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Day 322: MHT-CET Maths

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

  1. Question 1

    Line and Plane. Asked once: May 2022 S1 (same type asked 3 times) See all 3 of this type

    111
    The distance between parallel lines x−12=y−2−2=z−31\frac{x-1}{2} = \frac{y-2}{-2} = \frac{z-3}{1} and x2=y−2=z1\frac{x}{2} = \frac{y}{-2} = \frac{z}{1} is

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  2. Question 2

    Trigonometric Functions. Asked once: 4 May 2023 S2 (same type asked 3 times) See all 3 of this type

    118
    If (a+b)cos⁡C+(b+c)cos⁡A+(c+a)cos⁡B=72(a+b)\cos C+(b+c)\cos A+(c+a)\cos B=72 and if a=18,b=24a=18, b=24, then area of the triangle ABC is

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  3. Question 3

    Definite Integration. Asked once: 2 May 2023 S1 (same type asked 3 times) See all 3 of this type

    121
    Let ff and gg be continuous functions on [0,a][0,a] such that f(x)=f(a−x)f(x) = f(a-x) and g(x)+g(a−x)=4g(x) + g(a-x) = 4, then ∫0af(x)g(x) dx\displaystyle\int_0^a f(x)g(x)\,dx is equal to

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  4. Question 4

    Differentiation. Asked once: 2 May 2023 S1 (same type asked 3 times) See all 3 of this type

    120
    Let KK be the set of all real values of xx, where the function f(x)=sin⁡∣x∣−∣x∣+2(x−π)cos⁡∣x∣f(x) = \sin|x| - |x| + 2(x-\pi)\cos|x| is not differentiable. Then the set KK is

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  5. Question 5

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

    143
    The general solution of the differential equation dydx=y+x2−y2x\frac{dy}{dx} = \frac{y + \sqrt{x^2-y^2}}{x} is

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