Functions Ranker

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FUNCTIONS

1. Let 1 2 3tan tan tan2 3x xf x a x a a

1 2 3. tan , ,

n nxa where a a a an

are real numbers and

, tann Z f x x for ,2 2

x then 321 2 3

na aaa

n is

A) 1 B) 1 C) 1 D) 12

2. If : 0,f R defined by 10logxf x then 1f x A) 10logx B)

10x C) 10x D) None 3. The domain of sin cos x

A) 2 ,2 ,2

n n n I B) 2 ,2 ,

2n n n I

C) 32 ,2 ,2

n n n I D) 2 ,2 ,

2 2n n n I

4. Let sinxf x e x be defined on the interval [-4, 0], the odd extension of f x in the interval

[-4, 4] A) sin , 0, 4xe x x B) sin , 0,4xe x x C) sin , 0, 4xe x x D) sin , 0, 4xe x x

5. If :f R R is a function satisfying f x y f xy for all ,x y R and 3 34 4

f

,

then 916

f

A) 34

B) 916

C) 32

D) 0

6. If for nonzero x, 2 2212 3 1f x f xx

, then 2f x

A) 4 2

2

3 25x xx

B) 4 2

2

3 25x xx

C) 4 2

2

3 25x xx

D) 4 2

2

3 25x xx

7. If : 1,1g R is a function and the area of the equilateral triangle with two of its

vertices at (0,0) and (x,g(x)) is 34

, then g(x)=

A) 2 1x B) 21 x C) 21 x D) x

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8. The domain of the function 2

12sin log 2

xf x

is

A) 2, 2 B) 2, 1 C) 1,2 D) 2, 1 1, 2 9. If :f R R satisfies f x y f x f y for all ,x yR and f (1) =7, then

1

n

rf r

is

A) 7 12

n B) 7 12

n n C) 72n D) 7 1n n

10. : ,f f x x x R R Is A) one-one but not onto B) onto but not one-one C) Both one-one and onto D) neither one-one nor onto 11. If f is a real valued function satisfying 6 3 9f x f x f x f x , then f x = A) 3f x B) 6f x C) 9f x D) 12f x

12. If :f R R is defined by 2log 1f x x x , then consider the two statements STATEMENE I : 0f x f x STATEMENE II: f is an odd function, and then which one of the following is

correct? A) Only I is correct B) Only II is correct C) I and II are correct and I is correct explanation of II D) I and II are correct, I is not the correct explanation of II 13. If 1,1 , 2,3 , 3,5 , 4,7g is described by the formula g x x , then , A) (2, 1) B) (2,-1) C) (-2, 1) D) (-2,-1) 14. Given A={x, y,z}, B={u,v,w}, the function :f A B defined by

, ,f x u f y v f z w is A) Subjective B) objective C) injective D) all of the above 15. If 2 2cos cosf x x x , then (where is integral part of )

A) 12

f

B) 1f C) 1f D) 24

f

16. The domain of the function 11 1sin2

f x xx x

is

A) 1,1 \ 0 B) 1,1 C) 1,0 D)

17. If :f R R is defined by 2

sin tan

1

x xf x

x

, then the range of f= (where [x]

denotes integral part of x) A) 1,1 B) 1,1 C) 1 D) 0

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18. The range of 35 4sin 3

f xx

is

A) 1 ,33

B) 1 ,13

C) 1,3 D) 1, 3,3

19. Let : [0. )2

f R be defined by 1 2f x Tan x x a . Then the set of values of a for which f is onto is

A) [0, ) B) 1[ , )4 C) 1 1[ ,( , ]

4 4 D) 1

4

20. Set A has 3 elements and set B has 4 elements. The number of injections that can be defined from A to B is

A) 144 B) 12 C) 24 D) 64

21. :f N Z is defined by 2, 3 ,

10 , 3 1, . 2

0, 3 2,

if n k k Z

f n n if n k k Then n f n

if n k k

Z

Z

A) 3,6,3 B) 1,4,7 C) 4,7 D) 7 22. The range of 2 2 24 9 6 3 2x y z yz xz xy is A) B) R C) [0, ) D) ,0

