and c = 5, then d should be equal to _______

Question 19

Find the value of the integral of

from 5 to 11 by Simpson’s

rule taking number of intervals, n=6.

[Write the answer upto two decimal point]

Question 20

If C denotes the counterclockwise unit circle, the value of the contour integral $Description: Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE EC 10-Mar\GATE-ECE-2015-Paper-2_files\image323.png$ is ______

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ESE & GATE ME Engineering Mathematics

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