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Day 525: MHT-CET Maths

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

  1. Question 1

    Trigonometric Functions. Asked once: 20 Apr 2025 S2

    101
    If 3sin⁡2θ=2sin⁡3θ3\sin2\theta= 2\sin3\theta and 0<θ<π0 <\theta<\pi, then the value of sin⁡θ\sin\theta is equal to

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  2. Question 2

    Vectors. Asked once: 23 Apr 2025 S1

    144
    If aˉ,bˉ,cˉ\bar{a},\bar{b},\bar{c} are three vectors such that ∣a‾∣=31,4∣ b‾∣=∣c‾∣=2|\overline{a}| =\sqrt{31},4|\overline{\text{ }b}| = |\overline{c}| = 2 and 2(a‾×b‾)=3(c‾×a‾)2(\overline{a}\times\overline{b}) = 3(\overline{c}\times\overline{a}) and if the angle between bˉ\bar{b} and cˉ\bar{c} is 2π3\frac{2\pi}{3} then ∣a‾×c‾a‾⋅b‾∣2=\left| \frac{\overline{a}\times\overline{c}}{\overline{a}\cdot\overline{b}} \right|^{2}=

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  3. Question 3

    Applications of Derivative. Asked once: 10 May 2023 S1

    123
    A point moves along the arc of parabola y=2x2y=2x^2. Its abscissa increases uniformly at the rate of 2 units/sec. At the instant, the point is passing through (1,2)(1,2), its distance from origin is increasing at the rate of

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  4. Question 4

    Differentiation. Asked once: 12 May 2024 S2

    101
    If tan⁡y=xsin⁡α1−xcos⁡α\tan y = \frac{x\sin\alpha}{1 - x\cos\alpha} and dydx=mx2+2nx+1\frac{dy}{dx} = \frac{m}{x^2 + 2nx + 1}, then m2+n2m^2 + n^2 is

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  5. Question 5

    Indefinite Integration. Asked once: 20 Apr 2025 S1

    107
    ∫sin⁡5xdx=\int\sin^{5}xdx=

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