# GATE Mathematics Objective Questions Paper 25

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Q-1. If are the roots of , then are the roots of

(a)

(b)

(c)

(d)

Q-2. The number of real roots of the equation is

(a) 1

(b) 2

(c) 3

(d) None of these

Q-3. If S is the set containing values of x satisfying where [x] denotes GIF, then S contains

(a) (2,4)

(b) (2,4]

(c) [2,3]

(d) [2,4]

Q-4. Seven people are seated in a circle, How many relative arrangements are possible ?

(a) 7!

(b) 6!

(c)

(d)

Q-5. In how many ways can 4 people be seated on a square table, one on each side?

(a) 4!

(b) 3!

(c) 1

(d) None of these

Q-6. Four different items have to be placed in three different boxes. In how many ways can it be done such that any box can have any number of items?

(a)

(b)

(c)

(d)

Q-7. What is the probability that, if a number is randomly chosen from any 31 consecutive natural numbers. it is divisible by 5?

(a)

(b)

(c)

(d) None of these

Q-8. The mean of a binomial distribution is 5, and then its variance has to be

(a) > 5

(b) = 5

(c) < 5

(d) = 25

Q-9. If a is the single A.M. between two numbers a and b and S is the sum of n A.M.’s between them, then depends upon

(a) Depends upon

(b) n,a,b

(c) n,a

(d) n,b

Q-10. up to equal to

(a) 1

(b) 2

(c)

(d)

Q-11.The odds in favor of India winning any cricket match is 2 : 3. What is the probability that if India plays 5 matches, it wins exactly 3 of them?

(a)

(b)

(c)

(d)

Q-12. For an A.P., The value of is equall to

(a) 4

(b) 6

(c) 8

(d) 10

Q-13. 1+sin x+ then x=

(a)

(b)

(c)

(d)

Q-14.

(a)

(b) X

(c)

(d)

Q-15. The ends of a line segment are P (1, 3) and Q (1, 1). R is a point on the line segment PQ such that If R is an interior point of the parabola then

(a)

(b)

(c)

(d) None of these

Q-16. Set of values of which is true is

(a)

(b)

(c)

(d)

Q-17. The distance between the lines 3x + 4y = 9 and 6x + 8y + 15 = 0 is

(a)

(b)

(c)

(d) None of these

Q-18. Let A = (3, - 4), B(1, 2) and P -= (2k –1, 2k +1) is a variable point such that PA + PB is the minimum. Then k is

(a)

(b) 0

(c)

(d) None of these

Q-19. The length of the y-intercept made by the circle is

(a) 6

(b)

(c)

(d) 3

Q-20. If x+y=k is normal to then k=

(a) 3

(b) 6

(c) 9

(d) None of these

Q-21. T he number of values of c such that the straight line touches the curve is

(a) 0

(b) 1

(c) 2

(d) infinite

Q-22. =

(a) 1

(b)

(c)

(d)

Q-23. Locus of the point z satisfying Re is a non –zero real number, is

(a) a straight line

(b) a circle

(c) an ellipse

(d) a hyperbola

Q-24. The points of z satisfying arg lies on

(a) An arc of a circle

(b) A parabola

(c) An ellipse

(d) A straight line

Q-25. The coefficients of the term and the th term in the expansion are equal, then

(a) n = 2r

(b) n = 3r

(c) n = 2r + 1

(d) None of these

Q-26.

(a) 2e

(b) e

(c) e-1

(d) 3e

Q-27. If a = 13, b = 12, c = 5 in ∆ABC, then

(a)

(b)

(c)

(d)

Q-28.

(a)

(b)

(c)

(d)

Q-29. Two of straight lines have the equations y2 + xy –12x2 = 0 and ax2+ 2hxy +by2 = 12x2 = 0 and common among them if.

(a)

(b)

(c)

(d) Both (a) and (b)

Q-30. If circle passes through the point (3, 4) and cutes x2 + y2 = 9 orthogonally, then the locus of its centre is 3x + 4y = λ. Then λ =

(a) 11

(b) 13

(c) 17

(d) 23

Q-31. For what value of x, the matrix A is singular

(a) x=0,2

(b) x=1,2

(c) x=2,3

(d) x=0,3

Q-32. If 7 and 2 are two roots of the following equation=0, then its third root will be

(a) -9

(b) 14

(c)

(d) None of these

Q-33. Period of f(x) = sin4 x + cos4 x

(a)

(b)

(c)

(d) None of these

Q-34. The range of log n (sin x)

(a)

(b)

(c)

(d)

Q-35. is equal to

(a)

(b)

(c)

(d)

Q-36. let The value of is

(a) 0

(b) 1

(c)

(d)

Q-37. For the curve x = t2 –1, y = t2 –t tangent is parallel to x- axis where

(a)

(b)

(c)

(d)

Q-38. f(x) = x3 –6x2 + 12x –16 is strictly decreasing for

(a)

(b)

(c)

(d)

Q-39. The value of b for which the function is a strictly decreasing function is

(a)

(b)

(c)

(d)

Q-40. Maximum value of the expression 2 sin x + 4cosx + 3 is

(a)

(b)

(c)

(d) None of these

Q-41. If then the value of tan

(a) 3

(b) 2

(c) 1

(d) 0

Q-42. then is equal to

(a) 10

(b)

(c) 1

(d) -1

Q-43. If

(a)

(b)

(c)

(d) None of these

Q-44. Length of the sub tangent to the curve y is

(a)

(b) a

(c)

(d) None of these

Q-45. The value of c of mean value theorem when f(x) = x3 –3x –2 in [-2,3] is

(a)

(b)

(c)

(d)