Scroll:set and function >> Choose the correct answer >> mcq (4266)


Written Instructions:

For each Multiple Choice Question (MCQ), four options are given. One of them is the correct answer. Make your choice (1,2,3 or 4). Write your answers in the brackets provided..

For each Short Answer Question(SAQ) and Long Answer Question(LAQ), write your answers in the blanks provided.

Leave your answers in the simplest form or correct to two decimal places.



 

1)  

 If A = {7,8,9}, B = {3,4,5,6,7}

and ƒ:A"B is defined by ƒ(x) = x- 2, then the range of ƒ is ___






(                    )




2)  

If the range of a function is a singleton set, then it is _____






(                    )




3)  

If A = {p,q,r,s}, B = {r,s,t,u} then A\B is ______

(A) {p,q}  (B)  {t,u}   (C)  {r,s}   (D) {p,q,r,s}








(                    )




4)  

 Let A = {1,3,4,7,11}, B = {-1,1,2,5,7,9} and ƒ: A"B be given by ƒ = {(1,-1),(3,2),(4,1),(7,5),(11,9)}. Then ƒis ________








(                    )




5)  

 For any two sets A and B, {(A\B)∪(B\A)} ∩ (A∩B) is _____

(A) ∅   (B) (A∪B)   (C) (A∩B)    (D) A‘∩B‘






{(A\B)∪(B\A)} ∩ (A∩B) = {(A∪B)∖(A∩B)}∩(A∩B)

                                  = ∅

Ans (A) = ∅


(                    )




6)  

 If {(7,15), (3,j)} represent a constant function,

then the value of 'j' is _______

(A) 7    (B) 15     (C) 3    (D) 8








(                    )




7)  

 Which one of the following is not true

(A) A∖B = A∩B‘          (B) A\B = A∩B

(C) A\B = (A∪B)∩B‘    (D) = A\B = (A∪B)\B





 



(                    )




8)  

 If ƒ: A" B is a bijective function and if n(A) = 5,

then n(B) is equal to ____






(                    )




9)  

If ƒ(x) = x2 + 8, then ƒ(-7) = ____





 


(                    )




10)  

 If {(x,2)}, (6,y)} represent an identity function,

then (x,y) is _______

(A)  (2,6)    (B) (6,2)    (C)  (2,2)  (D) (6,6)







(                    )




 

1)  

 If A = {7,8,9}, B = {3,4,5,6,7}

and ƒ:A"B is defined by ƒ(x) = x- 2, then the range of ƒ is ___





Answer: 2



SOLUTION 1 :

 ƒ(x) = x - 2

ƒ (7) = 7 - 2 = 5

ƒ (8) = 8 - 2 = 6

ƒ (9) = 9 - 2 = 7

Range of ƒ = {5,6,7}

Ans (D) {5,6,7}.



2)  

If the range of a function is a singleton set, then it is _____





Answer: 4


SOLUTION 1 :

Range of a function is a singleton set ⇒ all elements of a domain is associated to unique element in the codomain.

It is a constant function.

Ans ⇒ a constant function.



3)  

If A = {p,q,r,s}, B = {r,s,t,u} then A\B is ______

(A) {p,q}  (B)  {t,u}   (C)  {r,s}   (D) {p,q,r,s}





Answer: 1




SOLUTION 1 :

 A|B = {p,q,r,s} {r,s,t,u}

       = {p,q}



4)  

 Let A = {1,3,4,7,11}, B = {-1,1,2,5,7,9} and ƒ: A"B be given by ƒ = {(1,-1),(3,2),(4,1),(7,5),(11,9)}. Then ƒis ________





Answer: 2




SOLUTION 1 :

 Each element in A is associated to a unique element in B.

     ƒ is one-one function.

Ans (A) one-one



5)  

 For any two sets A and B, {(A\B)∪(B\A)} ∩ (A∩B) is _____

(A) ∅   (B) (A∪B)   (C) (A∩B)    (D) A‘∩B‘






Answer: 4

{(A\B)∪(B\A)} ∩ (A∩B) = {(A∪B)∖(A∩B)}∩(A∩B)

                                  = ∅

Ans (A) = ∅


SOLUTION 1 :

{(A∖B)∪(B∖A)} ∩ (A∩B) = {(A∪B)∖(A∩B)}∩(A∩B)

                                  = ∅

Ans (A) = ∅



6)  

 If {(7,15), (3,f)} represent a constant function,

then the value of 'f' is _______

(A) 7    (B) 15     (C) 3    (D) 8





Answer: 2




SOLUTION 1 :

  If {(7,15), (3,f)} represent a constant function,

then the value of  f = 15

Ans   (B) ⇒ 15



7)  

 Which one of the following is not true

(A) A∖B = A∩B‘          (B) A\B = A∩B

(C) A\B = (A∪B)∩B‘    (D) = A\B = (A∪B)\B





Answer: 1

 



SOLUTION 1 :

 A∖B ≠ A∩B

Ans (B) ⇒  AB = A∩B



8)  

 If ƒ: A" B is a bijective function and if n(A) = 5,

then n(B) is equal to ____





Answer: 4


SOLUTION 1 :

ƒ: A" B is bijective ⇒ ƒ is one-one and onto.

ƒ(A) = n(B) ⇒ n(B) = 5

Ans 5 



9)  

If ƒ(x) = x2 + 8, then ƒ(-7) = ____





Answer: 3

 


SOLUTION 1 :

 ƒ (x) = x2 + 8

ƒ (-7) = (-7)2 + 8

                 = 49 + 8 = 57

Ans   ⇒  57



10)  

 If {(x,2)}, (6,y)} represent an identity function,

then (x,y) is _______

(A)  (2,6)    (B) (6,2)    (C)  (2,2)  (D) (6,6)





Answer: 3



SOLUTION 1 :

  If {(x,2)}, (6,y)} represent an identity function the x = 2, y = 6

(x,y) = (2,6)

Ans (A) ⇒(2,6)