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Functions — NDA Mathematics PYQs

129 previous year questions from Functions with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

129 questionsMathematicsSolutions on every page
1

Consider the following statements in respect of the function f(x)=x in the interval (-1,1) : I. The function attains maximum value. II. The function attains minimum value. Which of

NDA 2026 Solution View → 2

Passage: Consider the curves y=x^2 and y=2|x| . Question: What is the number of points of intersection of the curves ?

NDA 2026 Solution View → 3

If 2f(x)+f(1-x)=x , then what is f(x) equal to ?

NDA 2026 Solution View → 4

For the following two (02) items: Consider the function f(x) = 1 - [3] (x-1)^2 . What is the domain of the function?

NDA 2025 Solution View → 5

Consider the following for the two (02) items that follow: Let the function y = (1 - x)⁻¹ , where x 2n and n is an integer. What is the range of the function?

NDA 2025 Solution View → 6

For the following two (02) items: Consider the function f(x) = 10^x - 10^ -x 10^x + 10^ -x . What is f f f f f(0) equal to?

NDA 2025 Solution View → 7

Consider the following for the two (02) items that follow: Let the curve f(x) = |x - 3| . What is the domain of the function f(x) ?

NDA 2025 Solution View → 8

Consider the following for the two (02) items that follow: Let f = (1, 1), (2, 4), (3, 7), (4, 10) . If f(x) = px + q , then what is the value of (p + q) ?

NDA 2025 Solution View → 9

For the following two (02) items: Consider the function f(x) = x 1 - x ( x > 0 , x 1 ). What is (1 - x)f( x ) + xf( x + 1) equal to?

NDA 2025 Solution View → 10

Consider the following for the two (02) items that follow: The function f(x) satisfies f ( x y ) = f(x) f(y) for all positive real values of x and y , and f(2) = 3 . What is f(16)

NDA 2025 Solution View → 11

Consider the following for the two (02) items that follow: The function f(x) satisfies f ( x y ) = f(x) f(y) for all positive real values of x and y , and f(2) = 3 . What is f(1)f(

NDA 2025 Solution View → 12

Consider the following for the two (02) items that follow: A function f is such that f(xy) = f(x+y) for all real values of x and y , and f(5) = 10 . What is f(20) + f(-20) equal to

NDA 2025 Solution View → 13

For the following two (02) items: Consider the function f(x) = x 1 - x ( x > 0 , x 1 ). What is f(x) f(x+1) equal to?

NDA 2025 Solution View → 14

For the following two (02) items: Consider the function f(x) = 10^x - 10^ -x 10^x + 10^ -x . What is the inverse of the function?

NDA 2025 Solution View → 15

Consider the following for the two (02) items that follow: Let f = (1, 1), (2, 4), (3, 7), (4, 10) . Consider the following statements: I. f is one-one function. II. f is onto func

NDA 2025 Solution View → 16

Consider the following for the two (02) items that follow: A function f is such that f(xy) = f(x+y) for all real values of x and y , and f(5) = 10 . What is f(0) equal to?

NDA 2025 Solution View → 17

If f(x)=4 x+1 and g(x)=k x+2 such that f g(x)=g f(x) , then what is the value of k ?

NDA 2024 Solution View → 18

What is the minimum value of the function f(x)= ₁₀ (x^2+2 x+11 ) ?

NDA 2024 Solution View → 19

If f(x)=[x]^2-30[x]+221=0 , where [x] is the greatest integer function, then what is the sum of all integer solutions?

NDA 2024 Solution View → 20

If f(2 x)=4 x^2+1 , then for how many real values of x will f(2 x) be the GM of f(x) and f(4 x) ?

NDA 2024 Solution View → 21

Paragraph: Let f g(x)= ^2 x and g f(x)=| x| . Question: Which one of the following is f(x) ?

NDA 2024 Solution View → 22

Let f(x) f(y)=f(x y) for all real x, y . If f(2)=4 , then what is the value of f ( 1 2 ) ?

NDA 2024 Solution View → 23

Paragraph: Let f g(x)= ^2 x and g f(x)=| x| . Question: Which one of the following is g(x) ?

NDA 2024 Solution View → 24

Let A = x R :-1 x 1 . Which of the following is/are bijective functions from A to itself? 1. f(x)=x|x| 2. g(x)= ( x) Select the correct answer using the code given below:

NDA 2024 Solution View → 25

Paragraph: Let f(t)= (t+ 1+t^2 ) and g(t)= (f(t)) . Question: Consider the following statements : A. f(t) is an odd function. B. g(t) is an odd function. Which of the statements gi

NDA 2024 Solution View → 26

Paragraph: Let f(x)=[x]^2- [x^2 ] . Question: What is f(0.999)+f(1.001) equal to?

