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Day 148: MHT-CET Maths

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

  1. Question 1

    Indefinite Integration. This type asked 2 times: 9 May 2024 S2, 15 May 2026 S2. This one: 15 May 2026 S2 See all 2 of this type

    79
    If ∫(tan⁡x+cot⁡x) dx=atan⁡−1(tan⁡x−1btan⁡x)+c\int(\sqrt{\tan x} + \sqrt{\cot x})\, dx = a\tan^{-1}\left(\dfrac{\tan x - 1}{\sqrt{b\tan x}}\right) + c, for x∈(0,π2)x \in \left(0, \dfrac{\pi}{2}\right), then a10+b5=⋯a^{10} + b^5 = \cdots

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  2. Question 2

    Vectors. This type asked 2 times: 10 May 2024 S2, 15 May 2026 S2. This one: 15 May 2026 S2 See all 2 of this type

    89
    If aˉ=2i^−j^+k^\bar{a} = 2\hat{i} - \hat{j} + \hat{k}, bˉ=i^+3j^−k^\bar{b} = \hat{i} + 3\hat{j} - \hat{k}, cˉ=−2i^+j^−3k^\bar{c} = -2\hat{i} + \hat{j} - 3\hat{k} and dˉ=3i^+2j^+5k^\bar{d} = 3\hat{i} + 2\hat{j} + 5\hat{k}, then the value of x2+z2−yx^2 + z^2 - y is ⋯\cdots, where dˉ=xaˉ+ybˉ+zcˉ\bar{d} = x\bar{a} + y\bar{b} + z\bar{c}

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  3. Question 3

    Definite Integration. This type asked 2 times: 16 Apr 2026 S1, 15 May 2026 S1. This one: 15 May 2026 S1 See all 2 of this type

    83
    ∫π/6π/3sin⁡2xlog⁡(tan⁡x) dx=…\int_{\pi/6}^{\pi/3} \sin 2x \log(\tan x)\, dx = \ldots

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  4. Question 4

    Trigonometric Functions. This type asked 2 times: 15 Apr 2026 S1, 15 May 2026 S1. This one: 15 May 2026 S1 See all 2 of this type

    67
    If tan⁡−1[5+261−6]=a+tan⁡−1(2)\tan^{-1}\left[\dfrac{\sqrt{5 + 2\sqrt{6}}}{1 - \sqrt{6}}\right] = a + \tan^{-1}(\sqrt{2}), then csc⁡(a)=…\csc(a) = \ldots

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  5. Question 5

    Trigonometry - II. This type asked 2 times: 15 Apr 2026 S2, 15 May 2026 S1. This one: 15 May 2026 S1 See all 2 of this type

    52
    The value of the expression cos⁡(π24)cos⁡(π12)cos⁡(π6)cos⁡(π3)\cos\left(\dfrac{\pi}{24}\right)\cos\left(\dfrac{\pi}{12}\right)\cos\left(\dfrac{\pi}{6}\right)\cos\left(\dfrac{\pi}{3}\right) is:

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