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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.
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⎪ = _______.
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
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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