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Day 497: MHT-CET Maths

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

  1. Question 1

    Vectors. Asked once: 19 Apr 2026 S1

    92
    If ABCABC is a right-angled triangle in which BCBC is the longest side and the position vector of BB and CC are respectively 3i^−2j^+k^3\hat{i} - 2\hat{j} + \hat{k} and 5i^+j^−3k^5\hat{i} + \hat{j} - 3\hat{k}, then the value of AB‾⋅AC‾+BA‾⋅BC‾+CA‾⋅CB‾\overline{AB}\cdot\overline{AC} + \overline{BA}\cdot\overline{BC} + \overline{CA}\cdot\overline{CB} is

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  2. Question 2

    Applications of Derivative. Asked once: 23 Apr 2025 S1

    126
    The maximum value of x2/3+(x−2)2/3x^{2/3}+ (x- 2)^{2/3} is

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  3. Question 3

    Definite Integration. Asked once: 21 Apr 2025 S2

    130
    ∫0π4cos⁡2xsin⁡2x(cos⁡3x+sin⁡3x)2 dx=\displaystyle\int_{0}^{\frac{\pi}{4}} \frac{\cos^{2}x\sin^{2}x}{\left(\cos^{3}x+\sin^{3}x\right)^{2}}\,dx=

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  4. Question 4

    Differentiation. Asked once: 15 Apr 2026 S1

    70
    If y=log⁡xxy = \log x^x, then the value of (dydx)2\left(\dfrac{dy}{dx}\right)^2 at x=e2x = e^2 is

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  5. Question 5

    Indefinite Integration. Asked once: 17 Apr 2026 S2

    80
    If f(x)=sin⁡−1x1−x2f(x) = \dfrac{\sin^{-1}x}{\sqrt{1 - x^2}} and g(x)=esin⁡−1xg(x) = e^{\sin^{-1}x}, then the value of ∫f(x)g(x) dx=…\displaystyle\int f(x)g(x)\,dx = \ldots

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