Important Questions of Relations and Functions Mathematics | Zigya

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 Multiple Choice QuestionsMultiple Choice Questions

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321.

Let f : R  R be defined by

fx = x +2, x  - 1x2,   - 1 < x < 12 - x, x  1

Then, the value of f(- 1.75) + f(0.5) + f(1.5) is

  • 0

  • 1

  • 2

  • - 1


322.

Two functions f : R  R, g : R  R are defined as follows

fx = 0, x is rational1, x is irationalgx = - 1, x is rational0,     x is irrational

Then, (fog) π + (gof) (e) is equal to

  • 0

  • - 1

  • 2

  • 1


323.

If the functions f and g are defined by f(x) = 3x - 4, g(x) = 2 + 3x for x  R respective, then g-1(f-1(5)) is equal to

  • 1

  • 12

  • 13

  • 14


324.

The least number among 43, 54, 74, 83

  • 83

  • 74

  • 43

  •  54


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325.

The function f: R  R is defined by f(x)=3- x. Observe the following statements
of it
I. f is one-one
II. f is onto
III. f is a decreasing function
Out of these, true statement are

  • Only I, II

  • Only II, III

  • Only I, III

  • I, II, III


326.

If : RC is defined by f(x) =eix for x ∈ R, then f is (whereC denotes the set of all complex numbers)

  • one-one

  • onto

  • one-one and onto

  • neither one-one nor onto


327.

If f(x) = 2x4 - 13x2 + ax + b is divisible by x2 - 3x + 2, then (a, b) is equal to

  • (- 9, - 2)

  • (6, 4)

  • (9, 2)

  • (2, 9)


328.

A binary sequence is an array of O's and 1's. The number of n-digit binary sequences which contain even number of 0's is

  • 2n - 1

  • 2n - 1

  • 2n - 1 - 1n

  • 2n


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 Multiple Choice QuestionsMatch The Following

329.

Let R denote the set of all real numbers and RT denote the set of all positive real numbers. For the subsets A and B of R define f : A B by f(x) = x2 for x  A. Observe the two lists given below
       
A f is one-one and onto, 1. A = R, B = R
If
1 A = R+, B = R
B f is one-one but not
onto, If
2 A = B = R
f is onto but not
one-one, if
3 A = R, B = R+
D f is neither one-one
nor onto If
4 A = B + R+

 

A. A B C D (i) 1 2 3 4
B. A B C D (ii) 4 2 1 3
C. A B C D (iii) 4 1 3 2
D. A B C D (iv) 4 2 1 3

 Multiple Choice QuestionsMultiple Choice Questions

330.

If f : R  R2 and g : R  R are such that g{f(x)} = sin(x)and f{g(x)} = (sin x)2, then a possible choice for f and g is

  • f(x) = x2, g(x) = sinx

  • fx = sinx, gx = x

  • fx = sin2x, gx = x

  • f(x) = x2, g(x) = x 


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