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Day 536: MHT-CET Maths

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

  1. Question 1

    Vectors. Asked once: 19 Apr 2025 S1

    103
    If [2pˉ−3rˉqˉsˉ]+[3pˉ+2qˉ rˉ sˉ]=m[pˉrˉsˉ]+n[qˉrˉsˉ]+t[pˉqˉsˉ]\begin{bmatrix} 2\bar{p}- 3\bar{r} & \bar{q} & \bar{s} \end{bmatrix}+ \lbrack 3\bar{p}+ 2\bar{q}\ \bar{r}\ \bar{s}\rbrack =m\begin{bmatrix} \bar{p} & \bar{r} & \bar{s} \end{bmatrix}+n\begin{bmatrix} \bar{q} & \bar{r} & \bar{s} \end{bmatrix}+t\begin{bmatrix} \bar{p} & \bar{q} & \bar{s} \end{bmatrix}, then the values of m,n,tm,n,t respectively are ____\_\_\_\_

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  2. Question 2

    Applications of Derivative. Asked once: 2 May 2023 S1

    111
    The length of the longest interval, in which the function 3sin⁡x−4sin⁡3x3\sin x - 4\sin^3 x is increasing, is

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  3. Question 3

    Differentiation. Asked once: May 2022 S1

    135
    If y=cos⁡(sin⁡x2)y = \cos(\sin x^2), then dydx\frac{dy}{dx} at x=π2x = \sqrt{\frac{\pi}{2}} is

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  4. Question 4

    Indefinite Integration. Asked once: 12 May 2024 S1

    138
    ∫x2+1x(x2−1)dx=\displaystyle\int\frac{x^{2}+1}{x(x^{2}-1)}dx=

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  5. Question 5

    Line and Plane. Asked once: 15 May 2023 S2

    140
    The equation of a line passing through the point (2,−1,1)(2,-1,1) and parallel to the line joining the points i^+2j^+2k^\hat{i}+2\hat{j}+2\hat{k} and −i^+4j^+k^-\hat{i}+4\hat{j}+\hat{k} is

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