Engineering mathematics GATE CS PYQ Quiz

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Question 1

Consider a random variable X that takes values +1 and −1 with probability 0.5 each. The values of the cumulative distribution function F(x) at x = −1 and +1 are

  • 0 and 0.5

  • 0 and 1

  • 0.5 and 1

  • 0.25 and 0.75

Question 2

Suppose a fair six-sided die is rolled once. If the value on the die is 1, 2, or 3, the die is rolled a second time. What is the probability that the sum total of values that turn up is at least 6?

  • 10/21

  • 5/12

  • 2/3

  • 1/6

Question 3

Consider the function f(x) = sin(x) in the interval [π/4, 7π/4]. The number and location(s) of the local minima of this function are

  • One, at π/2

  • One, at 3π/2

  • Two, at π/2 and 3π/2

  • Two, at π/4 and 3π/2

Question 4

A class of 24 students occupies a classroom containing 4 rows of seats, with 7 seats in each row. If the students seat themselves randomly, what is the probability that the 5th seat in the 4th row is empty?

  • 1/7

  • 1/6

  • 1/2

  • 1/5

Question 5

In a permutation a1.....an of n distinct integers, an inversion is a pair (ai, aj) such that i < j and ai > aj. If all permutations are equally likely, what is the expected number of inversions in a randomly chosen permutation of 1.....n ?

  • n(n - 1)/2

  • n(n - 1)/4

  • n(n + 1)/4

  • 2n[log2 n]

Question 6

Consider an undirected random graph of eight vertices. The probability that there is an edge between a pair of vertices is 1/2. What is the expected number of unordered cycles of length three?
 

  • 7
     

  • 1
     

  • 1/8
     

  • 8
     

Question 7

Function f is known at the following points: 

 

gatecs201310



 

  • 9.003 
     

  • 9.017 
     

  • 8.983 
     

  • 9.045
     

Question 8

Which one of the following functions is continuous at x = 3?

  • [Tex]f(x)=\left\{\begin{array}{lll}2, & \text { if } & x=3 \\ x-1, & \text { if } & x>3 \\ \frac{x+3}{3}, & \text { if } & x<3\end{array}\right.[/Tex]

  • [Tex]f(x)=\left\{\begin{array}{lll}4, & \text { if } & x=3 \\ 8-x & \text { if } & x \neq 3\end{array}\right.[/Tex]

  • [Tex]f(x)=\left\{\begin{array}{lll}x+3, & \text { if } & x \leq 3 \\ x-4, & \text { if } & x>3\end{array}\right.[/Tex]

  • [Tex]f(x)=\frac{1}{x^3-27}, [/Tex]if x ≠ 3

Question 9

A deck of 5 cards (each carrying a distinct number from 1 to 5) is shuffled thoroughly. Two cards are then removed one at time from the deck. What is the probability that the two cards are selected with the number on the first card being one higher than the number on the second card?

  • 1/5

  • 4/25

  • 1/4

  • 2/5

Question 10

If the difference between expectation of the square of a random variable (E[X²]) and the square of the expectation of the random variable (E[X])² is denoted by R, then?

  • R = 0

  • R < 0

  • R >= 0

  • R > 0

There are 183 questions to complete.

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