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JEE Advanced (Single Correct MCQs): Functions - Question 1

Let R be the set of real numbers. If f : R → R is a function defined by f (x) = x^{2}, then f is :

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JEE Advanced (Single Correct MCQs): Functions - Question 2

The entire graphs of the equation y = x^{2} + kx – x + 9 is strictly above the x-axis if and only if

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JEE Advanced (Single Correct MCQs): Functions - Question 4

If x satisfies |x - 1| + |x - 2| + |x - 3| __>__ 6 , then

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JEE Advanced (Single Correct MCQs): Functions - Question 5

If f ( x) = cos(ln x), then the value

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JEE Advanced (Single Correct MCQs): Functions - Question 6

The domain of definition of the function

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JEE Advanced (Single Correct MCQs): Functions - Question 7

Which of the following functions is periodic?

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JEE Advanced (Single Correct MCQs): Functions - Question 8

Let f(x) = sin x and g(x) = ln | x |. If th e ran ges of th e composition functions fog and gof are R_{1} and R_{2 }respectively, th en

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JEE Advanced (Single Correct MCQs): Functions - Question 9

Let f ( x) = ( x + 1)^{2} - 1,x __>__ -1 . Th en th e set {x : f (x) = f ^{-1} (x)} is

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JEE Advanced (Single Correct MCQs): Functions - Question 10

Th e fun ction f(x) = |px – q| + r | x |, x ∈ (-∞,∞) where p > 0, q > 0, r > 0 assumes its minimum value only on one point if

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JEE Advanced (Single Correct MCQs): Functions - Question 11

Let f(x) be defined for all x > 0 and be continuous. Let f(x) for all x, y and f(e) = 1. Then

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JEE Advanced (Single Correct MCQs): Functions - Question 12

If the function f: [1, ∞) → [1, ∞) is defined by f(x) = 2^{x (x-1)}, then f^{–1} (x) is

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JEE Advanced (Single Correct MCQs): Functions - Question 13

Let f : R → R be any function. Define g : R → R by g(x) = |f(x)| for all x. Then g is

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JEE Advanced (Single Correct MCQs): Functions - Question 14

The domain of definition of the function f(x) given by the equation 2^{x} + 2^{y} = 2 is

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JEE Advanced (Single Correct MCQs): Functions - Question 15

Let g(x) = 1 + x - [x] and Then for allx, f(g(x)) is equal to

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JEE Advanced (Single Correct MCQs): Functions - Question 16

If f:[1, ∞) → [2, ∞) is given by equals

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JEE Advanced (Single Correct MCQs): Functions - Question 18

Let E = {1, 2, 3, 4} and F = {1, 2}. Then the number of onto functions from E to F is

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JEE Advanced (Single Correct MCQs): Functions - Question 19

Then, for what value of a is f (f(x)) = x ?

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JEE Advanced (Single Correct MCQs): Functions - Question 20

Suppose f(x) = (x + 1)^{2} for x __>__ -1. If g(x) is the function whose graph is the reflection of the graph of f (x) with respect to the line y = x, then g(x) equals

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JEE Advanced (Single Correct MCQs): Functions - Question 21

Let f unction f : R → R be defined by f(x) = 2x + sin x for x ∈ R , then f is

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JEE Advanced (Single Correct MCQs): Functions - Question 23

Domain of definition of the function

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JEE Advanced (Single Correct MCQs): Functions - Question 25

If f (x) = x^{2} + 2bx + 2c^{2} and g (x) = - x^{2} -2cx+ b^{2} such that min f (x) > max g (x), then the relation between b and c, is

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JEE Advanced (Single Correct MCQs): Functions - Question 26

If f(x) = sin x + cos x, g (x) = x^{2} – 1, then g (f(x)) is invertible in the domain

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JEE Advanced (Single Correct MCQs): Functions - Question 27

If the functions f(x) and g(x) are defined on R → R such that

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JEE Advanced (Single Correct MCQs): Functions - Question 28

X an d Y are two sets and f : X → Y. If {f(c) = y; c ⊂ X, y ⊂ Y} and {f–1(d) = x; d ⊂ Y, x ⊂ X}, then the true statement is

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JEE Advanced (Single Correct MCQs): Functions - Question 29

If g(x) = f '(x) and given that F(5) = 5, then F(10) is equal to

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JEE Advanced (Single Correct MCQs): Functions - Question 31

Let f, g and h be real-valued functions defined on the interval and . If a, b and c denote, respectively, the absolute maximum of f, g and h on [0, 1], then

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JEE Advanced (Single Correct MCQs): Functions - Question 32

Let f (x) = x^{2} and g(x) = sin x for all x ∈ R. Then the set of all x satisfying (f o g o g o f) (x) = (g o g o f) (x), where (f o g) (x) = f (g(x)), is

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JEE Advanced (Single Correct MCQs): Functions - Question 33

Th e function f : [0, 3] → [1, 29], defi n ed by f(x) = 2x^{3} – 15x^{2} + 36x + 1, is

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