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Day 7: MHT-CET Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    Limits. 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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  2. Question 2

    Vectors. This type asked 10 times: 2 May 2023 S1, 3 May 2023 S1, 4 May 2023 S2, 9 May 2023 S1, 15 May 2023 S1, 10 May 2024 S1, 11 May 2024 S1, 11 May 2024 S2, 14 May 2024 S2, 15 Apr 2026 S2. This one: 15 Apr 2026 S2 See all 10 of this type

    91
    Let a⃗=i^+2j^−2k^\vec{a} = \hat{i} + 2\hat{j} - 2\hat{k} and b⃗=i^−j^+k^\vec{b} = \hat{i} - \hat{j} + \hat{k}. If c⃗\vec{c} is a vector such that a⃗⋅c⃗=∣c⃗∣,∣c⃗−a⃗∣=22\vec{a}\cdot\vec{c} = |\vec{c}|, |\vec{c} - \vec{a}| = 2\sqrt{2} and the angle between a⃗×b⃗\vec{a} \times \vec{b} and c⃗\vec{c} is 60∘60^\circ, then ∣(a⃗×b⃗)×c⃗∣|(\vec{a} \times \vec{b}) \times \vec{c}| is equal to

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  3. Question 3

    Indefinite Integration. This type asked 10 times: May 2022 S1, 3 May 2023 S1, 4 May 2023 S1, 9 May 2023 S1, 16 May 2023 S1, 16 May 2023 S2, 12 May 2024 S2, 22 Apr 2025 S2, 26 Apr 2025 S1, 15 Apr 2026 S1. This one: 15 Apr 2026 S1 See all 10 of this type

    76
    If ∫1cos⁡3xsin⁡2x dx=p(tan⁡2x+q)tan⁡x+c\displaystyle\int\dfrac{1}{\cos^3 x\sqrt{\sin 2x}}\,dx = p(\tan^2 x + q)\sqrt{\tan x} + c, then the values of pp and qq respectively are

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  4. Question 4

    Line and Plane. This type asked 9 times: 15 May 2023 S2, 16 May 2023 S1, 9 May 2024 S2, 10 May 2024 S2, 19 Apr 2025 S2, 20 Apr 2025 S2, 26 Apr 2025 S2, 13 Apr 2026 S2, 19 May 2026 S2. This one: 19 May 2026 S2 See all 9 of this type

    96
    The equation of a plane passing through the intersection of two planes r⃗⋅(i^−2j^+3k^)=4\vec{r} \cdot (\hat{i} - 2\hat{j} + 3\hat{k}) = 4 and r⃗⋅(2i^+j^−3k^)=7\vec{r} \cdot (2\hat{i} + \hat{j} - 3\hat{k}) = 7 and parallel to Y-axis is

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  5. Question 5

    Mathematical Logic. This type asked 9 times: 10 May 2023 S2, 11 May 2023 S1, 11 May 2023 S2, 15 May 2023 S1, 12 May 2024 S1, 12 May 2024 S2, 20 Apr 2025 S2, 17 Apr 2026 S1, 19 May 2026 S2. This one: 19 May 2026 S2 See all 9 of this type

    60
    Consider the following statements - (i) If a person is social, then he is happy. (ii) If a person is not social, then he is not happy. (iii) If a person is not happy, then he is not social. (iv) If a person is happy, then he is social. Which of the above statements are equivalent?

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