PYQ Vault

Day 530: MHT-CET Maths

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

  1. Question 1

    Vectors. Asked once: 20 Apr 2025 S2

    103
    In a triangle ABC with usual notations if ∣BC‾∣=8,∣CA‾∣=7,∣AB‾∣=10|\overline{BC}| = 8,|\overline{CA}| = 7,|\overline{AB}| = 10 then the projection of AB‾\overline{AB} on AC‾\overline{AC} is

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  2. Question 2

    Applications of Derivative. Asked once: 4 May 2023 S2

    148
    If f(x)=sin⁡4x+cos⁡4x, 0<x<π2f(x)=\sin^4x+\cos^4x,\, 0<x<\frac{\pi}{2}, then the function has minimum value ___ at x=x=

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  3. Question 3

    Differentiation. Asked once: 16 May 2023 S1

    137
    Let the function g:(−∞,∞)→(−π2,π2)g:(-\infty,\infty) \to \left(-\frac{\pi}{2},\frac{\pi}{2}\right) be given by g(u)=2tan⁡−1(eu)−π2g(u) = 2\tan^{-1}(e^u) - \frac{\pi}{2}. Then g is

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  4. Question 4

    Indefinite Integration. Asked once: 14 May 2024 S2

    136
    If ∫dxcot⁡2x−1=1Alog⁡∣sec⁡2x+tan⁡2x∣−xB+c\int \frac{dx}{\cot^2 x - 1} = \frac{1}{A}\log|\sec 2x + \tan 2x| - \frac{x}{B} + c, then A+BA+B =

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  5. Question 5

    Line and Plane. Asked once: 11 May 2024 S1

    116
    The mirror image of the point (1,2,3)(1,2,3) in a plane is (−73,−43,−13)\left(-\frac{7}{3},-\frac{4}{3},-\frac{1}{3}\right). Thus, the point lies on this plane.

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