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Day 456: MHT-CET Maths

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

  1. Question 1

    Indefinite Integration. Asked once: 12 May 2026 S2

    78
    The value of the integral ∫1cos⁡x⋅log⁡(tan⁡(π4+x2)) dx\displaystyle\int\dfrac{1}{\cos x \cdot \log\left(\tan\left(\dfrac{\pi}{4} + \dfrac{x}{2}\right)\right)}\,dx is....

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  2. Question 2

    Limits. Asked once: 25 Apr 2025 S2

    122
    Let f:R→Rf:\mathbb{R}\rightarrow\mathbb{R} is differentiable function having f(3)=3,f′(3)=127f(3) = 3,f^{'}(3) =\frac{1}{27} and g(x)={∫3f(x)3t2x−3dt, if x≠3 K, if x=3g(x) =\left\{ \begin{matrix} \int_{3}^{f(x)} \frac{3t^{2}}{x- 3}dt, & \text{~if~}x\neq 3 \\ \text{ }K, & \text{~if~}x= 3 \end{matrix} \right. is continuous at x=3x= 3, then K=K =

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  3. Question 3

    Line and Plane. Asked once: 12 May 2026 S1

    95
    The ratio in which the plane rˉ⋅(i^−2j^+3k^)=17\bar{r}\cdot(\hat{i} - 2\hat{j} + 3\hat{k}) = 17 divides the line segment joining the points (−1,4,7)(-1, 4, 7) and (3,−5,8)(3, -5, 8) is ...

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  4. Question 4

    Measures of Dispersion. Asked once: 2 May 2023 S2

    131
    Consider three observations a,b,ca, b, c such that b=a+cb = a+c. If the standard deviation of a+2,b+2,c+2a+2, b+2, c+2 is dd, then

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  5. Question 5

    Pair of Straight Lines. Asked once: 11 May 2024 S1

    105
    If the angle between the lines represented by the equation x2+λxy−y2tan⁡2θ=0x^2 + \lambda xy - y^2\tan^2\theta = 0 is 2θ2\theta, then the value of λ\lambda is

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