NDA 2024 Solution View → 27

If f(x)=a x-b and g(x)=c x+d are such that f(g(x))=g(f(x)) , then which one of the following holds?

NDA 2024 Solution View → 28

Let A = 1,2,3,4,5 and B = 6,7 . What is the number of onto functions from A to B ?

NDA 2024 Solution View → 29

Which one of the following is correct in respect of f(x)= 1 |x|-x and g(x)= 1 x-|x| ?

NDA 2024 Solution View → 30

Let f(x) and g(x) be two functions such that g(x)=x- 1 x and f o g(x)=x^3- 1 x^3 . What is g[f(x)-3 x] equal to?

NDA 2024 Solution View → 31

Let 3 f(x)+f ( 1 x )= 1 x +1 What is f(x) equal to?

NDA 2024 Solution View → 32

Let z=[y] and y=[x]-x , where [.] is the greatest integer function. If x is not an integer but positive, then what is the value of z ?

NDA 2024 Solution View → 33

Consider the following statements: 1. The relation f defined by f(x)= array ll x^3, & 0 x 2 4 x, & 2 x 8 array . is a function 2. The relation g defined by g(x)= array ll x^2, & 0

NDA 2023 Solution View → 34

Let f(x)=x^2-1 and gof (x)=x- x +1 Which one of the following is a possible expression for g(x)?

NDA 2023 Solution View → 35

A mapping f: A B defined as f(x)= 2 x+3 3 x+5 , x A . If f is to be onto, then what are A and B equal to?

NDA 2023 Solution View → 36

Paragraph: Consider the function f(x)=|x-2|+|3-x|+|4-x| , where x R Question: At what value of x does the function attain minimum value?

NDA 2023 Solution View → 37

If f(x)=x^2+2 and g(x)=2 x-3 , then what is (f g)(1) equal to?

NDA 2023 Solution View → 38

What is the range of the function f(x)=x+|x| if the domain is the set of real numbers?

NDA 2023 Solution View → 39

A function is defined by f(x)= + ^2 x What is the range of the function?

NDA 2023 Solution View → 40

Let a function f be defined on R - 0 and 2 f(x)+f ( 1 x )=x+3 What is f(0.5) equal to?

NDA 2023 Solution View → 41

A function satisfies f(x-y)= f(x) f(y) , where f(y) 0 . If f(1)=0.5 , then what is f(2)+f(3)+f(4)+f(5)+f(6) equal to?

NDA 2023 Solution View → 42

Let f(x)= 2-x + 2+x . What is the domain of the function?

NDA 2023 Solution View → 43

Paragraph: Consider the function f(x)=|x-2|+|3-x|+|4-x| , where x R Question: What is the minimum value of the function?

NDA 2023 Solution View → 44

Let f(x)=x^2-1 and gof (x)=x- x +1 What is g(15) equal to?

NDA 2023 Solution View → 45

Paragraph: Let f(x) be a function satisfying f(x+y)=f(x) f(y) for all x, y N such that f(1)=2 : Question: What is _ x=1 ^5 f(2 x-1) equal to ?

NDA 2022 Solution View → 46

Let z=[y] and y=[x]-x , where [.] is the greatest integer function. If x is not an integer but positive, then what is the value of z ?

NDA 2022 Solution View → 47

If f(x)=4 x+1 and g(x)=k x+2 such that f o g(x)= gof (x) , then what is the value of k ?

NDA 2022 Solution View → 48

Consider the following statements in respect of the function y=[x], x (-1,1) where [.] is the greatest integer function: 1. Its derivative is 0 at x=0.5 2. It is continuous at x=0

NDA 2022 Solution View → 49

If 4 f(x)-f ( 1 x )= (2 x+ 1 x ) (2 x- 1 x ) , then what is f(2) equal to?

NDA 2022 Solution View → 50

What is the domain of the function f(x)= 1-(x-1)^2 ?

NDA 2022 Solution View → 51

What is the minimum value of the function f(x)= ₁₀ (x^2+2 x+11 ) ?

NDA 2022 Solution View → 52

If f(x)=4 x+3 , then what is f^ f^ f(-1) equal to?

NDA 2022 Solution View → 53

Consider the following in respect of the function f(x)=10^x : 1. Its domain is (- , ) 2. It is a continuous function 3. It is differentiable at x=0 Which of the above statements ar

NDA 2022 Solution View → 54

If f(x)= (x+ 1+x^2 ) , then which one of the following is correct?

NDA 2022 Solution View → 55

Consider the following statements in respect of the function f(x)= array cc |x|+1, & 0 |x| 3 1, & x=0 array . 1. The function attains maximum value only at x=3 2. The function atta

NDA 2022 Solution View → 56

What is the period of the function f(x)= (2+ ^2 x ) ?

NDA 2021 Solution View → 57

If f(x+1)=x^2-3 x+2 , then what is f(x) equal to?

