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Day 260: MHT-CET Maths

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

  1. Question 1

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

    127
    If tan⁡−1a+tan⁡−1b+tan⁡−1c=π\tan^{-1}a+\tan^{-1}b+\tan^{-1}c=\pi, then which of the following statement is true?

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  2. Question 2

    Trigonometry - II. Asked once: 4 May 2023 S1 (same type asked 2 times) See all 2 of this type

    138
    The value of the expression 3csc⁡20∘−sec⁡20∘\sqrt{3}\csc20^\circ-\sec20^\circ is equal to

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  3. Question 3

    Trigonometry - II. Asked once: 16 May 2023 S1 (same type asked 2 times) See all 2 of this type

    142
    The maximum value of cos⁡α1⋅cos⁡α2⋯cos⁡αn\cos\alpha_1 \cdot \cos\alpha_2 \cdots \cos\alpha_n under the constraints 0≤α1,…,αn≤π20 \leq \alpha_1,\ldots,\alpha_n \leq \frac{\pi}{2} and cot⁡α1⋅cot⁡α2⋯cot⁡αn=1\cot\alpha_1 \cdot \cot\alpha_2 \cdots \cot\alpha_n = 1 is

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  4. Question 4

    Differentiation. Asked once: 9 May 2024 S2 (same type asked 2 times) See all 2 of this type

    137
    If xk+yk=ak    (a,k>0)x^k + y^k = a^k\;\;(a,k > 0) and dydx+(yx)1/3=0\dfrac{dy}{dx} + \left(\dfrac{y}{x}\right)^{1/3} = 0, then kk has the value

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  5. Question 5

    Line and Plane. Asked once: 14 May 2024 S1 (same type asked 2 times) See all 2 of this type

    128
    If the shortest distance between the lines x−12=y−23=z−3λ\dfrac{x-1}{2}=\dfrac{y-2}{3}=\dfrac{z-3}{\lambda} and x−21=y−44=z−55\dfrac{x-2}{1}=\dfrac{y-4}{4}=\dfrac{z-5}{5} is 13\dfrac{1}{\sqrt{3}}, then sum of possible values of λ\lambda is

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