Home Quantitative Aptitude Sets,Functions and Relations-Test 2

Sets,Functions and Relations-Test 2

Subject :- QT

Chapter :- Sets,Functions and Relations-Test 2

Questions :- 25

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Question 1 of 25

1. Question
1 points
On the set of lines ,begin perpendicular is a ___relation.
- Reflexive
- Symmentric
- Transitive
- none of these
Correct

A set of lines ,begin perpendicular is a symmentric relation

Incorrect

A set of lines ,begin perpendicular is a symmentric relation
Question 2 of 25

2. Question
1 points
$T h e r a n g e o f t h e f u n c t i o n f : N \to R f (x) = (- 1)^{x - 1} x = 1, f (1) = (- 1)^{1 - 1} = 1 x = 2, f (2) = (- 1)^{2 - 1} = - 1 x = 3, f (3) = (- 1)^{3 - 1} = 1 x = 4, f (4) = (- 1)^{4 - 1} = - 1 R a n g e o f f u n c t i o n = {1, - 1}$
- {0,-1}
- {1,-1}
- {1,0}
- {1,0,-1}
Correct

Incorrect
Question 3 of 25

3. Question
1 points
For a group of 200 persons ,100 are interested in music,70 in photography and 40 in swimming.Further more 40 are interested in both music and photography,30 in both music and swimming ,20 in photography and swimming and 10 in all the three.how many are interested in photography but not in music and swimming?
- 30
- 15
- 25
- 20
Correct

let photography =P

music=M

swimming=S

n(PUMUS=200,n(M)=100,n(P)=70,n(S)=40

n(M∩P)=40,n(M∩S)=30,n(P∩S)=20

n(P∩M∩S)=10

n(P∩M’∩S’)=n(P)-n(P∩M)-n(P∩S)+n(P∩M∩S)

=70-40-20+10=80-60=20

Incorrect

let photography =P

music=M

swimming=S

n(PUMUS=200,n(M)=100,n(P)=70,n(S)=40

n(M∩P)=40,n(M∩S)=30,n(P∩S)=20

n(P∩M∩S)=10

n(P∩M’∩S’)=n(P)-n(P∩M)-n(P∩S)+n(P∩M∩S)

=70-40-20+10=80-60=20
Question 4 of 25

4. Question
1 points
$i f f : R \to R i s a f u n c t i o n, d e f i n e d b y f (x) = 10 x - 7, i f g (x) = f^{- 1} (x), t h e n g (x) =$
- 1/10x-7
- 1/10x+7
- x+7/10
- x-7/10
Correct

Incorrect
Question 5 of 25

5. Question
1 points
The number of elements in range of constant function is
- one
- zero
- infinite
- indetermined
Correct

The number of elements in range of constant function is infinite

Incorrect

The number of elements in range of constant function is infinite
Question 6 of 25

6. Question
1 points
let A={1,2,3} then the relation R={(1,1),(2,3),(2,2),(3,3),(1,2)} is
- Symmetric
- Transitive
- Reflexive
- Equivalence
Correct

if A={1,2,3}

R={(1,1),(2,3),(2,2),(3,3),(1,2)}

here,R={(1,1),(2,2),(3,3)} shows reflexive relation

Incorrect

if A={1,2,3}

R={(1,1),(2,3),(2,2),(3,3),(1,2)}

here,R={(1,1),(2,2),(3,3)} shows reflexive relation
Question 7 of 25

7. Question
1 points
$i f f (x) = \log (\frac{1 + x}{1 - x}), t h e n f (\frac{- 2 x}{1 + x^{2}}) =$
- f(x)
- 2f(x)
- 3f(x)
- -f(x)
Correct

Incorrect
Question 8 of 25

8. Question
1 points
Of the 200 candidates who were interviewed for a position at call center ,100 had 2 wheeler,70 had a credit card and 140 had a mobile phone,40 of them had both a two wheeler and a credit card , 30 had both a credit card and a mobile phone , 60 had both two wheeler and a mobile phone and 10 had all the three.how many candidates had none of the three?
- 0
- 20
- 10
- 18
Correct

Incorrect
Question 9 of 25

9. Question
1 points
$i f f (x) = \frac{x^{2} - 25}{x - 5}, t h e n f (5) i s$
- 0
- 1
- 10
- not defined
Correct

$i f f (x) = \frac{x^{2} - 25}{x - 5} f (5) = \frac{5^{2} - 25}{5 - 5} = 0 = n o t d e f i n e d$

Incorrect

$i f f (x) = \frac{x^{2} - 25}{x - 5} f (5) = \frac{5^{2} - 25}{5 - 5} = 0 = n o t d e f i n e d$
Question 10 of 25

10. Question
1 points
let A={1,2,3} and B={6,4,7} then , the relation R={(2,4)(3,6)} will be
- function from A to B
- function from B to A
- both A and B
- not a function
Correct

A={1,2,3} and B={6,4,7}

relation R={(2,4)(3,6)} will be function from A to B.

