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Day 526: MHT-CET Maths

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

  1. Question 1

    Line and Plane. Asked once: 19 Apr 2025 S2

    114
    The projection of the line segment joining the points (2,1,−3)(2,1, - 3) and (−1,0,2)( - 1,0,2) on the line whose direction ratios are 3,2,63,2,6 is

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  2. Question 2

    Trigonometric Functions. Asked once: 20 Apr 2025 S2

    122
    If 2tan⁡−1(cos⁡x)=tan⁡−1(2csc⁡x)2\tan^{- 1}(\cos x) =\tan^{- 1}(2\csc x), then the value of xx is

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  3. Question 3

    Vectors. Asked once: 23 Apr 2025 S1

    102
    Let a‾,b‾,c‾,d‾\overline{a},\overline{b},\overline{c},\overline{d} are vectors such that a‾×b‾=2i‾+3j‾−k‾\overline{a}\times\overline{b}= 2\overline{i}+ 3\overline{j}-\overline{k} and c‾×d‾=3i^+2j^+λk^\overline{c}\times\overline{d}= 3\widehat{i}+ 2\widehat{j}+\lambda\widehat{k} and if ∣aˉ⋅cˉbˉ⋅cˉaˉ⋅dˉbˉ⋅dˉ∣=0\left| \begin{matrix} \bar{a}\cdot\bar{c} & \bar{b}\cdot\bar{c} \\ \bar{a}\cdot\bar{d} & \bar{b}\cdot\bar{d} \end{matrix} \right|= 0, then λ=\lambda=

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  4. Question 4

    Applications of Derivative. Asked once: 10 May 2023 S1

    108
    The curve x4−2xy2+y2+3x−3y=0x^4-2xy^2+y^2+3x-3y=0 cuts the X-axis at (0,0)(0,0) at an angle of

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  5. Question 5

    Differentiation. Asked once: 11 May 2024 S2

    130
    If f(x)=3xf(x)=3^x, g(x)=4xg(x)=4^x, then f′(0)−g′(0)1+f′(0)g′(0)\frac{f'(0)-g'(0)}{1+f'(0)g'(0)} is

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