Mathematics GATE CS and IT previous year questions with Answer
Ques 21 Gate 2020
Consider the functions
I. e-x
II. x2 - sin x
III. √x^3+1
Which of the above functions is/are increasing everywhere in [0, 1] ?
Ques 22 Gate 2020
For n>2, let a∈{0, 1}n be a non-zero vector. Suppose that x is chosen uniformly at random from {0,1}n. Then, the probability that Σi=1i=n aixi is an odd number is _________
0.50 is the correct answer.
Ques 23 Gate 2019
Let X be a square matrix. Consider the following two statements on X.
II. Determinant of X is non-zero
Which one of the following is TRUE?
Ques 24 Gate 2019
Suppose Y is distributed uniformly in the open interval (1, 6). The probability that the polynomial 3x2 + 6xY + 3Y + 6 has only real roots is (rounded off to 1 decimal place) _________.
0.80 is the correct answer.
Ques 25 Gate 2017 Set-2
Consider a quadratic equation x2 - 13x + 36 = 0 with coefficients in a base b. The solutions of this equation in the same base b are x = 5 and x = 6. Then b = ______.
a is the correct answer.
Ques 26 Gate 2017 Set-2
The representation of the value of a 16-bit unsigned integer X in a hexadecimal number system is BCA9. The representation of the value of X in octal number system is:
Ques 27 Gate 2017 Set-1
The number of integers between 1 and 500 (both inclusive) that are divisible by 3 or 5 or 7 is ______.
271 is the correct answer.
Ques 28 Gate 2017 Set-1
Let u and v be two vectors in R2 whose Euclidean norms satisfy ||u|| = 2||v||. What is the value α such that w = u + αv bisects the angle between u and v ?
Ques 29 Gate 2017 Set-1
Let X be a Gaussian random variable with mean 0 and variance σ2. Let Y = max(X,0) where max(a,b) is the maximum of a and b. The median of Y is _____.
0 is the correct answer.
Ques 30 Gate 2016 Set-2
Suppose that the eigenvalues of matrix A are 1, 2, 4. The determinant of (A−1)T is _________.
a is the correct answer.