7/25/2019 Stp - 7 (Function) Que.

1/2

CENTERS : MUMBAI / DELHI / AKOLA / KOLKATA / LUCKNOW / NASHIK / GOA / PUNE # 1

ANDHERI / BORIVALI / DADAR / THANE / POWAI / CHEMBUR / NERUL / KHARGHARIIT JEE: 2017 STP - 7 (FUNCTION) VC - I TIME: 20 Min.

Solving any 5 problems

Only one option is correct [+5, -1]

1. Suppose that f is an even, periodic function with period 2, and that f (x) = x for all x in the interval

[0, 1]. The value of f (3.14) equals

(A) 3.14 (B) 0.14 (C) 0.14 (D) 0.86

2. Domain of the function 1 2 3x x is

(A) 0,2 (B) 1,1 (C) 1,2 (D) none of these

3. The function f : R R defined as f(x) = ln

x1xx1x 22 is

(A) One-one and onto both (B) One-one but not onto

(C) Onto but not one-one (D) Neither one-one nor onto

4. The maximum value of f(x) = 1|x|

x2|x| 2

is

(A) 4 (B) 3 (C) 2 (D) 1

5. Number of integral solutions of the equation sgn

6

xsin 1 = 1,

where [x] denotes the greatest integer less than or equal to x and sgn x denotes signum function of x.

(A) 2 (B) 3 (C) 5 (D) 7

6. Let two functions f(x) and g(x) are defined on R R such that f (x) =

rationalx,x2

irrationalx,x2

2

and g(x) =

rationalx,x

irrationalx,x22

2

. Then the function f + g : R R is

(A) injective as well as surjective. (B) injective but not surjective.

(C) surjective but not injective. (D) neither surjective nor injective.

7. The range of f (x) =

1(sin1x + tan1x) +

5x2x

1x2

is equals to

(A)

5

1,

4

3(B)

1,

4

3(C)

1,

4

3(D)

1,

4

3

7/25/2019 Stp - 7 (Function) Que.

2/2

CENTERS : MUMBAI / DELHI / AKOLA / KOLKATA / LUCKNOW / NASHIK / GOA / PUNE # 2

ANDHERI / BORIVALI / DADAR / THANE / POWAI / CHEMBUR / NERUL / KHARGHAR

IIT JEE: 2017 STP - 7 (FUNCTION) VC - I

ANSWER KEY

1. (D)

2. (C)

3. (D)

4. (D)

5. (A)

6. (D)

7. (D)