Mathematics GATE CS and IT previous year questions with Answer

Ques 51 GATE 2015 SET-2

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Let X and Y denote the sets containing 2 and 20 distinct objects respectively and F denote the set of all possible functions defined from X to Y. Let f be randomly chosen from F. The probability of f being one-to-one is _______.

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Ques 52 GATE 2015 SET-1

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Given Set A = {2, 3, 4, 5} and Set B = {11, 12, 13, 14, 15}, two numbers are randomly selected, one from each set. What is the probability that the sum of the two numbers equals 16?

A

0.20

B

0.25

C

0.30

D

0.33

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Ques 53 GATE 2015 SET-1

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The probabilities that a student passes in Mathematics, Physics and Chemistry are m, p, and c respectively. Of these subjects, the student has 75% chance of passing in at least one, a 50% chance of passing in at least two and a 40% chance of passing in exactly two. Following relations are drawn in m, p, c:
(I) p + m + c = 27/20
(II) p + m + c = 13/20
(III) (p) x (m) x (c) = 1/10
(A) Only relation I is true.
(B) Only relation II is true.
(C) Relations II and III are true.
(D) Relations I and III are true.

A

A

B

B

C

C

D

D

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Ques 54 GATE 2015 SET-1

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The number of students in a class who have answered correctly, wrongly, or not attempted each question in an exam, are listed in the table below. The marks for each question are also listed. There is no negative or partial marking.

What is the average of the marks obtained by the class in the examination?

A

2.290

B

2.970

C

6.795

D

8.795

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Ques 55 GATE 2015 SET-1

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If g(x) = 1 - x and h(x) = x / (x - 1), then g(h(x)) / h(g(x)) is:

A

h(x) / g(x)

B

-1 / x

C

g(x) / h(x)

D

x / (1 - x)²

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Ques 56 GATE 2015 SET-1

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lim_{x → ∞} x^1/x is

A

0^∞

B

0

C

1

D

Not defined

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Ques 57 GATE 2015 SET-1

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In the LU decomposition of the matrix

, if diagonal elements of U are both 1, then the lower diagonal entry l₂₂ of L is _______.

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Ques 58 GATE 2015 SET-1

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∑_x=1^∞ 1 / (x(x+1)) = _______.

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Ques 59 GATE 2015 SET-1

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Suppose L = {p, q, r, s, t} is a lattice represented by the following Hasse diagram:

For any x, y ∈ L, not necessarily distinct, x ∨ y and x ∧ y are join and meet of x, y, respectively. Let L³ = {(x, y, z): x, y, z ∈ L} be the set of all ordered triplets of the elements of L. Let p_r be the probability that an element (x, y, z) ∈ L³ chosen equiprobably satisfies x ∨ (y ∧ z) = (x ∨ y) ∧ (x ∨ z). Then

A

p_r = 0

B

p_r = 1

C

0 < p_r ≤ 1/5

D

1/5 < p_r < 1

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Ques 60 GATE 2015 SET-1

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∫_1/π^2/π cos(1/x) / x² dx = _______.

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