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Day 512: MHT-CET Maths

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

  1. Question 1

    Vectors. Asked once: 16 Apr 2026 S1

    85
    If a vector 3i^+4j^−5k^3\hat{i} + 4\hat{j} - 5\hat{k} is rotated through a certain angle about the origin in the anti-clockwise direction, then the components of the new vector are a+1,−3,5a + 1, -3, 5 . The possible values of aa is

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  2. Question 2

    Applications of Derivative. Asked once: 14 May 2024 S2

    133
    The diagonal of a square is changing at the rate of 0.5 cm/sec. Then the rate of change of area when the area is 400 cm2^2 is equal to

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  3. Question 3

    Definite Integration. Asked once: May 2021 S1

    150
    ∫π/6π/2csc⁡x⋅cot⁡x1+csc⁡2x dx\int_{\pi/6}^{\pi/2}\frac{\csc x\cdot\cot x}{1+\csc^2 x}\,dx

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  4. Question 4

    Differentiation. Asked once: 21 Apr 2025 S2

    136
    If f(θ)=cos⁡θ1⋅cos⁡θ2⋅cos⁡θ3f(\theta) = \cos\theta_{1}\cdot \cos\theta_{2}\cdot \cos\theta_{3} ____\_\_\_\_ cos⁡θn\cos\theta_{n}, then tan⁡θ1+tan⁡θ2+tan⁡θ3+………+tan⁡θn=\tan\theta_{1}+ \tan\theta_{2}+ \tan\theta_{3}+ \ldots\ldots\ldots + \tan\theta_{n}=

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  5. Question 5

    Indefinite Integration. Asked once: 13 Apr 2026 S2

    79
    If ∫x+1x2+1 dx=tan⁡−1x+g(x)+c\displaystyle\int\dfrac{x + 1}{x^2 + 1}\,dx = \tan^{-1}x + g(x) + c, where cc is constant of integration, then the function g(x)g(x) is monotonically increasing in the interval

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