PYQ Vault
EbooksTutor

Sets, Relations and Functions

MHT-CET Maths. Try each one first, then open its answer.

Top 10 MHT-CET PYQs to practise first

The questions and kinds of question asked most often come first. Each one says how often and in which papers.

  1. Question 1

    This type asked 6 times: 11 Apr 2026 S1, 13 Apr 2026 S1, 18 Apr 2026 S2, 20 Apr 2026 S1, 14 May 2026 S2, 19 May 2026 S2. This one: 19 May 2026 S2 See all 6 of this type

    51
    The domain of the function f(x)=1∣x∣−xf(x) = \dfrac{1}{\sqrt{|x| - x}} is

    Tap an option to check your answer.

  2. Question 2

    Asked 5 times: 9 May 2023 S2*, 10 May 2023 S1*, 11 May 2024 S1*, 13 May 2024 S2*, 16 Apr 2026 S2 (* = numbers or wording changed that year) See all 5 times it was asked

    69
    If ex+ef(x)=ee^x + e^{f(x)} = e, then the domain of f(x)f(x) is

    Tap an option to check your answer.

  3. Question 3

    This type asked 5 times: May 2022 S1, 11 May 2023 S1, 15 May 2023 S2, 26 Apr 2025 S1, 14 May 2026 S1. This one: 14 May 2026 S1 See all 5 of this type

    51
    If [⋅][\cdot] represents the greatest integer function of less than or equal to type then the solution set of the equation [x]2−5[x]+6=0[x]^2 - 5[x] + 6 = 0 is

    Tap an option to check your answer.

  4. Question 4

    This type asked 4 times: May 2021 S1, 16 May 2023 S1, 14 May 2024 S1, 15 May 2026 S1. This one: 15 May 2026 S1 See all 4 of this type

    51
    Let f:R→Rf : R \rightarrow R be defined by f(x)=x2+2x+3x2+x+1f(x) = \dfrac{x^2 + 2x + 3}{x^2 + x + 1}. If the range of f(x)f(x) is [a,b][a, b], then a+b=…a + b = \ldots

    Tap an option to check your answer.

  5. Question 5

    This type asked 4 times: May 2021 S1, 16 May 2023 S2, 10 May 2024 S2, 13 May 2026 S2. This one: 13 May 2026 S2 See all 4 of this type

    52
    If f(x)=sin⁡−1[log⁡1/2(x22)]f(x) = \sin^{-1}\left[\log_{1/2}\left(\dfrac{x^2}{2}\right)\right], then the domain of the function f(x)f(x) is:

    Tap an option to check your answer.

  6. Question 6

    This type asked 4 times: 9 May 2024 S1, 12 May 2024 S2, 17 Apr 2026 S1, 19 Apr 2026 S1. This one: 19 Apr 2026 S1 See all 4 of this type

    70
    If f(x)=x2f(x) = x^2 and g(x)=[x2]g(x) = [x^2] where [⋅][\cdot] represents the greatest integer function then, (f∘g)(32)+(g∘f)(32)(f \circ g)\left(\dfrac{3}{2}\right) + (g \circ f)\left(\dfrac{3}{2}\right) is equal to ...

    Tap an option to check your answer.

  7. Question 7

    This type asked 3 times: 14 May 2024 S2, 13 Apr 2026 S2, 20 Apr 2026 S2. This one: 20 Apr 2026 S2 See all 3 of this type

    68
    If f(x)=2x−1x+5,x≠−5f(x) = \dfrac{2x - 1}{x + 5}, x \neq -5 then f−1(x)f^{-1}(x) is equal to

    Tap an option to check your answer.

  8. Question 8

    This type asked 3 times: 4 May 2023 S2, 11 May 2024 S2, 17 Apr 2026 S2. This one: 17 Apr 2026 S2 See all 3 of this type

    67
    If f(x)=1−x1+xf(x) = \dfrac{1 - x}{1 + x}, then f(f(cos⁡x))=f(f(\cos x)) =

    Tap an option to check your answer.

  9. Question 9

    This type asked 3 times: 2 May 2023 S1, 10 May 2023 S2, 16 Apr 2026 S1. This one: 16 Apr 2026 S1 See all 3 of this type

    69
    If f(x)=4x+36x−4,x≠23f(x) = \dfrac{4x + 3}{6x - 4}, x \neq \dfrac{2}{3} and (fof)(x)=g(x)(x) = g(x) where g:R−{23}→R−{23}g : \mathbb{R} - \left\{\dfrac{2}{3}\right\} \to \mathbb{R} - \left\{\dfrac{2}{3}\right\}, then (g∘g∘g∘g∘g)(3)=(g \circ g \circ g \circ g \circ g)(3) =

    Tap an option to check your answer.

  10. Question 10

    Asked 2 times: 11 Apr 2026 S1*, 20 Apr 2026 S1 (* = numbers or wording changed that year) See all 2 times it was asked

    68
    The domain of the function f(x)=x−1+6−xf(x) = \sqrt{x - 1} + \sqrt{6 - x} is...

    Tap an option to check your answer.