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Day 514: MHT-CET Maths

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

  1. Question 1

    Applications of Derivative. Asked once: 11 May 2024 S2

    113
    If a and b are positive numbers such that a>ba>b, then the minimum value of asec⁡θ−btan⁡θa\sec\theta - b\tan\theta (0<θ<π2)\left(0<\theta<\frac{\pi}{2}\right) is

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  2. Question 2

    Differentiation. Asked once: 21 Apr 2025 S2

    149
    If y=ax⋅b2x−1y=a^{x}\cdot b^{2x- 1}, then d2ydx2\frac{d^{2}y}{dx^{2}} is equal to

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  3. Question 3

    Indefinite Integration. Asked once: 13 Apr 2026 S1

    78
    If ∫sin⁡2xsin⁡4x+cos⁡4x dx=f(x)+c\displaystyle\int\dfrac{\sin 2x}{\sin^4 x + \cos^4 x}\,dx = f(x) + c where c is constant of integration, then the value of tan⁡(f(x))\tan(f(x)) is

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  4. Question 4

    Line and Plane. Asked once: 22 Apr 2025 S2

    102
    The line L is passing through (1,2,3)(1,2,3). The distance of any point on the line L from the line r‾=(3λ−1)i^+(−2λ+3)j^+(4+λ)k^\overline{r}= (3\lambda - 1)\widehat{i}+ ( - 2\lambda + 3)\widehat{j}+ (4 + \lambda)\widehat{k} is constant. Then the line L does not pass through the point

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  5. Question 5

    Trigonometric Functions. Asked once: 23 Apr 2025 S1

    130
    In a triangle ABC , with usual notations, if a=5, b=4,cos⁡( A−B)=3132a = 5,\text{ }b = 4,\cos(\text{ }A - B) =\frac{31}{32}, then c=c =

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