NCERT Class 11-Math՚S Exemplar Chapter 1 Sets CBSE Board Problems (For CBSE, ICSE, IAS, NET, NRA 2022)

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Objective Type Questions

Choose the correct answer from the given four options in each of the Examples 14 to 16: (M. C. Q.)

Question 14:

Each set contains elements and each set contains elements and

If each element of S belong to exactly 10 of the and to exactly 4 of the , then n is

(A) 10

(B) 20

(C) 100

(D) 50

Answer:

The correct answer is (B)

Since,

But each element of S belong to exactly of the

So, are the number of distinct elements in S.

Also each element of S belong to exactly of the and each contain 2 elements. If S has n number of in it. Then

Which gives

Question 15:

Two finite sets have m and n elements respectively. The total number of subsets of first set is 56 more than the total number of subsets of the second set. The values of and respectively are.

(A) 7,6

(B) 5,1

(C) 6,3

(D) 8,7

Answer:

The correct answer is (C) .

Since, let A and B be such sets, i.e.. ,

So

Thus

Question 16:

The is equal to

(A)

(B)

(C)

(D)

Answer:

The correct choice is (A) .

Since

Fill in the blanks in Examples and :

Question 17:

If A and B are two finite sets, then is equal to ________

Answer:

Since

So

Question 18:

If A is a finite set containing n element, then number of subsets of A is ________

Answer:

State true or false for the following statements given in Examples 19 and 20.

Question 19:

Let R and S be the sets defined as follows:

Then

Answer:

False

Since 6 is divisible by both 3 and 2.

Thus