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Day 243: MHT-CET Maths

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

  1. Question 1

    Vectors. Asked once: 10 May 2024 S2 (same type asked 2 times) See all 2 of this type

    136
    If a⃗=mb⃗+nc⃗\vec{a}=m\vec{b}+n\vec{c}, where a⃗=4i^+13j^−18k^\vec{a}=4\hat{i}+13\hat{j}-18\hat{k}, b⃗=i^−2j^+3k^\vec{b}=\hat{i}-2\hat{j}+3\hat{k}, c⃗=2i^+3j^−4k^\vec{c}=2\hat{i}+3\hat{j}-4\hat{k}, then m+n=m+n=

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  2. Question 2

    Definite Integration. Asked once: 16 Apr 2026 S1 (same type asked 2 times) See all 2 of this type

    79
    ∫π/6π/3sin⁡x−cos⁡x1+sin⁡xcos⁡x dx=\displaystyle\int_{\pi/6}^{\pi/3}\dfrac{\sin x - \cos x}{1 + \sin x\cos x}\,dx =

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  3. Question 3

    Trigonometric Functions. Asked once: 15 Apr 2026 S1 (same type asked 2 times) See all 2 of this type

    67
    If tan⁡−1[5−261+6]=π3−tan⁡−1(k)\tan^{-1}\left[\dfrac{\sqrt{5 - 2\sqrt{6}}}{1 + \sqrt{6}}\right] = \dfrac{\pi}{3} - \tan^{-1}(k), then sec⁡−1(k)=…\sec^{-1}(k) = \ldots

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  4. Question 4

    Trigonometry - II. Asked once: 15 Apr 2026 S2 (same type asked 2 times) See all 2 of this type

    56
    If 33θ=π33\theta = \pi, then the value of cos⁡θcos⁡2θcos⁡4θcos⁡8θcos⁡16θ\cos\theta\cos 2\theta\cos 4\theta\cos 8\theta\cos 16\theta is

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  5. Question 5

    Probability Distribution. Asked once: 20 Apr 2025 S2 (same type asked 2 times) See all 2 of this type

    143
    Two numbers are selected at random, without replacement from the first 6 positive integers. Let X denote the larger of the two numbers. Then E(X)=E(X) =

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