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Day 279: MHT-CET Maths

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

  1. Question 1

    Differentiation. Asked once: 13 May 2026 S1 (same type asked 7 times) See all 7 of this type

    74
    If x=2tan⁡−1tx = \sqrt{2^{\tan^{-1}t}} and y=2cot⁡−1t3y = \sqrt[3]{2^{\cot^{-1}t}}, then dydx=…\dfrac{dy}{dx} = \ldots

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  2. Question 2

    Line and Plane. Asked once: 11 Apr 2026 S2 (same type asked 7 times) See all 7 of this type

    93
    The point of intersection of the two lines x−33=y−3−1,z−1=0\dfrac{x - 3}{3} = \dfrac{y - 3}{-1}, z - 1 = 0 and x−62=z−13,y−2=0\dfrac{x - 6}{2} = \dfrac{z - 1}{3}, y - 2 = 0 is....

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  3. Question 3

    Trigonometric Functions. Asked once: 18 Apr 2026 S1 (same type asked 7 times) See all 7 of this type

    71
    If ∑n=12026tan⁡−1(1n2+n+1)=tan⁡−1(1−1x)\displaystyle\sum_{n=1}^{2026}\tan^{-1}\left(\dfrac{1}{n^2 + n + 1}\right) = \tan^{-1}\left(1 - \dfrac{1}{x}\right), where x≠0x \neq 0, then x=x =

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  4. Question 4

    Trigonometric Functions. Asked once: 16 Apr 2026 S2 (same type asked 7 times) See all 7 of this type

    54
    The general solution of the equation cot⁡θ⋅cot⁡2θ=1\cot\theta \cdot \cot 2\theta = 1 is...

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  5. Question 5

    Line and Plane. Asked once: 25 Apr 2025 S1 (same type asked 7 times) See all 7 of this type

    118
    The length of the foot of the perpendicular from the point (1,32,2)\left( 1,\frac{3}{2},2 \right) to the plane 2x−2y+4z+17=02x- 2y+ 4z+ 17 = 0 is

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