NDA 2021 Solution View → 58

Consider the following statements : 1. A function f: Z Z , defined by f(x)=x+1 , is oneone as well as onto. 2. A function f: N N , defined by f(x)=x+1 , is oneone but not onto. Whi

NDA 2021 Solution View → 59

What is the domain of the function f(x)=3^x ?

NDA 2021 Solution View → 60

Which one of the following is correct in respect of the graph of y= 1 x-1 ?

NDA 2020 Solution View → 61

If f(x)=2 x-x^2 , then what is the value of f(x+2)+f(x-2) when x=0 ?

NDA 2020 Solution View → 62

Paragraph: Let f(x) = x^2 , g(x) = tan x and h(x) = ln x. Question: For x= 2 , what is the value of [h o(g f)](x) ?

NDA 2019 Solution View → 63

Paragraph: Let f(x) = x^2 , g(x) = tan x and h(x) = ln x. Question: What is [f o(f o f)] (2) equal to?

NDA 2019 Solution View → 64

A function f defined by f ( x )= ( x^2+1 -x ) is

NDA 2019 Solution View → 65

If f(x)=3^ 1+x , then f(x) f(y) f(z) is equal to

NDA 2019 Solution View → 66

The domain of the function f defined by f(x)= _x 10 is

NDA 2019 Solution View → 67

Paragraph: Let f(x)=x^2+2 x-5 and g(x)=5 x+30 Question: Consider the following statements: 1. f[g(x)] is a polynomial of degree 3 . 2. g[g(x)] is a polynomial of degree 2 . Which o

NDA 2019 Solution View → 68

The domain of the function f ( x )= (2-x)(x-3) is

NDA 2019 Solution View → 69

If f ( x )= x-2 x+2 , x -2 , then what is f ⁻¹( x ) equal to ?

NDA 2019 Solution View → 70

Which one of the following is correct in respect of the function f : R R ⁺ defined as f ( x )=| x +1| ?

NDA 2018 Solution View → 71

Let [ x ] denote the greatest integer function. What is the number of solutions of the equation x^2-4 x+[x]=0 in the interval [0,2] ?

NDA 2018 Solution View → 72

Suppose f: R R is defined by f(x)= x^2 1+x^2 . What is the range of the function?

NDA 2018 Solution View → 73

If f: R S defined by f(x)=4 x-3 x+1 is onto, then what is S equal to?

NDA 2018 Solution View → 74

For f to be a function, what is the domain of f , if f(x)= 1 |x|-x ?

NDA 2018 Solution View → 75

Afunction f: A R is defined by the equation f(x)=x^2-4 x+5 where A=(1,4) . What is the range of the function?

NDA 2018 Solution View → 76

If f(x)= x-1 x-4 defines a function of R , then what is its domain?

NDA 2018 Solution View → 77

The inverse of the function y=5^ x is

NDA 2017 Solution View → 78

If x is any real number, then x^2 1+x^4 belongs to which one of the following intervals?

NDA 2017 Solution View → 79

If f(x)= 4 x+x^4 1+4 x^3 and g(x)= In ( 1+x 1-x ) , then what is the value of f^ g ( e -1 e +1 ) equal to?

NDA 2017 Solution View → 80

The function f: X Y defined by f( x )= x , where x X , is one-one and onto if X and Y are respectively equal to

NDA 2017 Solution View → 81

If f( x )= x x -1 , then what is f( a ) f( a +1) equal to?

NDA 2017 Solution View → 82

Let f:[-6,6] IR defined by f(x)=x^2-3 . Consider the following: 1. (fofof )(-1)= (fofof )(1) 2. (fofof )(-1)-4 (fofof )(1)= (f^ f )(0) Which of the above is correct?

NDA 2017 Solution View → 83

Let f( x )= px + q and g ( x )= mx + n . Then f( ~g ( x ))= g (f( x )) is equivalent to

NDA 2017 Solution View → 84

Let f( x ): cases x , & x is rational 0, & x is irrational cases and g ( x ): cases 0, & x is rational x , & x is irrational cases If f: R R and g : R R , then (f- g ) is

NDA 2017 Solution View → 85

Which one of the following functions is neither even nor odd?

NDA 2017 Solution View → 86

Let f( a )= a -1 a +1 . Consider the following : 1) (f(2 a)=f(a)+1 ) 2) (f ( 1 a )=-f(a) ) Which of the above is/are correct?

NDA 2017 Solution View → 87

The function f(x)=|x|-x^3 is

NDA 2017 Solution View → 88

Which one of the following graph represents the function f( x )= x x , x 0 ?

NDA 2017 Solution View → 89

What is the domain of the function f(x)= 1 |x|-x ?

