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Day 484: MHT-CET Maths

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

  1. Question 1

    Conic Sections. Asked once: 25 Apr 2025 S1

    103
    The eccentricity of the curve represented by x=3(cos⁡t+sin⁡t),y=4(cos⁡t−sin⁡t)x= 3(\cos t+ \sin t),y= 4(\cos t- \sin t) is

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  2. Question 2

    Definite Integration. Asked once: 13 Apr 2026 S2

    82
    If ∫π/6π/311+sin⁡x+cos⁡x dx=log⁡2\int_{\pi/6}^{\pi/3}\dfrac{1}{1 + \sin x + \cos x}\,dx = \log 2, then the value of ∫π/6π/3cos⁡x1+sin⁡x+cos⁡x dx=\int_{\pi/6}^{\pi/3}\dfrac{\cos x}{1 + \sin x + \cos x}\,dx = ............

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  3. Question 3

    Differentiation. Asked once: 18 Apr 2026 S2

    72
    Let y=x3ypy = \sqrt[p]{x^3y}. If dydx=32\dfrac{dy}{dx} = \dfrac{3}{2} when y=1y = 1, then the value of pp is equal to …\ldots

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  4. Question 4

    Indefinite Integration. Asked once: 18 Apr 2026 S2

    79
    Let f(x)=x,f1(x)=f(log⁡x),f2(x)=f1(log⁡x),f3(x)=f2(log⁡x),…f(x) = x, f_1(x) = f(\log x), f_2(x) = f_1(\log x), f_3(x) = f_2(\log x), \ldots and so on. Then ∫1f(x) f1(x) f2(x)…f2026(x) dx=…\displaystyle\int\dfrac{1}{f(x)\,f_1(x)\,f_2(x)\ldots f_{2026}(x)}\,dx = \ldots

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  5. Question 5

    Limits. Asked once: 10 May 2023 S2

    138
    lim⁡x→09x−4xx(9x+4x)=\lim_{x\to 0}\frac{9^x - 4^x}{x(9^x + 4^x)} =

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