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Day 31: MHT-CET Maths

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

  1. Question 1

    Vectors. Asked 5 times: 2 May 2023 S1*, 11 May 2023 S2, 11 May 2024 S1*, 13 May 2024 S2, 25 Apr 2025 S1 (* = numbers or wording changed that year) See all 5 times it was asked

    144
    If aˉ,bˉ,cˉ\bar{a},\bar{b},\bar{c} are non coplanar unit vectors such that a‾×(b‾×c‾)=b‾+c‾2\overline{a}\times (\overline{b}\times\overline{c}) =\frac{\overline{b}+\overline{c}}{\sqrt{2}} then the angle between a‾\overline{a} and b‾\overline{b} is

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  2. Question 2

    Applications of Derivative. Asked 5 times: 3 May 2023 S2*, 11 May 2023 S2*, 16 May 2023 S1*, 16 May 2023 S2*, 12 May 2024 S1 (* = numbers or wording changed that year) See all 5 times it was asked

    121
    If x=−1x=-1 and x=2x=2 are extreme points of f(x)=αlog⁡∣x∣+βx2+xf(x)=\alpha\log|x|+\beta x^{2}+x, α\alpha and β\beta are constants, then the value of α2+2β\alpha^{2}+2\beta is

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  3. Question 3

    Differentiation. Asked 5 times: 10 May 2023 S1, 10 May 2023 S2, 9 May 2024 S2, 10 May 2024 S2, 12 May 2024 S1 See all 5 times it was asked

    133
    If log⁡(x+y)=2xy\log(x+y)=2xy, then dydx\frac{dy}{dx} at x=0x=0 is

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  4. Question 4

    Indefinite Integration. Asked 5 times: 2 May 2023 S2, 4 May 2023 S2, 10 May 2023 S2, 10 May 2024 S1, 10 May 2024 S2 See all 5 times it was asked

    138
    The value of ∫dxx2(x4+1)3/4\displaystyle\int\frac{dx}{x^2(x^4+1)^{3/4}} is

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  5. Question 5

    Applications of Derivative. This type asked 5 times: 10 May 2023 S2, 14 May 2024 S2, 17 Apr 2026 S2, 20 Apr 2026 S2, 19 May 2026 S2. This one: 19 May 2026 S2 See all 5 of this type

    75
    If the slope of the tangent to the curve 2y2=ax2+b2y^2 = ax^2 + b at (1,−1)(1, -1) is −1-1, then ...

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