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] ?

A

Ⅲ only

B

Ⅱ only

C

Ⅱ and Ⅲ only

D

Ⅰ and Ⅲ only



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.

I. X is invertible
II. Determinant of X is non-zero


Which one of the following is TRUE?

A

I implies II; II does not imply I

B

II implies I; I does not imply II

C

I does not imply II; II does not imply I

D

I and II are equivalent statements



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:

A

571244

B

736251

C

571247

D

136251



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 ?

A

2

B

1

C

1/2

D

-1/2



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.