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Day 127: MHT-CET Maths

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

  1. Question 1

    Vectors. Asked 2 times: 2 May 2023 S1*, 14 May 2024 S2 (* = numbers or wording changed that year) See all 2 times it was asked

    127
    Let x0x_0 be the point of local minima of f(x)=a⃗⋅(b⃗×c⃗)f(x) = \vec{a}\cdot(\vec{b}\times\vec{c}) where a⃗=xi^−2j^+3k^\vec{a} = x\hat{i}-2\hat{j}+3\hat{k}, b⃗=−2i^+xj^−k^\vec{b} = -2\hat{i}+x\hat{j}-\hat{k}, c⃗=7i^−2j^+xk^\vec{c} = 7\hat{i}-2\hat{j}+x\hat{k}, then value of a⃗⋅b⃗\vec{a}\cdot\vec{b} at x=x0x = x_0 is

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  2. Question 2

    Applications of Definite Integral. Asked 2 times: 9 May 2023 S1, 14 May 2024 S1 See all 2 times it was asked

    105
    The area bounded by the curves y=(x−1)2y=(x-1)^2, y=(x+1)2y=(x+1)^2 and y=14y=\dfrac{1}{4} is

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  3. Question 3

    Binomial Distribution. Asked 2 times: 4 May 2023 S2*, 14 May 2024 S1 (* = numbers or wording changed that year) See all 2 times it was asked

    138
    For an initial screening of an entrance exam, a candidate is given fifty problems to solve. If the probability that the candidate can solve any problem is 45\dfrac{4}{5}, then the probability that he is unable to solve less than two problems, is

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  4. Question 4

    Definite Integration. Asked 2 times: 13 May 2024 S2, 14 May 2024 S1 See all 2 times it was asked

    114
    The integral ∫π/6π/3sec⁡2/3x⋅csc⁡4/3x dx\displaystyle\int_{\pi/6}^{\pi/3}\sec^{2/3}x\cdot\csc^{4/3}x\,dx is equal to

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  5. Question 5

    Differential Equations. Asked 2 times: 10 May 2024 S1, 14 May 2024 S1 See all 2 times it was asked

    135
    General solution of the differential equation cos⁡x(1+cos⁡y) dx−sin⁡y(1+sin⁡x) dy=0\cos x(1+\cos y)\,dx-\sin y(1+\sin x)\,dy=0 is

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