CAT Mathematics Objective Questions Paper 25

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

(a) Equation

(b) Equation

(c) Equation

(d) Equation

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

(a) 1

(b) 2

(c) 3

(d) None of these

Q-3. If S is the set containing values of x satisfying Equation 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) Equation

(d) Equation

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) Equation

(b) Equation

(c) Equation

(d) Equation

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) Equation

(b) Equation

(c) Equation

(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 Equation depends upon

(a) Depends upon

(b) n,a,b

(c) n,a

(d) n,b

Q-10. Equation up to Equation equal to

(a) 1

(b) 2

(c) Equation

(d) Equation

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) Equation

(b) Equation

(c) Equation

(d) Equation

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

(a) 4

(b) 6

(c) 8

(d) 10

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

(a) Equation

(b) Equation

(c) Equation

(d) Equation

Q-14. Equation

Equation

(a) Equation

(b) X

(c) Equation

(d) Equation

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 Equation If R is an interior point of the parabola Equation then

(a) Equation

(b) Equation

(c) Equation

(d) None of these

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

(a) Equation

(b) Equation

(c) Equation

(d) Equation

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

(a) Equation

(b) Equation

(c) Equation

(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) Equation

(b) 0

(c) Equation

(d) None of these

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

(a) 6

(b) Equation

(c) Equation

(d) 3

Q-20. If x+y=k is normal to Equation 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 Equation touches the curve Equation is

(a) 0

(b) 1

(c) 2

(d) infinite

Q-22. Equation =

(a) 1

(b) Equation

(c) Equation

(d) Equation

Q-23. Locus of the point z satisfying Re Equation 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 Equation lies on

(a) An arc of a circle

(b) A parabola

(c) An ellipse

(d) A straight line

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

(a) n = 2r

(b) n = 3r

(c) n = 2r + 1

(d) None of these

Q-26. Equation

(a) 2e

(b) e

(c) e-1

(d) 3e

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

(a) Equation

(b) Equation

(c) Equation

(d) Equation

Q-28. Equation

(a) Equation

(b) Equation

(c) Equation

(d) Equation

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) Equation

(b) Equation

(c) Equation

(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

Equation

(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 Equation =0, then its third root will be

(a) -9

(b) 14

(c) Equation

(d) None of these

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

(a) Equation

(b) Equation

(c) Equation

(d) None of these

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

(a) Equation

(b) Equation

(c) Equation

(d) Equation

Q-35. Equation is equal to

(a) Equation

(b) Equation

(c) Equation

(d) Equation

Q-36. let Equation The value of Equation is

(a) 0

(b) 1

(c) Equation

(d) Equation

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

(a) Equation

(b) Equation

(c) Equation

(d) Equation

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

(a) Equation

(b) Equation

(c) Equation

(d) Equation

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

(a) Equation

(b) Equation

(c) Equation

(d) Equation

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

(a) Equation

(b) Equation

(c) Equation

(d) None of these

Q-41. If Equation then the value of tan Equation

(a) 3

(b) 2

(c) 1

(d) 0

Q-42. Equation then Equation is equal to

(a) 10

(b) Equation

(c) 1

(d) -1

Q-43. If Equation

(a) Equation

(b) Equation

(c) Equation

(d) None of these

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

(a) Equation

(b) a

(c) Equation

(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) Equation

(b) Equation

(c) Equation

(d) Equation