Explore topic-wise MCQs in Graduate Aptitude Test (GATE).

This section includes 67 Mcqs, each offering curated multiple-choice questions to sharpen your Graduate Aptitude Test (GATE) knowledge and support exam preparation. Choose a topic below to get started.

51.

 What would be the probability of an event ‘G’ if H denotes its complement, according to the axioms of probability?
A. P (G) = 1 / P (H)
B. P (G) = 1 – P (H)
C. P (G) = 1 + P (H)
D. P (G) = P (H)
Answer» C. P (G) = 1 + P (H)
Discussion
52.

When do the conditional density functions get converted into the marginally density functions ?
A. Only if random variables exhibit statistical dependency
B. Only if random variables exhibit statistical independency
C. Only if random variables exhibit deviation from its mean value
D. If random variables do not exhibit deviation from its mean value
Answer» C. Only if random variables exhibit deviation from its mean value
Discussion
53.

Which of the following mentioned standard Probability density functions is applicable to discrete Random Variables ?
A. Gaussian Distribution
B. Poisson Distribution
C. Rayleigh Distribution
D. Exponential Distribution
Answer» C. Rayleigh Distribution
Discussion
54.

 

Find the critical points of the function
A. (0,0)
B. (0,-90)
C. (90, 0)
D. None exist
Answer» E.
Discussion
55.

Consider the vertical cone. The minimum value of the function in the region f(x,y) = c is
A. constant
B. 1
C. 0
D. -1
Answer» B. 1
Discussion
56.

 let s(1) be the set of all critical points of f1(x, y) = g1(x).g2(y) and s(2) be the set of critical points of f2(g1(x), g2(y)) Which of the following is the right relation between s(1) and s(2), given that minimum number of elements in s(1) is 2.
A. s(1) = s(2)
B. s(1) ≠ s(2)
C. s(1) ∩ s(2) ≠ 0
D. depends on the functions
Answer» C. s(1) ∩ s(2) ≠ 0
Discussion
57.

A man travelling onf(x, y) = sin(xy). His shadow passing through the origin in a straight line (sun travels with him overhead).
What is the slope of the line travelling on which would lead him to the lowest elevation.
A. There isn’t such a line
B. 1
C. -1
D. 0
Answer» B. 1
Discussion
58.

The point (0,0) in the domain of f(x, y) = sin(xy) is a point of
A. Saddle
B. Minima
C. Maxima
D. Constant
Answer» E.
Discussion
59.

 The gradient of a function is parallel to the velocity vector of the level curve
A. True
B. False
Answer» C.
Discussion
60.

 Given that limit exists 
A. 99
B. 0
C. 1
D. 100
Answer» D. 100
Discussion
61.

Given that limit exists find 
A. ∞
B. 0
C. 1
D. ln(4⁄5)
Answer» B. 0
Discussion
62.

. Given that limit exists find 
A. 1
B. 1⁄2
C. 1⁄7
D. 2⁄7
Answer» E.
Discussion
63.

The curvature of a circle depends inversely upon its radius r
A. True
B. False
Answer» B. False
Discussion
64.

 The curvature of a function f(x) is zero. Which of the following functions could be f(x)
A. ax + b
B. ax+ bx + c
C. sin(x)
D. cos(x)
Answer» B. ax+ bx + c
Discussion
65.

Evaluate 
A. 1⁄4
B. 1⁄3
C. 1⁄2
D. 1
Answer» D. 1
Discussion
66.

Find n for which  , has non zero value.
A. >=1
B. >=2
C. <=2
D. ~2
Answer» C. <=2
Discussion
67.

 
A. True
B. False
Answer» B. False
Discussion