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Frequently Asked Gate Latest Exam Pattern - Gate Sample Question with Solutions Page 81

(#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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(#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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(#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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(#M40021684) GATE QUESTION MATHS Keep an EYE

Let f(x) be the continuous probability density function of a random variable X. the
probability that a < X < b, is:
(c) ff(x)dx
(d) fxf(x)dx

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(#M40021681) GATE QUESTION MATHS Keep an EYE

What is the result of evaluating the following two expressions using three-digit floating point arithmetic with rounding?
(113.+111.)+ 7.51
113.+(111.+ 7.51)
(a) 9.51 and 10.0 respectively
(b) 10.0 and 9.51 respectively
(c) 9.51 and 9.51 respectively
(d) 10.0 and 10.0 respectively.

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(#M40021680) GATE QUESTION MATHS Keep an EYE

In how many ways can a given positive integer n 3 be expressed as the sum of 3 positive
integers (which are not necessarily distinct). For example, for n = 4, the number of ways is 3,i.e., 1+2+1, 2+1+1. Give only the answer without any explanation.

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(#M40021679) GATE QUESTION MATHS Keep an EYE

In how many ways can a given positive integer n 2 be expressed as the sum of 2 positive integers (which are not necessarily distinct). For example, for n = 3, the number of ways is 2, i.e., 1+2, 2+1. Give ANSWER??

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(#M40021676) GATE QUESTION MATHS Keep an EYE

Let f: A - B be a function, and let E and F be subsets of A. Consider the following
statements about images.
Si:f(EuF)=f(E) uf(F)
S2:f(EnF)=f(E) nf(F)
Which of the following is true about Si and S2?
(a) Only Si is correct
(b) Only S2 is correct
(c) Both Si and S2 are correct
(d) None of Si and S2 is correct

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(#M40021674) GATE QUESTION MATHS Keep an EYE

Consider two well-formed formulas in prepositional logic
El: P - iP
E2: (Pi - iP)v(--iPiP)
Which of the following statements is correct?
(a) Fl is satisfiable, F2 is valid
(b) Fl unsatisfiable, F2 is satisfiable
(c) Fl is unsatisfiable, F2 is valid
(d) Fl and F2 are both satisfiable

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