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Day 545: MHT-CET Maths

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

  1. Question 1

    Vectors. Asked once: 4 May 2023 S1

    119
    Let p⃗\vec{p} and q⃗\vec{q} be the position vectors of P and Q respectively, with respect to O and ∣p⃗∣=p|\vec{p}|=p, ∣q⃗∣=q|\vec{q}|=q. The points R and S divide PQ internally and externally in the ratio 2:3 respectively. If OR and OS are perpendiculars, then

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  2. Question 2

    Indefinite Integration. Asked once: 15 May 2023 S1

    112
    The value of ∫sec⁡x⋅tan⁡x9−16tan⁡2x dx\int \frac{\sec x \cdot \tan x}{\sqrt{9-16\tan^{2}x}}\,dx is equal to

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  3. Question 3

    Trigonometric Functions. Asked once: 3 May 2023 S2

    132
    Let α\alpha and β\beta be two real roots of the equation (k+1)tan⁡2x−2 λtan⁡x=(1−k)(k+1)\tan^{2}x-\sqrt{2}\,\lambda\tan x=(1-k) where k(≠−1)k(\neq-1) and λ\lambda are real numbers. If tan⁡2(α+β)=50\tan^{2}(\alpha+\beta)=50, then a value of λ\lambda is

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  4. Question 4

    Vectors. Asked once: May 2021 S1

    133
    If a⃗=3i^−2j^+k^\vec{a} = 3\hat{i} - 2\hat{j} + \hat{k} and b⃗=2i^−4j^−3k^\vec{b} = 2\hat{i} - 4\hat{j} - 3\hat{k}, then ∣a⃗−2b⃗∣|\vec{a} - 2\vec{b}| will be

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  5. Question 5

    Indefinite Integration. Asked once: 11 May 2023 S2

    124
    If f(x)=1+x; g(x)=log⁡xf(x)=1+x;\ g(x)=\log x, then ∫g(f(x)) dx\int g(f(x))\,dx is equal to

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