Incorrect

A={1,2,3} and B={6,4,7}

relation R={(2,4)(3,6)} will be function from A to B.
Question 11 of 25

11. Question
1 points
In a class of 50 students,35 opted for maths and 37 for opted for commerce.The number of such students who opted for both maths and commerce are
- 13
- 15
- 22
- 28
Correct

given, n(muc)=50

n(m)=35

n(c)=37

n(muc)=n(m)+n(c)-n(m∩c)

50=35+37-n(m∩c)

n(m∩c)=22

Incorrect

given, n(muc)=50

n(m)=35

n(c)=37

n(muc)=n(m)+n(c)-n(m∩c)

50=35+37-n(m∩c)

n(m∩c)=22
Question 12 of 25

12. Question
1 points
The range of {(1,0),(2,0),(3,0),(4,0),(0,0)} is
- {1,2,3,4,0}
- {0}
- {1,2,3,4}
- none of these
Correct

range = {(1,0),(2,0),(3,0),(4,0),(0,0)}={0}

Incorrect

range = {(1,0),(2,0),(3,0),(4,0),(0,0)}={0}
Question 13 of 25

13. Question
1 points
$L e t N b e t h e s e t o f a l l n a t u r a l n u m b e r s; E b e t h e s e t o f a l l e v e n n a t u r a l n u m b e r s t h e n t h e f u n c t i o n f : N \to E d e f i n e d a s f (x) = 2 x \forall x \in N$
- one-one into
- one-one onto
- many-one into
- many-one onto
Correct

Incorrect
Question 14 of 25

14. Question
1 points
If A={2,3} , B={4,5},C={5,6},then Ax(B∩C)=_____
- {5,2),(5,3)}
- {(2,5),(3,5)}
- {(2,4),(3,5)}
- none of these
Correct

A={2,3} , B={4,5},C={5,6}

B∩C=5

Ax(B∩C)={2,3}x{5}={(2,5),(3,5)}

Incorrect

A={2,3} , B={4,5},C={5,6}

B∩C=5

Ax(B∩C)={2,3}x{5}={(2,5),(3,5)}
Question 15 of 25

15. Question
1 points
If S={1,2,3} then the relation {(1,1),(2,2),(1,2),(2,1)} is symmetric and
- reflexive but not transitive
- reflexive as well as transitive
- symmetric and transitive but not reflexive
- none of these
Correct

If S={1,2,3} then the relation {(1,1),(2,2),(1,2),(2,1)} is symmetric and transitive but not reflexive

Incorrect

If S={1,2,3} then the relation {(1,1),(2,2),(1,2),(2,1)} is symmetric and transitive but not reflexive
Question 16 of 25

16. Question
1 points
$i f f (x) = \frac{x}{x - 1} t h e n \frac{f (x / y)}{f (y / x)} =____$
- x/y
- y/x
- -x/y
- -y/x
Correct

Incorrect
Question 17 of 25

17. Question
1 points
$I f N b e t h e s e t o f a l l n a t u r a l n u m b e r s a n d E b e t h e s e t o f a l l e v e n n u m b e r s t h e n t h e f u n c t i o n f : N \to E s u c h t h a t f (x) = 2 x f o r a l l X \in N i s$
- one-one onto
- one-one into
- many-one onto
- constant
Correct

$N = {1, 2, 3, 4, . . . . . . . . . . . . . . . . . . . . . . \infty} E = {2, 4, 6.8, . . . . . . . . . . . . . . . . . . . . . . . \infty} f : N \to E f (x) = 2 x f (1) = 2 x 1 = 2 f (2) = 2 x 2 = 4 f (3) = 2 x 3 = 6 (i) R a n g e o f f u n c t i o n (R) = E (i i) f (x_{1}) = f (x_{2}) t h e n t h e f u n c t i o n i s o n e - o n e o n t o$

