# ACT Mathematics Objective Questions Paper 23

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Q-1. The number of surjections from A = {1,2,…n), onto B=(a, b) is

(a)

(b)

(c)

(d) none of these

Q-2. Set A has 3 elements and set B has 4 elements. The number of injection that can be defined from A to B is

(a) 144

(b) 12

(c) 24

(d) 64

Q-3. is a function defined by f(x) = 10x-7. if then g(x) =

(a)

(b)

(c)

(d)

Q-4. The number of objective function from set A to itself when A contains 106 elements is

(a) 106

(b)

(c)

(d)

Q-5. f(x) = |sin x| has an inverse if its domain is

(a)

(b) (c)

(d) none

Q-6. If the area of the triangle formed by points z, iz and z+iz is 50 square units, then |z| is

(a) 5

(b) 10

(c) 15

(d) none of these

Q-7. if area of triangle on plane turned by number z,then |z| is

(a) 4

(b) 2

(c) 6

(d) 3

Q-8. The locus of point z satisfying when k is a non-real real number is

(a) Straight line

(b) A circle

(c) An ellipse

(d) A hyperbola

Q-9. The locus of point z satisfying is

(a) Point of straight lines

(b) Circle

(c) Hyperbola

(d) None of these

Q-10. If are in G.P with common ratio r, then value of holds if

(a)

(b)

(c) r < 3 or r < 1

(d) none of these

Q-11 Let a,b,c be in A.P. and |a| <1,|b| <1, |c| <1.

If

Then x,y,z are in

(a)

(b)

(c)

(d)

Q-12. Let denotes set of values of x.

If

(a)

(b)

(c)

(d)

Q-13. If and are in G.P. then x is equal to

(a)

(b)

(c)

(d)

Q-14. IF has integral roots ,then values of a are

(a) 10,8

(b) 12,10

(c) 12,8

(d) none

Q-15. If has equal roots, then p is equal to

(a) 0

(b) 2

(c)

(d) None

Q-16. The value of a for which and have atleast one root, in common are

(a) 0,

(b)

(c)

(d)

Q-17. There are m copies of each n different books in libaray. The number of ways in which one or more than one book can be selected as

(a)

(b)

(c)

(d)

Q-18. The number of ways in which one or more balls. can be selected out of 10 white, 9 green and 7 blues balls, is

(a) 892

(b) 881

(c) 891

(d) 879

Q-19. The number of all 3 elements subsets of det which contains is

(a)

(b)

(c)

(d) None of these

Q-20. The number of terms which are free from radical signs in expansion is

(a) 5

(b) 6

(c) 7

(d) None of these

Q-21. If sum of coefficient of is 4096, then greatest coefficient is

(a) 924

(b) 792

(c) 1594

(d) None of these

Q-22. term in the expansion of x>1 is 1000, then x is

(a) 100

(b) 1000

(c) 1

(d)

Q-23. If A is square matrix of order n, then adj (adj A) is equal to

(a)

(b)

(c)

(d)

Q-24. If A is singular, then A adj A is matrix

(a) Identify

(b) Null

(c) Scalar

(d) None of these

Q-25. If and then equals

(a)

(b)

(c)

(d) None of these

Q-26. If = (x-y)(y-z)(z-x) then n equals

(a) 1

(b) -1

(c) 2

(d) -2

Q-27. The orthocenter of the triangle formed by lines xy=0 and x+y=1 is

(a)

(b)

(c) (0, 0)

(d)

Q-28. The area of figure formed by is

(a)

(b)

(c)

(d) None of these

Q-29. The equation represent pair of lines if

(a)

(b)

(c)

(d) None of these

Q-30. If an equilatual triangle is inscribed in circle then length of each side is

(a)

(b)

(c) a

(d) None of these

Q-31. The lotus rectum of parabola whose focal chord is P S Q is such that SP=3 and SQ=2 is given by

(a)

(b)

(c)

(d) None of these

Q-32. Find c such that straight line touches curve is

(a) 0

(b) 3

(c) 2

(d) Infinite

Q-33. The eccentricity of the conic represented by

(a) 1

(b)

(c) 2

(d)

Q-34. If f(x+2y, x-2y)=xy, then f(x, y) equal

(a)

(b)

(c)

(d)

Q-35. The period of f(x) =

(a)

(b)

(c)

(d) None of these

Q-36. is equal to

(a) 3

(b) 4

(c) 1

(d) 2

Q-37. is equal to

(a)

(b)

(c) e

(d) 1

Q-38. If is differentiable on

(a) [-1,1]

(b) R-[-1,1]

(c) R-(-1,1)

(d) None of these

Q-39. If is continuous, then

(a)

(b)

(c)

(d) None of these

Q-40. If equals

(a)

(b)

(c)

(d) None of these