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Day 414: MHT-CET Maths

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

  1. Question 1

    Limits. Asked once: May 2021 S1 (same type asked 10 times) See all 10 of this type

    119
    If f(x)={sin⁡3(x)⋅log⁡(1+3x)(tan⁡−1x)2(e5x−1)xx≠0ax=0f(x) = \begin{cases} \dfrac{\sin^{3}(\sqrt{x}) \cdot \log(1 + 3x)}{\left(\tan^{-1}\sqrt{x}\right)^{2}\left(e^{5\sqrt{x}} - 1\right)x} & x \neq 0 \\ a & x = 0 \end{cases} is continuous in [0,1][0,1], then aa equals

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  2. Question 2

    Mathematical Logic. Asked once: 16 May 2023 S1 (same type asked 19 times) See all 19 of this type

    102
    The proposition (∼p)∨(p∧∼q)(\sim p) \vee (p \wedge \sim q) is equivalent to

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  3. Question 3

    Definite Integration. Asked once: 3 May 2023 S2 (same type asked 13 times) See all 13 of this type

    119
    The value of the integral ∫−π/2π/2[x2+log⁡ ⁣(π−xπ+x)]cos⁡x dx\int_{-\pi/2}^{\pi/2}\left[x^{2}+\log\!\left(\frac{\pi-x}{\pi+x}\right)\right]\cos x\,dx is equal to

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  4. Question 4

    Linear Programming. Asked once: 2 May 2023 S2 (same type asked 12 times) See all 12 of this type

    118
    The shaded region in the following figure is the solution set of the inequations

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  5. Question 5

    Vectors. Asked once: 2 May 2023 S1 (same type asked 11 times) See all 11 of this type

    112
    The scalar a⃗⋅[(b⃗+c⃗)×(a⃗+b⃗+c⃗)]\vec{a} \cdot [(\vec{b} + \vec{c}) \times (\vec{a} + \vec{b} + \vec{c})] equals

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