Incorrect

$N = {1, 2, 3, 4, . . . . . . . . . . . . . . . . . . . . . . \infty} E = {2, 4, 6.8, . . . . . . . . . . . . . . . . . . . . . . . \infty} f : N \to E f (x) = 2 x f (1) = 2 x 1 = 2 f (2) = 2 x 2 = 4 f (3) = 2 x 3 = 6 (i) R a n g e o f f u n c t i o n (R) = E (i i) f (x_{1}) = f (x_{2}) t h e n t h e f u n c t i o n i s o n e - o n e o n t o$
Question 18 of 25

18. Question
1 points
If A={x,y,z},B={a,b,c,d},then which of the following relation from the set A to set B is a function?
- {(x,a)(x,b)(y,c)(z,d)}
- {(x,a)(y,b),(z,d)}
- {(x,c)(z,b)(z,c)}
- none of these
Correct

A={x,y,z}

B={a,b,c,d}

AxB={x,y,z}x{a,b,c,d}

={(x,a)(x,b)(x,c)(x,d)(y,a)(y,b)(y,c)(y,d)(z,a)(z,b)(z,c)(z,d)}

then {(x,a)(y,b),(z,d)} is a function

Incorrect

A={x,y,z}

B={a,b,c,d}

AxB={x,y,z}x{a,b,c,d}

={(x,a)(x,b)(x,c)(x,d)(y,a)(y,b)(y,c)(y,d)(z,a)(z,b)(z,c)(z,d)}

then {(x,a)(y,b),(z,d)} is a function
Question 19 of 25

19. Question
1 points
In a class of 80 students,35% students can play only cricket ,45% students can play only table tennis and the remaining students can play both the games.In all how many students can play cricket?
- 55
- 44
- 33
- 22
Correct

Incorrect
Question 20 of 25

20. Question
1 points
If f(x)=2x+2 and g(x)=x.x,then the value of fog(4) is:
- 12
- 24
- 34
- 128
Correct

$f (x) = 2 x + 2 a n d g (x) = x^{2} f o g (x) = f [g (x)] = f [x^{2}] = 2 x^{2} + 2 f o g (4) = 2 (4)^{2} + 2 = 2 x 16 + 2 = 34$

Incorrect

$f (x) = 2 x + 2 a n d g (x) = x^{2} f o g (x) = f [g (x)] = f [x^{2}] = 2 x^{2} + 2 f o g (4) = 2 (4)^{2} + 2 = 2 x 16 + 2 = 34$
Question 21 of 25

21. Question
1 points
The number of subsets of the set formed by the word Allahabad is
- 128
- 16
- 32
- 64
Correct

A=set of the letter of the word ALLAHABAD={A,L,H,B,D}

n(A)=5

no.of sub set =
$2^{n} = 2^{5} = 32$

Incorrect

A=set of the letter of the word ALLAHABAD={A,L,H,B,D}

n(A)=5

no.of sub set =
$2^{n} = 2^{5} = 32$
Question 22 of 25

22. Question
1 points
In a group of students 80 can speak hindi,60 can speak english and 40 can speak english and hindi both then number of students is
- 100
- 140
- 180
- 60
Correct

A=hindi ,B=english

n(A)=80,n(B)=60,n(A∩B)=40

n(AUB)=n(A)+n(B)-n(A∩B)

=80+60-40=140-40=100

Incorrect

A=hindi ,B=english

n(A)=80,n(B)=60,n(A∩B)=40

n(AUB)=n(A)+n(B)-n(A∩B)

=80+60-40=140-40=100
Question 23 of 25

23. Question
1 points
$T h e i n v e r s e f u n c t i o n f^{- 1} o f f (x) = 100 x i s$
- x/100
- 1/100x
- 1/x
- none of these
Correct

Incorrect
Question 24 of 25

24. Question
1 points
If f(x)=x-1/x and g(x)=1/1-x then fog(x) =
- x-1
- x
- 1-x
- -x
Correct

Incorrect
Question 25 of 25

25. Question
1 points
$I f R i s t h e s e t o f a l l r e a l n u m b e r s, t h e n t h e f u n c t i o n f : R \to R d e f i n e d b y f (x) = 2^{x}$
- one-one onto
- one-one into
- many-one into
- many-one onto
Correct

Incorrect

Sets,Functions and Relations-Test 2

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