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Day 228: MHT-CET Maths

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

  1. Question 1

    Indefinite Integration. Asked once: 12 May 2026 S2 (same type asked 3 times) See all 3 of this type

    77
    If ∫x7ex dx=exf(x)+c\displaystyle\int x^7e^x\,dx = e^xf(x) + c, then f(x)f(x) is equal to...

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  2. Question 2

    Indefinite Integration. Asked once: 10 May 2023 S2 (same type asked 3 times) See all 3 of this type

    128
    If ∫dxex−1=2tan⁡−1(f(x))+c\int \frac{dx}{\sqrt{e^x - 1}} = 2\tan^{-1}(f(x)) + c where x>0x > 0, then f(x)f(x) is

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  3. Question 3

    Limits. Asked once: 15 Apr 2026 S2 (same type asked 3 times) See all 3 of this type

    62
    If lim⁡x→∞(2x−1)19⋅(3x+2)11(6x−5)30=2a⋅3b\displaystyle\lim_{x \to \infty}\dfrac{(2x - 1)^{19}\cdot(3x + 2)^{11}}{(6x - 5)^{30}} = 2^a \cdot 3^b, then a+b=a + b =

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  4. Question 4

    Vectors. Asked once: 13 May 2026 S2 (same type asked 3 times) See all 3 of this type

    90
    If the vector a⃗=xi^−j^+k^\vec{a} = x\hat{i} - \hat{j} + \hat{k} and b⃗=i^+yj^+zk^\vec{b} = \hat{i} + y\hat{j} + z\hat{k} are collinear, then a possible unit vector parallel to the vector i^+yj^+zk^\hat{i} + y\hat{j} + z\hat{k} is...

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  5. Question 5

    Definite Integration. Asked once: 16 Apr 2026 S2 (same type asked 3 times) See all 3 of this type

    80
    The value of integral ∫01cot⁡−1(1+x2−x) dx\displaystyle\int_0^1\cot^{-1}(1 + x^2 - x)\,dx is...

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