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Gate Latest Exam Pattern - Gate Sample Question with Solutions Page 74

(#M40021696) GATE QUESTION MATHS Keep an EYE

The set {1,2,3,5,7,8,91 under multiplication modulo 10 is not a group. Given
below are four plausible reasons. Which one of them is false?
(A) It is not closed
(B) 2 does not have an inverse
(C) 3 does not have an inverse
(D) 8 does not have an inverse

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(#M40021693) GATE QUESTION MATHS Keep an EYE

A random bit string of length n is constructed by tossing a fair coin n times and setting a
bit to 0 or 1 depending on outcomes head and tail, respectively. The probability that two such
randomly generated strings are not identical is:

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(#M40021692) GATE QUESTION MATHS Keep an EYE

What are the eigen values of the following 2 x 2 matrix?
2 -1
-4 5
(a) -1 and 1
(b) 1 and 6
(C) 2 and 5
(d) 4 and -1

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(#M40021690) GATE QUESTION MATHS Keep an EYE

Consider three decision problems P1,P2 and P3. It is known that P1 is decidable and P2 is undecidable. Which one of the following is TRUE?
option
(a) P3 is decidable if P is reducible to P3
(b) P3 is undecidable if P3 is reducible to P2
(c) P3 is undecidable if P2 is reducible to P3
(d) P3 is decidable if P3 is reducible to P2 ‘s complement

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(#M40021691) GATE QUESTION MATHS Keep an EYE

Consider the set H of all 3 x 3 matrices of the type
a f e
O b d
O O c
where a,b,c,d,e and f are real numbers and abcO. under the matrix
multiplication operation, the set H is:
option
(a) a group
(b) a monoid but not a group
(c) a semi group but not a monoid
(d) neither a group nor a semi group

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(#M40021689) GATE QUESTION MATHS Keep an EYE

What is the minimum number of ordered pairs of non-negative numbers that should be
chosen to ensure that there are two pairs (a,b) and (c,d) in the chosen set such that ac mod
3andbd mod 5
(a) 4
(b) 6
(c) 16
(d) 24

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(#M40021688) GATE QUESTION MATHS Keep an EYE

Let P, Q and R be tree atomic prepositional assertions. Let X denote (P v Q) - R and Y
denote (P - R) v (Q - R). which one of the following is a tautology?
(a) XY
(b) X-Y
(c) Y-X
(d) 1-YX

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(#M40021687) GATE QUESTION MATHS Keep an EYE

The hexadecimal representation of 6578 is:
(a) 1AF
(b) D78
(c) D71
(d) 32F

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(#M40021686) GATE QUESTION MATHS Keep an EYE

The range of integers that system is:
(a) _2?_1 to (2_1 - i)
(c) _2?_1 to 2?_1

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(#M40021685) GATE QUESTION MATHS Keep an EYE

The set {1, 2, 4, 7, 8, 11, 13, 14} is a group under multiplication modulo 15. the inverses
of 4 and 7 are respectively:
(a) 3 and 13
(b) 2 and 11
(c) 4 and 13
(d) 8 and 14

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