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Day 273: MHT-CET Maths

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

  1. Question 1

    Differentiation. Asked once: 22 Apr 2025 S2 (same type asked 9 times) See all 9 of this type

    105
    If f(1)=3,f′(1)=2f(1) = 3,f^{'}(1) = 2, then ddx{log⁡[f(ex+2x)]}\frac{d}{dx}\left\{ \log\left\lbrack f\left( e^{x}+ 2x \right) \right\rbrack \right\} at x=0x = 0 is

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  2. Question 2

    Differentiation. Asked once: 12 May 2024 S1 (same type asked 9 times) See all 9 of this type

    143
    If y=(1+x)(1+x2)(1+x4)⋯(1+x2n)y=(1+x)(1+x^{2})(1+x^{4})\cdots(1+x^{2^{n}}) then the value of dydx\frac{dy}{dx} at x=0x=0 is

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  3. Question 3

    Binomial Distribution. Asked once: 16 May 2023 S1 (same type asked 9 times) See all 9 of this type

    150
    A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one by one, with replacement, then the variance of the number of green balls drawn is

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  4. Question 4

    Differential Equations. Asked once: 11 Apr 2026 S2 (same type asked 8 times) See all 8 of this type

    85
    The solution of the differential equation 2xdydx−y=32x\dfrac{dy}{dx} - y = 3 represents a family of

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  5. Question 5

    Line and Plane. Asked once: 17 Apr 2026 S2 (same type asked 8 times) See all 8 of this type

    96
    If the distance of point B(2,1,−3)B(2, 1, -3) from the line passing through the point A(4,−2,2)A(4, -2, 2), and parallel to the vector c⃗=−4i^−6j^−2k^\vec{c} = -4\hat{i} - 6\hat{j} - 2\hat{k} is xx, then x4+x2+541=x^4 + x^2 + 541 =

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