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This mock test of Competition Level Test: Relations And Functions- 1 for JEE helps you for every JEE entrance exam.
This contains 30 Multiple Choice Questions for JEE Competition Level Test: Relations And Functions- 1 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

The domain of the function f(x)= is

Solution:

QUESTION: 2

The domain of the function f(x) = log_{1/2} is

Solution:

QUESTION: 3

If q^{2} – 4pr = 0, p > 0, then the domain of the function, f(x) = log (px^{3} + (p + q) x^{2} + (q + r) x + r) is

Solution:

QUESTION: 4

Find domain of the function f(x) =

Solution:

QUESTION: 5

The domain of the function is (where [x] denotes greatest integer function)

Solution:

QUESTION: 6

Range of f(x) = 4^{x} + 2^{x} + 1 is

Solution:

QUESTION: 7

Range of f(x) = log_{√5} {√2 (sin x –cos x) + 3} is

Solution:

QUESTION: 8

The range of the functin f(x) = log_{√2}(2– log_{2} (16 sin^{2} x + 1)) is

Solution:

QUESTION: 9

Range of the function f(x)= is

Solution:

QUESTION: 10

If f(x) = , then range of f(x) is

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QUESTION: 11

The sum is equal to (where [*] denotes the greatest integer function)

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QUESTION: 12

Which of the following represents the graph of f(x) = sgn ([x + 1])

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QUESTION: 13

If f(x) = 2 sin^{2}q+4 cos (x+q) sin x. sin q+cos (2x+2q) then value of f^{2}(x) + f^{2} is

Solution:

QUESTION: 14

Let f(x) = ax^{2} + bx + c, where a, b, c are rational and f : Z → Z, where Z is the set of integers. Then a+ b is

Solution:

f : Z → Z

f(x) = ax^{2} + bx + c

x=0, f(0) = a(0)^{2} + b(0) + c

= c [it is an integer]

x=1, f(1) = a + b+ c should be an integer

a + b+ c = 1

a + b = 1-c

a+b should be an integer.

QUESTION: 15

Which one of the following pair of functions are identical ?

Solution:

QUESTION: 16

The function f : [2, ∞) → Y defined by f(x) = x^{2} – 4x + 5 is both one–one & onto if

Solution:

QUESTION: 17

Let f : R → R be a function defined by f(x) = then f is

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QUESTION: 18

Let f : R → R be a function defined by f(x) = x^{3} + x^{2} + 3x + sin x. Then f is

Solution:

QUESTION: 19

If f(x) = x^{3} + (a – 3) x^{2} + x + 5 is a one–one function, then

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QUESTION: 20

The graph of the function y = f(x) is symmetrical about the line x = 2, then-

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QUESTION: 21

The function f : R → R defined by f(x) = 6^{x} + 6^{|x|} is

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QUESTION: 22

Let `f' be a function from R to R given by f(x) = . Then f(x) is

Solution:

QUESTION: 23

If f(x) = cot^{-1} x : R^{+} → and g(x) = 2x – x^{2} : R → R. Then the range of the function f(g(x)) wherever define is

Solution:

g(x) = 2x-x^{2}

x(2-x)

-b/2a =. -2/(-2)

=> 1

x implies (0,2)

g(x) implies (0,1]

f(g(x)) = [π/4, π/2)

QUESTION: 24

Let g(x) = 1 + x – [x] and f(x) = , then x, fog(x) equals (where [*] represents greatest integer function).

Solution:

QUESTION: 25

Let f: [0, 1] → [1, 2] defined as f(x) = 1 + x and g : [1, 2] → [0, 1] defined as g(x) = 2 – x then the composite function gof is

Solution:

QUESTION: 26

Let f & g be two functions both being defined from R → R as follows f(x) = and g(x) = . Then

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QUESTION: 27

If y = f (x) satisfies the condition f = x^{2} + (x > 0) then f(x) equals

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QUESTION: 28

The function f(x) = log is

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QUESTION: 29

It is given that f(x) is an even function and satisfy the relation f(x) = then the value of f(10) is

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QUESTION: 30

Fundamental period of f(x) = sec (sin x) is

Solution:

### Relations and Functions Test-2

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### Relations and Functions Test-6

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### Solution- Relations and Functions Test-3

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### Solution- Relations and Functions Test-4

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