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Limits

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 10 times: 21 Apr 2025 S1, 21 Apr 2025 S2, 23 Apr 2025 S1, 25 Apr 2025 S2, 16 Apr 2026 S2, 18 Apr 2026 S2, 12 May 2026 S1, 14 May 2026 S1, 15 May 2026 S1, 15 May 2026 S2. This one: 15 May 2026 S2 See all 10 of this type

    65
    If k>5k > 5 and lim⁡x→0k2x+25x−2⋅(5k)xtan⁡3x⋅ln⁡(1+3x)=lim⁡n→∞(n+1)!+n!(n+1)!−n!\lim_{x \to 0}\dfrac{k^{2x} + 25^x - 2\cdot(5k)^x}{\tan 3x \cdot \ln(1 + 3x)} = \lim_{n \to \infty}\dfrac{(n + 1)! + n!}{(n + 1)! - n!}, then value of kk is...

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  2. Question 2

    This type asked 10 times: 4 May 2023 S1, 9 May 2024 S2, 10 May 2024 S2, 12 May 2024 S1, 25 Apr 2025 S1, 16 Apr 2026 S2, 19 Apr 2026 S1, 13 May 2026 S2, 14 May 2026 S2, 15 May 2026 S2. This one: 15 May 2026 S2 See all 10 of this type

    64
    Let f(x)f(x) be a function continuous at x=0x = 0, defined for x≠0x \ne 0 as f(x)=1−cos⁡(1−cos⁡(6x))x2sin⁡2(3x)f(x) = \dfrac{1 - \cos(1 - \cos(6x))}{x^2\sin^2(3x)}. Then the value of f(0)f(0) is...

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  3. Question 3

    This type asked 10 times: May 2022 S1, 4 May 2023 S1, 10 May 2023 S1, 15 May 2023 S2, 10 May 2024 S1, 11 May 2024 S1, 12 May 2024 S1, 13 May 2024 S2, 22 Apr 2025 S1, 12 May 2026 S1. This one: 12 May 2026 S1 See all 10 of this type

    70
    If the function defined by f(x)={ax2+bx+1,∣2x−3∣≥23x+2,12<x<52f(x) = \begin{cases} ax^2 + bx + 1, & |2x - 3| \ge 2 \\ 3x + 2, & \dfrac{1}{2} < x < \dfrac{5}{2} \end{cases} is continuous in its domain, then the values of aa and bb respectively are

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  4. Question 4

    This type asked 10 times: May 2021 S1, 9 May 2023 S1, 14 May 2024 S2, 20 Apr 2025 S1, 20 Apr 2025 S2, 13 Apr 2026 S1, 13 Apr 2026 S2, 15 Apr 2026 S1, 16 Apr 2026 S1, 20 Apr 2026 S1. This one: 20 Apr 2026 S1 See all 10 of this type

    62
    lim⁡x→0[x⋅log⁡(1+4x)(e4x−1)2]=⋯\lim_{x \to 0}\left[\dfrac{x \cdot \log(1 + 4x)}{(e^{4x} - 1)^2}\right] = \cdots

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  5. Question 5

    This type asked 9 times: 11 May 2023 S2, 9 May 2024 S2, 11 May 2024 S2, 12 May 2024 S2, 19 Apr 2025 S1, 20 Apr 2025 S1, 22 Apr 2025 S2, 20 Apr 2026 S2, 19 May 2026 S1. This one: 19 May 2026 S1 See all 9 of this type

    71
    If f(x)={1−sin⁡5x5cos⁡2x,x<π2a,at x=π2b(1−sin⁡x)8(π−2x)2,x>π2f(x) = \begin{cases} \dfrac{1 - \sin^5 x}{5\cos^2 x} & , x < \dfrac{\pi}{2} \\ a & , \text{at } x = \dfrac{\pi}{2} \\ \dfrac{b(1 - \sin x)}{8(\pi - 2x)^2} & , x > \dfrac{\pi}{2} \end{cases} is continuous at x=π2x = \dfrac{\pi}{2}, then (ba)53=…\left(\dfrac{b}{a}\right)^{\frac{5}{3}} = \ldots

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  6. Question 6

    This type asked 7 times: 3 May 2023 S2, 10 May 2023 S2, 22 Apr 2025 S1, 22 Apr 2025 S2, 11 Apr 2026 S1, 19 Apr 2026 S2, 15 May 2026 S2. This one: 15 May 2026 S2 See all 7 of this type

    63
    If lim⁡x→0(f(x)x2)\lim_{x \to 0}\left(\dfrac{f(x)}{x^2}\right) exists finitely and lim⁡x→0(1+x+f(x)x)1/x=e3\lim_{x \to 0}\left(1 + x + \dfrac{f(x)}{x}\right)^{1/x} = e^3, then ∫f(x)⋅log⁡x dx\int f(x) \cdot \log x\, dx is equal to:

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  7. Question 7

    This type asked 6 times: 3 May 2023 S1, 16 May 2023 S1, 16 May 2023 S2, 19 Apr 2026 S1, 12 May 2026 S2, 19 May 2026 S2. This one: 19 May 2026 S2 See all 6 of this type

    58
    The value of lim⁡x→π4[4−(cos⁡x+sin⁡x)41−sin⁡2x]\lim_{x \to \frac{\pi}{4}}\left[\dfrac{4 - (\cos x + \sin x)^4}{1 - \sin 2x}\right] is equal to

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  8. Question 8

    This type asked 6 times: 16 May 2023 S2, 10 May 2024 S1, 10 May 2024 S2, 13 May 2024 S2, 14 May 2024 S1, 13 May 2026 S1. This one: 13 May 2026 S1 See all 6 of this type

    63
    The value of lim⁡x→∞(x3+6x2+13−x)\lim_{x \to \infty}\left(\sqrt[3]{x^3 + 6x^2 + 1} - x\right) is:

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  9. Question 9

    This type asked 6 times: 2 May 2023 S1, 3 May 2023 S2, 11 May 2024 S2, 19 Apr 2025 S2, 11 Apr 2026 S1, 12 May 2026 S2. This one: 12 May 2026 S2 See all 6 of this type

    62
    Consider the function: f(x)={x2+1if x<25if x=23x−1if x>2f(x) = \begin{cases} x^2 + 1 & \text{if } x < 2 \\ 5 & \text{if } x = 2 \\ 3x - 1 & \text{if } x > 2 \end{cases} Which of the following statements is correct ?

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  10. Question 10

    This type asked 5 times: 9 May 2023 S2, 15 May 2023 S1, 9 May 2024 S1, 18 Apr 2026 S1, 13 May 2026 S1. This one: 13 May 2026 S1 See all 5 of this type

    70
    The number of points of discontinuity of the function f(x)=1log⁡∣x2−1∣f(x) = \dfrac{1}{\log|x^2 - 1|} (where ∣⋅∣|\cdot| denotes the modulus function) is:

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