NDA PYQ Functions - Chapter-wise Questions with Solutions

About Functions PYQs

Functions has 129 previous year questions in the Quantrex Academy NDA Mathematics bank. The 129 questions in this list come from NDA (129), spanning 2010 to 2026. Each question opens on its own page with the options, the correct answer and the worked solution where available.

NDA Functions PYQs with Solutions

About Functions PYQs

Questions by year (this list)

Functions questions with solutions

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

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

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

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

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

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?

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) ?

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) ?

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?

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

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

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

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?

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?

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

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?

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 ?

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

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?

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) ?

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

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))?

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

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)= (π x) Select the correct answer using the code given below:

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

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

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?

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

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

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?

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

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 ?

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

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

A mapping f: A arrow 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?

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?

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

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

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

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?

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?

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

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

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

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 ?

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 ?

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 ?

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

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

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

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

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

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

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

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

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

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

Consider the following statements : 1. A function f: ℤ arrow ℤ , defined by f(x)=x+1 , is oneone as well as onto. 2. A function f: ℕ arrow ℕ , defined by f(x)=x+1 , is oneone but

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

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

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

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

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?

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

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

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

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 of

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

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

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

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] ?

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

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

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

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

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