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Day 544: MHT-CET Maths

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

  1. Question 1

    Indefinite Integration. Asked once: 15 May 2023 S2

    131
    If ∫ex2⋅x3 dx=ex2f(x)+c\int e^{x^2}\cdot x^3\,dx = e^{x^2}f(x)+c and f(1)=0f(1)=0 (where cc is a constant of integration), then the value of f(x)f(x) is

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  2. Question 2

    Trigonometric Functions. Asked once: 9 May 2023 S2

    146
    The number of solutions, of 21+∣cos⁡x∣+∣cos⁡x∣2+⋯=42^{1+|\cos x|+|\cos x|^2+\cdots} = 4 in (−π,π)(-\pi, \pi), is

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  3. Question 3

    Vectors. Asked once: 4 May 2023 S1

    134
    Let the vectors a⃗,b⃗,c⃗\vec{a},\vec{b},\vec{c} and d⃗\vec{d} be such that (a⃗×b⃗)×(c⃗×d⃗)=0⃗(\vec{a}\times\vec{b})\times(\vec{c}\times\vec{d})=\vec{0}. Let P1P_1 and P2P_2 be the planes determined by the pair of vectors a⃗,b⃗\vec{a},\vec{b} and c⃗,d⃗\vec{c},\vec{d} respectively, then the angle between P1P_1 and P2P_2 is

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  4. Question 4

    Indefinite Integration. Asked once: 15 May 2023 S2

    144
    If f(x)=xx+1, x≠−1f(x)=\frac{x}{x+1},\, x\neq -1 and (f∘f)(x)=F(x)(f\circ f)(x) = F(x), then ∫F(x) dx\int F(x)\,dx is

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  5. Question 5

    Trigonometric Functions. Asked once: 9 May 2023 S1

    128
    Domain of definition of the real valued function f(x)=sin⁡−1(2x)+π6f(x) = \sqrt{\sin^{-1}(2x)+\frac{\pi}{6}} is

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