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Day 385: MHT-CET Maths

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

  1. Question 1

    Applications of Definite Integral. Asked once: 16 May 2023 S1 (same type asked 10 times) See all 10 of this type

    123
    The area (in sq. units) of the region described by {(x,y):y2≤2x}\{(x,y) : y^2 \leq 2x\} and y≥(4x−1)y \geq (4x-1) is

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  2. Question 2

    Limits. Asked once: 20 Apr 2025 S2 (same type asked 10 times) See all 10 of this type

    138
    lim⁡x→0(7x−1)4tan⁡(xk)⋅log⁡(1+x23)⋅sin⁡4x=3(log⁡7)3\lim_{x\rightarrow 0} \frac{\left( 7^{x}- 1 \right)^{4}}{\tan\left( \frac{x}{k} \right)\cdot \log\left( 1 +\frac{x^{2}}{3} \right)\cdot \sin4x}= 3(\log7)^{3}, then k=k =

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  3. Question 3

    Mathematical Logic. Asked once: 11 May 2023 S1 (same type asked 9 times) See all 9 of this type

    117
    Let p: A man is judge. q: He is honest. The inverse of p→qp \to q is

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  4. Question 4

    Probability Distribution. Asked once: 3 May 2023 S2 (same type asked 9 times) See all 9 of this type

    113
    For the probability distribution
    X:-2-10123
    p(x):0.10.20.20.30.150.05
    Then Var(X)\text{Var}(X) is (Given: (0.25)2=0.0625, (0.35)2=0.1225, (0.45)2=0.2025(0.25)^2=0.0625,\,(0.35)^2=0.1225,\,(0.45)^2=0.2025)

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  5. Question 5

    Limits. Asked once: 9 May 2024 S2 (same type asked 9 times) See all 9 of this type

    144
    f(x)={1−cos⁡kxx2,x≤0x16+x−4,x>0f(x) = \begin{cases}\dfrac{1-\cos kx}{x^2}, & x \leq 0 \\ \dfrac{\sqrt{x}}{\sqrt{16+\sqrt{x}}-4}, & x > 0\end{cases} is continuous at x=0x=0, then the value of kk is

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