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Day 132: MHT-CET Maths

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

  1. Question 1

    Trigonometry - II. Asked 2 times: 9 May 2024 S1, 12 May 2024 S2 See all 2 times it was asked

    110
    cos⁡248°−sin⁡212°=\cos^2 48° - \sin^2 12° = ……. if sin⁡18°=5−14\sin 18° = \frac{\sqrt{5}-1}{4}

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  2. Question 2

    Vectors. Asked 2 times: 11 May 2023 S2*, 12 May 2024 S2 (* = numbers or wording changed that year) See all 2 times it was asked

    144
    If a⃗,b⃗,c⃗\vec{a}, \vec{b}, \vec{c} are three non-zero vectors, no two of them are collinear, a⃗+2b⃗\vec{a}+2\vec{b} is collinear with c⃗\vec{c}, b⃗+3c⃗\vec{b}+3\vec{c} is collinear with a⃗\vec{a}, then a⃗+2b⃗\vec{a}+2\vec{b} is

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  3. Question 3

    Vectors. Asked 2 times: 2 May 2023 S2*, 12 May 2024 S2 (* = numbers or wording changed that year) See all 2 times it was asked

    111
    The unit vector which is orthogonal to the vector 3i^+2j^+6k^3\hat{i}+2\hat{j}+6\hat{k} and coplanar with the vectors 2i^+j^+k^2\hat{i}+\hat{j}+\hat{k} and i^+j^+k^\hat{i}+\hat{j}+\hat{k} is

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  4. Question 4

    Differentiation. Asked 2 times: 9 May 2024 S1*, 12 May 2024 S1 (* = numbers or wording changed that year) See all 2 times it was asked

    109
    The derivative of f(tan⁡x)f(\tan x) w.r.t. g(sec⁡x)g(\sec x) at x=π4x=\frac{\pi}{4}, where f′(1)=2f'(1)=2 and g′(2)=4g'(\sqrt{2})=4, is

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  5. Question 5

    Vectors. Asked 2 times: 16 May 2023 S2*, 12 May 2024 S1 (* = numbers or wording changed that year) See all 2 times it was asked

    101
    If a⃗,b⃗,c⃗\vec{a}, \vec{b}, \vec{c} are three vectors, ∣a⃗∣=2|\vec{a}|=2, ∣b⃗∣=4|\vec{b}|=4, ∣c⃗∣=1|\vec{c}|=1, ∣b⃗×c⃗∣=15|\vec{b}\times\vec{c}|=\sqrt{15} and b⃗=2c⃗+λa⃗\vec{b}=2\vec{c}+\lambda\vec{a}, then the value of λ\lambda is

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