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Frequently Asked Gate Latest Exam Pattern - Gate Sample Question with Solutions Page 82

(#M40021673) GATE QUESTION MATHS Keep an EYE

Consider the following relations:
R1 (a,b) iff (a+b) is even over the set of integers
R2 (a,b) iff (a+b) is odd over the set of integers
R3 (a,b) iff a.b > 0 over the set of non-zero rational numbers
R4 (a,b) iff a + bi 2 over the set of natural numbers
Which of the following statements is correct?
(a) Ri and R2 are equivalence relations, R3 and R4 are not
(b) Ri and R3 are equivalence relations, R2 and R4 are not
(c) Ri and R4 are equivalence relations, R2 and R3 are not
(d) Ri, R2, R3 and R4 are all equivalence relations

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(#M40021671) GATE QUESTION MATHS Keep an EYE

X,Y and Z are closed intervals of unit length on the real line. The overlap of X and Y is half
a unit. The overlap of Y and Z is also half a unit. Let the overlap of X and Z be k units. Which
of the following is true?
(a) k must be 1
(b) k must be 0
(c) k can take any value between 0 and 1
(d) None of the above
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(#M40019952) GATE QUESTION PERMUTATION AND COMBINATION Keep an EYE

If A and B are two independent events such that and P(A'∩B)=2/7 and P(A∩B')=1/5, then P(A) is

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(#M40019951) GATE QUESTION PERMUTATION AND COMBINATION Keep an EYE

Let α, β and γ be the cube roots of p (p < 0). For any real numbers x, y and z, the value of (xα+yβ+zγ) ⁄(xβ+yγ+zα) is

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(#M40019950) GATE QUESTION COMPLEX NUMBERS Keep an EYE

The number of roots of equations z15 = 1 and Iarg zI< π/2 is

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(#M40019949) GATE QUESTION STRAIGHT LINES Keep an EYE

show that line perpendicular to x-axis and a line perpendecular to y-axis having slope multipication -1

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(#M40019948) GATE QUESTION APPLICATION OF DIFFERENTIATION Keep an EYE

f(x+y) = f(x) + f(y) + 2xy - 1 " x,y. f is differentiable and f'(0) = cos a. Prove that f(x) > 0 " x Î R.

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(#M40019947) GATE QUESTION CONICS Keep an EYE

The radius of the largest circle, which passes through the focus of the parabola y^2=4(x+y) and contained in it is ???

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(#M40019945) GATE QUESTION PERMUTATION AND COMBINATION Keep an EYE

Let a number n have its base -7 representation as n= 1223334444. the highest power of 7, that divides the number n! is

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(#M40019944) GATE QUESTION TRIGONOMETRY Keep an EYE

if x,y,z are acute and cos x= tan y , cos y = tanz , cos z = tan x, then the value of sin x is ;

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