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GATE 2021 : Toppers Weekly Maths Quiz 1 (App update required to attempt this test)

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Question 1

The boundary will value problem y′′ + λy = 0. y′(0) = y(π) = 0 will have non-zero solutions if the values of λ are

Question 2

What will be the value of the following integral

Question 3

A real valued continuous time x(t) has a fundamental period T = 8. The non-zero Fourier series coefficients for x(t) are:

Question 4

Given a two-variable function v = 2xy, where x and y are independent variables, determine the corresponding analytic function f(z) =u + iv is

Question 5

The solution of

with initial value y(0) = ½ is bounded in the interval:

Question 6

Let X be a random variable with probability density function

The probability p(0.5<x<5) is ________

Question 7

In eight throws of a dice, 5 (or) 6 is considered as a success then standard deviation of success is

Question 8

Given that u = x ⋅ log(xy), where x³ + y³ + 3xy = 1, then

is equal to

Question 9

Find the absolute minimum value of a function, f(x) = 2x³ – 15x² + 36x + 1 in the interval [1, 5].

Question 10

The partial differential equation

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Nov 16ESE & GATE EE