NDA 2016 Solution View → 90

Paragraph: Let f(x)=[|x|-|x-1|]^2 Question: Which of the following equations is/are correct? 1. f (-2)= f (5) 2. f ^ (-2)+ f ^ (0.5)+ f ^ (3)=4 Select the correct answer using the

NDA 2016 Solution View → 91

If f ( x ₁ )- f ( x ₂ )= f ( x ₁- x ₂ 1- x ₁ x ₂ ) for x ₁, x ₂ (-1,1) , then what is f ( x ) equal to?

NDA 2016 Solution View → 92

What is the range of the function y = x ^2 1+ x ^2 , where x R ?

NDA 2016 Solution View → 93

Paragraph: Let f(x)=[x] , where [.] is the greatest integer function and g(x)= x be two real valued functions over R . Question: Which of the following statements are correct? 1. (

NDA 2016 Solution View → 94

Consider the curves f(x)=x|x|-1 and g(x)= cases 3 x 2 , & x 0 2 x, & x 0 cases Where do the curves intersect?

NDA 2016 Solution View → 95

Consider the function f ( x )= 27 ( x ^ 2 / 3 - x ) 4 How many solutions does the function f(x)=-1 have?

NDA 2016 Solution View → 96

Consider the curves y =| x -1| and | x |=2 What is/are the point(s) of intersection of the curves?

NDA 2016 Solution View → 97

Let f(x) be the greatest integer function and g(x) be the modulus function. What is (f f) (- 9 5 )+(g g)(-2) equal to?

NDA 2016 Solution View → 98

Consider the function f ( x )= 27 ( x ^ 2 / 3 - x ) 4 How many solutions does the function f ( x )=1 have?

NDA 2016 Solution View → 99

Let f(x) be the greatest integer function and g(x) be the modulus function. What is ( g f ) (- 5 3 )-( f g ) (- 5 3 ) equal to?

NDA 2016 Solution View → 100

Consider the equation x+|y|=2 y . Which of the following statements are not correct? 1. y as a function of x is not defined for all real x . 2. y as a function of x is not continuo

NDA 2016 Solution View → 101

If f: R R, g: R R be two functions given by f(x)=2 x-3 and g(x)=x^3+5 , then (f g)⁻¹(x) is equal to

NDA 2015 Solution View → 102

If g(x)= 1 f(x) and f(x)=x, x 0 , then which one of the following is correct

NDA 2015 Solution View → 103

The domain of the function f(x)= 1 |x|-x is

NDA 2015 Solution View → 104

Consider the following statements : Statement 1: The function f R R such that f ( x )= x ^3 for all x R is one-one. Statement 2: f(a) f(b) for all a, b R if the function f is one-o

NDA 2015 Solution View → 105

For each non-zero real number x , let f(x)= x |x| . The range of f is

NDA 2015 Solution View → 106

f(x y)=f(x)+f(y) is true for all

NDA 2015 Solution View → 107

If f(x)= _e ( 1+x 1-x ), g(x)= 3 x+x^3 1+3 x^2 and g f(t)=g(f(t)) , then what is g f ( e-1 e+1 ) equal to?

NDA 2015 Solution View → 108

Consider the following functions: 1. f(x)=x^3, x R 2. f(x)= x, 0 x 2 3. f(x)=e^x, x R Which of the above functions have inverse defined on their ranges?

NDA 2015 Solution View → 109

Consider the function f(x)= x^2-1 x^2+1 , where x R What is the minimum value of f(x) ?

NDA 2015 Solution View → 110

If f(x)=a x+b and g(x)=c x+d such that f(g(x))=g(f(x)) , then which one of the following is correct?

NDA 2014 Solution View → 111

Consider the function f(x)= x-1 x+1 . What is f(2 x) equal to?

NDA 2014 Solution View → 112

Let N denote the set of all non-negative integers and Z denote the set of all integers. The function f: Z N given by f(x)=|x| is:

NDA 2014 Solution View → 113

The function f: N N , N being the set of natural numbers, defined by f(x)=2 x+3 is

NDA 2014 Solution View → 114

Consider the function f(x)= x-1 x+1 . What is f(x)+1 f(x)-1 +x equal to?

NDA 2014 Solution View → 115

Consider the function f(x)= x-1 x+1 . What is f(f(x)) equal to?

NDA 2014 Solution View → 116

The minimum value of the function f(x)=|x-4| exists at

NDA 2013 Solution View → 117

Let f be a function from the set of natural numbers to the set of even natural numbers given by f(x)=2 x . Then f is

NDA 2013 Solution View → 118

What is the range of the function f(x)= |x| x , x 0 ?

NDA 2013 Solution View → 119

Let f: R R be a function whose inverse is x+5 3 . What is f(x) equal to?

NDA 2012 Solution View → 120

Consider the following statements: 1. If f(x)=x^3 and g(y)=y^3 then f=g . 2. Identity function is not always a bijection. Which of the above statements is/are correct?

NDA 2012 Solution View →
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