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Day 533: MHT-CET Maths

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

  1. Question 1

    Indefinite Integration. Asked once: 13 May 2024 S2

    103
    ∫2+cos⁡x(2x+sin⁡x)2 dx=\int\frac{2+\cos x}{(2x+\sin x)^2}\,dx=

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  2. Question 2

    Line and Plane. Asked once: 16 May 2023 S2

    112
    A line having direction ratios 1,−4,21, -4, 2 intersects the lines x−73=y−1−1=z+21\frac{x-7}{3} = \frac{y-1}{-1} = \frac{z+2}{1} and x2=y−73=z1\frac{x}{2} = \frac{y-7}{3} = \frac{z}{1} at points A and B respectively. Then co-ordinates of A and B are

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  3. Question 3

    Trigonometric Functions. Asked once: 12 May 2024 S2

    114
    The lengths of sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one. Then the length of the sides of the triangle (in units) are

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  4. Question 4

    Vectors. Asked once: 20 Apr 2025 S1

    115
    If aˉ=4i^+3j^+k^,bˉ=i^−2j^+2k^\bar{a}= 4\widehat{i}+ 3\widehat{j}+\widehat{k},\bar{b}=\widehat{i}- 2\widehat{j}+ 2\widehat{k} then a‾×(a‾×(a‾×(a‾×b‾)))=\overline{a}\times (\overline{a}\times (\overline{a}\times (\overline{a}\times\overline{b}))) =

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  5. Question 5

    Applications of Derivative. Asked once: 3 May 2023 S2

    123
    If f(x)=x3+bx2+cx+df(x)=x^{3}+bx^{2}+cx+d and 0<b2<c0<b^{2}<c, then in (−∞,∞)(-\infty,\infty)

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