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Day 510: MHT-CET Maths

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

  1. Question 1

    Trigonometry - II. Asked once: 9 May 2023 S1

    119
    If α+β=π2\alpha+\beta=\frac{\pi}{2} and β+γ=α\beta+\gamma=\alpha, then tan⁡α\tan\alpha equals

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  2. Question 2

    Vectors. Asked once: 16 Apr 2026 S2

    91
    Let aˉ,bˉ\bar{a}, \bar{b} and cˉ\bar{c} be three coplanar unit vectors. A unit vector dˉ\bar{d} is perpendicular to them. If (aˉ×bˉ)×(cˉ×dˉ)=326i^−213j^+613k^(\bar{a} \times \bar{b}) \times (\bar{c} \times \bar{d}) = \dfrac{3}{26}\hat{i} - \dfrac{2}{13}\hat{j} + \dfrac{6}{13}\hat{k} and the angle between aˉ\bar{a} and bˉ\bar{b} is 30∘30^\circ, then cˉ\bar{c} is equal to...

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  3. Question 3

    Applications of Derivative. Asked once: 14 May 2024 S2

    140
    Let P(x)P(x) be a polynomial of degree 2 with P(2)=−1,P′(2)=0,P′′(2)=2P(2)=-1, P'(2)=0, P''(2)=2, then P(1.001)P(1.001) is

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  4. Question 4

    Definite Integration. Asked once: 3 May 2023 S1

    108
    If ∫0π/3tan⁡θ2ksec⁡θ dθ=1−12, (k>0)\int_0^{\pi/3}\frac{\tan\theta}{\sqrt{2k\sec\theta}}\,d\theta=1-\frac{1}{\sqrt{2}},\ (k>0), then the value of kk is

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  5. Question 5

    Differentiation. Asked once: 26 Apr 2025 S1

    148
    If f(x)=sin⁡2x1+cot⁡x+cos⁡2x1+tan⁡xf\left( x \right)=\frac{\sin^{2}x}{1 + \cot x}+\frac{\cos^{2}x}{1 + \tan x}, then the value of f′(π6)f^{'}\left( \frac{\pi}{6} \right) is equal to

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