Important Questions of Relations and Functions Mathematics | Zigya

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31.

Let f : [- 6, 6]  R be defined by f(x) = x2 - 3.

Consider the following :

I. (f o f o f)( - 1) = (f o f o f)(1)

2. (f o f o f)( - 1) - 4(f o f o f)(1) = (f o f)(0)

Which of the above is/are correct ?

  • 1 only

  • 2 only

  • both 1 and 2

  • neither 1 nor 2


32.

Let f(x) = px + q and g(x) = mx + n. Then f(g(x)) = g(f(x)) is equivalent to

  • f(p) = g(m)

  • f(q) = g(n)

  • f(n) = g(q)

  • f(m) = g(p)


33.

Let fa = a - 1a + 1

Consider the following :

1. f2a = fa + 12. f1a = - fa

Which of the above is/are correct ?

  • 1 only

  • 2 only

  • both 1 and 2

  • beither 1 nor 2


34.

Which one of the following functions is neither even nor odd ?

  • x2 - 1

  • x + 3x

  • x

  • x2(x - 3)


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35.

The remainder and the quotient of the binary division (101110)2 : (110)2, are respectively :

  • 1112 and 1002

  • 1002 and 1112

  • 1012 and 1012

  • 1002 and 1002


36.

If we define a relation R on the set N x N as (a, b) R(c, d)  a + d = b + c for all (a, b), (c, d)  N x N, then the relation is :

  • symmetric only

  • symmetric and transitive only

  • equivalence relation

  • reflexive only


37.

The inverse of the function y - 5ln(x) is :

  • x = y1ln5, y > 0

  • x = yln5, y > 0

  • x = y1ln5, y< 0

  • x = 5lny, y > 0


38.

A function is defined in (0, ) by : 

fx = 1 - x2                   for 0< x  1lnx                       for 1 < x  2ln2 - 1 + 0.5x for 2 < x < 

Which one of the following is correct in respect of the derivative of the function, i.e., f'(x) ?

  • f'(x) = 2x for 0 < x  1

  • f'(x) = - 2x for 0 < x  1

  • f'x = - 2x for 0 < x 1

  • f'x = 0 for 0 < x < 


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39.

The function f (x) = x - x3 is : 

  • odd

  • even

  • both even and odd

  • neither even nor odd


40.

The maximum value of lnxx is :

  • e

  • 1e

  • 2e

  • 1


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