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Chapter: 9th Maths : UNIT 1 : Set Language

Exercise 1.7: Multiple Choice Questions

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Exercise 1.7

Multiple Choice Questions


1. Which of the following is correct?

(1) {7}  {1,2,3,4,5,6,7,8,9,10}

(2) 7  {1,2,3,4,5,6,7,8,9,10}

(3) 7  {1,2,3,4,5,6,7,8,9,10}

(4) {7}  {1,2,3,4,5,6,7,8,9,10}

[Answer: (2)]


2. The set P = {x | x   , –1< x < 1} is a

(1) Singleton set

(2) Power set

(3) Null set

(4) Subset

Solution: P = {0}

[Answer: (1) Singleton set]


3. If U ={x | x  x < 10} and A = {x | x  , 2 ≤ x < 6} then (A) is

(1) {1, 6, 7, 8, 9}

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

(3) {2, 3, 4, 5}

(4) { }

Solution: (A') = A= {2, 3,4, 5}

[Answer: (3) {2, 3,4, 5}]


4. If B A then n(AB) is

(1) n(AB)

(2) n(B)

(3) n(B – A)

(4) n(A)

Solution: B A A∩B = B

[Answer: (2)]


5. If A = {xyz} then the number of non- empty subsets of A is

(1) 8

(2) 5

(3) 6

(4) 7

Solution: Number of non-empty subsets =2-1=8-1=7

[Answer:(4) 7]


6. Which of the following is correct?

(1)   {ab}

(2)   {ab}

(3) {a}  {ab}

(4) a  {ab}

Solution: Empty set is an improper subset

[Answer: (1)]


7. If AB = AB, then

 (1) A≠B

(2) A = B

(3) A  B

(4)BA

[Answer: (2) A=B ]


8. If B – A is B, then A∩B is

(1) A

(2) B

(3) U

(4) 

Solution: B - A = B A and B are disjoint sets.

[Answer: (4)]


9. From the adjacent diagram n[P(A∆B)] is


(1) 8

(2) 16

(3) 32

(4) 64

Solution: A Δ B = { 60, 85, 75, 90, 70}

n(A Δ B) = 5

n(P (A Δ B)) = 25 = 32

[Answer: (3) 32]


10. If n(A) = 10 and n(B) = 15, then the minimum and maximum number of elements in  B is

(1) 10,15

(2) 15,10

(3) 10,0

(4) 0,10

[Answer: (4) (0,10) ]


11. Let A = {} and B = P(A), then AB is

(1) {,{}}

(2) {}

(3) 

(4) {0}

Solution: P(A) = { Ø{Ø}}

[Answer: (2) { Ø } ]


12. In a class of 50 boys, 35 boys play Carrom and 20 boys play Chess then the number of boys play both games is

(1) 5

(2) 30

(3) 15

(4) 10.

Solution: n(AB) = n(A) + n(B) — n(A∩B) 50 = 35 + 20 — n(A∩B) n(A∩B) = 5

[Answer: (1) 5]


13. If U = {x : x   and x < 10} , A = { 1,2,3,5,8 } and B = { 2,5,6,7,9 }, then n [(A  B)′] is

(1) 1

(2) 2

(3) 4

(4) 8

Solution: U = {1, 2, 3,4, 5, 6, 7, 8, 9}

A = {1,2, 3, 5, 8}

B = {2, 5, 6, 7, 9}

AB = {1,2, 3,5, 6, 7, 8, 9}

(AB)' = {4},

n(AB)' = 1

 [Answer: (1) 1]


14. For any three sets P, Q and R, P  (Q  R) is

(1) P −(Q R)

(2) (P ∩Q)−R

(3) (P −Q)(P −R)

(4) (P −Q)∩(P −R)

Solution: P-(Q∩R) = (P-Q)(P-R)

[Answer: (3) (P-Q)(P-R)]


15. Which of the following is true?

(1) A−B =A∩B

(2) A−B=B−A

(3) (AB)′ =A′ B′

(4) (A∩B)′ =A′ B′

Solution :

(1) (A-B) = A∩B   False

(2) A-B = B-A False

(3) (AB)' = A' B' False

(4) (A∩B)' = A' B' True

[Answer: (4) (A∩B)' = A' B']


16. If n (A  B C) = 100, n (A) = 4x, n (B) = 6x, n (C ) = 5x, n (A ∩ B) = 20, n (B ∩ C) = 15, n (A ∩ C) = 25 and n(A ∩ B ∩C) = 10 , then the value of x is

(1) 10

(2) 15

(3) 25

(4) 30

Solution:

n(ABC) = n(A) + n(B) + n(C) - n(A∩B) - n(B∩C) - n(C∩A) + n(A∩B∩C)

100 = 4x + 6x + 5x - 20 – 15 -25 + 10

100 = 15x-60+10

100 = 15x-50

15x = 100 + 50 = 150

x = 10

[Answer: (1)10]


17. For any three sets A, B and C, (A − B) ∩ (B −C) is equal to

(1) A only

(2) B only

(3) C only

(4) ϕ

Solution: (A - B) ∩ (B - C) is equal to ϕ

[Answer: (4) ϕ ]


18. If J = Set of three sided shapes, K = Set of shapes with two equal sides and L = Set of shapes with right angle, then J  K  L is

(1) Set of isoceles triangles

(2) Set of equilateral triangles

(3) Set of isoceles right triangles

(4) Set of right angled triangles

Solution:


[Answer: (3) Set of isoceles right triangles]


19. The shaded region in the Venn diagram is


(1) Z −(X Y)

(2) (X Y)∩Z

(3) Z −(X ∩Y)

(4) Z (X ∩Y)

Solution: Z – (X ∩Y)

[Answer: (3) Z – (X ∩Y) ]


20. In a city, 40% people like only one fruit, 35% people like only two fruits, 20% people like all the three fruits. How many percentage of people do not like any one of the above three fruits?

(1) 5

(2) 8

(3) 10

(4) 15

Solution:


40 + 35 + 20 + x = 100%

95% + x = 100%

x = 5%

[Answer: (1) 5]

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