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GATE CSE 2020 National Champion Quiz: Engg. Mathematics (App update required to attempt this test)

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Question 1

Find the value of the following limit : _______________

Question 2

If and then the constants R and S are, respectively

Question 3

Consider the following function

Find the points at which f has absolute minimum and absolute maximum repectively.

Question 4

A function f(x) is continuous in the interval [0,2]. It is known that f(0) = f(2) = -1 and f(1) = 1. Which one of the following statements must be true?

Question 5

If A is 3 × 3 matrix, whose elements are given by aij = i2 – j2 where 1 ≤ i, j ≤ 3 then  = _____

Question 6

If the system of equations
x – ky – z = 0, kx – y – z = 0, x + y – z = 0 has a non-zero solution, then the possible values of k are: ‘–a’ and ‘b’ then a + b = _______.

Question 7

Find the value of the determinant of A.

Question 8

For any discrete random variable X, with probability mass function
and define the polynomial function
For a certain discrete random variable Y, there exists a scalar such that The expectation of Y is

Question 9

Let X be an exponential random variable with rate parameter.Then find variance of X.

Question 10

Consider a company that assembles computers. The probability of a faulty assembly of any computer is p. The company therefore subjects each computer to a testing process. This testing process gives the correct result for any computer with a probability of q. What is the probability of a computer being declared faulty?

Question 11

If the difference between the expectation of the square of a random variable  and the square of the expectation of the random variable is denoted by R,  , then

Question 12

Which one of the following random variable is discrete?
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