23. The range of 2

2

11

x xx x

is

A) 1 ,33

B) 1 ,13

C) 1,3 D) 1( , ] [3, )3

24. The range of 2 5x x is A) [2, ) B) [3, ) C) [4, ) D) [5, ) 25. The range of the function 7 3x xf x P is A) 1, 2,3 B) 1,2,3, 4,5 C) 1, 2,3, 4 D) 1, 2,3, 4,5,6 26. The range of 1 1sin cosx x is

A) 3 ,2 2

B) 5 ,

2 3

C) 3 ,

2

D) 0,2

27. The range of the function 2 , 22

xf x xx

is

A) R B) R-{-1} C) R-{1} D) R-{2}

28. The domain of 31023 log

4f x x x

x

is

A) (1, 2) B) 1,0 1, 2 C) 1,0 2, D) 1,0 1, 2 2,

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29. The domain of 2 2x xx

is

A) [-2, 2] B) (-2, 2) C) [ 2,0) (0,2] D) 0R 30. If 2 3 4 .........f x x x x x when 1x then 1f x

A) 1

xx

B) 1

xx

C) 11 x

D) 11 x

KEY

1 2 3 4 5 6 7 8 9 10 B C D B A C B D B C 11 12 13 14 15 16 17 18 19 20 D C B D A D D A D C 21 22 23 24 25 26 27 28 29 30 B C A B A A B D C A

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KEY & SOLUTIONS

1. B

Clearly 1 0f is required 10

0 ln

f hf t

h

0 0

tan hl l 1h h

f ht t

h h

2. C 1 110log 10 10y x xf x y x f y x y f x 3. D F(x) is defined when sin cos 0x

1cos sin 0 cos 0x x

X lies on I and IV quadrant

2 2 ,

2 2n x n n I

4. B f x f x 5. A

Let f(0)=k, then f(x) = f(x+0) = f(0) = k, f is a constant function. But 3 34 4

f

3

4f x

For all x and hence 9 3

16 4f

6. C

2 2 2 22 21 12 3 1 4 6 2 2 ......... 1f x f x f x f xx x

2 22 2 2 2

1 1 1 32 3 1 9 6 3 ......... 2f f x f x fx x x x

4 22 2 2

2 2

3 3 22 1 5 2 15x xf x x f x

x x

7. B If a = length of a side = 22 2 20 0x g x x g x

Area of an equilateral triangle = 2 2 2 23 3 1 14 4

a x g x g x x

8. D

2 2 2

1 22 2

1sin log 1 log 1 2 1 4 2, 1 1, 22 2 2 2x x xf x x x

R

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9. B 1 7, 2 1 1 1 1 2 1 , 1f f f f f f f n nf 10. C

Give that

2

2

00 0

0

x if xf x if x

x if x

11. D Replace x with x+3 12. C 0f x f x 13. B 1 1g

2 2 3g 14. D Conceptual 15. A 2cos9 cos10 , 9 10f x x x 16. D 0, 1 1, 2 0x x x 17. D sin tan 0x n Z x x 18. A 1 sin3 1x 19. D 2 0x x a has a real solution 1 4 0a 20. C

n Bn AP =

43 4.3.2 24P

21. B \ 2 \10 2, 3 1n f n n n n k

\ 8, 3 1n n n k 22. C 2 2 22 2 24 9 6 3 2 2 3 2 3 3 2 0x y z yz xz xy x y z y z x z x y

Range = [0, ) . 23. A

Let 2

2 2 22

1 1 1 1 1 02 7

x xy yx yx y x x y x y x yx x

x R Discriminate 2 2 20 1 4 1 0 3 10 3 0y y y y

2 13 10 3 0 3 1 3 0 33

y y y y y

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Range = 1 ,33

24. B 2 5f x x x and domain f=R For x