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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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(#M40021683) GATE QUESTION SET THEORY Keep an EYE

The inclusion of which of the following sets into
S {{i, 2} , {1, 2, 3}, {1, 3, 5} , {1, 2, 4} , {1, 2,3,4, 5}}
is necessary and sufficient to make S a complete lattice under the partial order
defined by set containment?
(a) {1}
(b) {1},{2,3}
(c) {1},{1,3}
(d) {1},{1,3},{1,2,3,4},{1,2,3,5}

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(#M40021682) GATE QUESTION MATHS Keep an EYE

A and B are the only two stations on an Ethernet. Each has a steady queue of frames to
send. Both A and B attempt to transmit a frame, collide, and A wins the first backoff race. At
the end of this successful transmission by A, both A and B attempt to transmit and collide. The
probability that A wins the second backoff
race is
(a) 0.5
(b) 0.625
(c) 0.75
(d) 1.0

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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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(#M40021678) GATE QUESTION MATHS Keep an EYE

The minimum number of colours required to colour the vertices of a cycle with n nodes in
such a way that no two adjacent nodes have the same colour is
(a) 2
(b) 3
(c) 4
(d) n_2[+2

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(#M40021677) GATE QUESTION MATHS Keep an EYE

The trapezoidal rule for integration gives exact result when the integrand is a polynomial
of degree
(a) 0 but not 1
(b) 1 but not 0
(c) 0 or 1
(d) 2

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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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(#M40021675) GATE QUESTION MATHS Keep an EYE

How many 4-digit even numbers have all 4 digits distinct?
(a) 2240
(b) 2296
(c) 2620
(d) 4536

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