Important Questions of Sets Mathematics | Zigya

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21.

Let A and B be two non-empty sets having n elements in common. Then, the number of elements common to A x B and B x A is

  • 2n

  • n

  • n2

  • None of these


22.

If a set A contains n elements, then which of the following. cannot be the number of reflexive relations on the set A?

  • 2n + 1

  • 2n - 1

  • 2n

  • 2n2 - 1


23.

If A and B be two sets such that A x B consists of 6 elements. If three elements A x B are (1, 4), (2, 6) and (3, 6), find B x A.

  • {(1, 4), (1, 6), (2, 4), (2, 6), (3, 4), (3, 6)}

  • {(4, 1), (4, 2), (4, 3), (6, 1), (6, 2), (6, 3)}

  • {(4, 4), (6, 6)}

  • {(4, 1), (6, 2), (6, 3)}


24.

If f (x) = log10x2. The set of all values of x for which f(x) is real, is

  • [- 1, 1]

  • [1, )

  • (- , - 1]

  • (- , - 1]  [1, )


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25.

The solution set contained in R of the inequation

3 + 31 - x - 4 < 0, is:

  • (1, 3)

  • (0, 1)

  • (1, 2)

  • (0, 2)


26.

If f(x) = x, if - 3 < x  - 1x, if - 1 < x <1x,   if 1  x < 3 then the set x : fx  0 is equal to

  • (- 1, 3)

  • [- 1, 3)

  • (- 1, 3]

  • [- 1, 3)


27.

x  R : x - x = 5 is equal to

  • R, the set of all real numbers

  • ϕ, the empty set

  • x  x < 0

  • x  R : x  0


28.

If N denotes the set of all positive integers and if f : N  N efined by f(n) = the sum of positive divisors of n then, f(2k, 3), where k is a positive integers, is

  • 2k + 1 - 1

  • 2(2k + 1 - 1)

  • 3(2k + 1 - 1)

  • 4(2k + 1 - 1)


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29.

If f : R  R is defined by f(x)=x - [ x] - 12 for x  R, where [x] is the greatest mteger not exceeding x, then x  R : fx = 12 is equal to :

  • Z, the set of all integers

  • N, the set of all natural numbers

  • ϕ, the empty set

  • R


30.

If Q denotes the set of all rational numbers and fpq = p2 - q2 for any pq  Q, then observe the following statements.I. fpq is real for each pq  QII. fpq is  a complex number for each  pq  Q.Which of the following is correct ?

  • Both I and II are true

  • I is true, II is false

  • I is false, II is true

  • Both I and II are false


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