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Day 139: MHT-CET Maths

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

  1. Question 1

    Applications of Derivative. Asked 2 times: 10 May 2023 S1, 16 May 2023 S2 See all 2 times it was asked

    137
    The equation of the normal to the curve y=xlog⁡xy = x\log x parallel to 2x−2y+3=02x-2y+3=0 is

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  2. Question 2

    Vectors. Asked 2 times: 4 May 2023 S2*, 16 May 2023 S2 (* = numbers or wording changed that year) See all 2 times it was asked

    114
    If a⃗=i^−2j^+3k^\vec{a} = \hat{i} - 2\hat{j} + 3\hat{k} and b⃗=2i^+3j^−k^\vec{b} = 2\hat{i} + 3\hat{j} - \hat{k} are two vectors, then the angle between the vectors 3a⃗+5b⃗3\vec{a} + 5\vec{b} and 5a⃗+3b⃗5\vec{a} + 3\vec{b} is

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  3. Question 3

    Circle. Asked 2 times: 3 May 2023 S1*, 16 May 2023 S1 (* = numbers or wording changed that year) See all 2 times it was asked

    130
    The equation of the circle, concentric with the circle 2x2+2y2−6x+8y+1=02x^2+2y^2-6x+8y+1=0 and double of its area is

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  4. Question 4

    Differentiation. Asked 2 times: 3 May 2023 S1, 16 May 2023 S1 See all 2 times it was asked

    131
    If y=sec⁡(tan⁡−1x)y = \sec(\tan^{-1}x), then dydx\frac{dy}{dx} at x=1x=1 is equal to

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  5. Question 5

    Limits. Asked 2 times: 3 May 2023 S1, 16 May 2023 S1 See all 2 times it was asked

    121
    Let f(x)=1−tan⁡x4x−π,  x≠π4,  x∈[0,π2)f(x) = \frac{1-\tan x}{4x-\pi},\; x \neq \frac{\pi}{4},\; x \in \left[0, \frac{\pi}{2}\right). f(x)f(x) is continuous in [0,π2)\left[0, \frac{\pi}{2}\right), then f ⁣(π4)f\!\left(\frac{\pi}{4}\right) is

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