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Day 258: MHT-CET Maths

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

  1. Question 1

    Sets, Relations and Functions. Asked once: 10 May 2024 S1 (same type asked 2 times) See all 2 of this type

    115
    f(x)=2x−3f(x)=2x-3, g(x)=x3+5g(x)=x^3+5. Value of (f∘g)−1(−9)(f\circ g)^{-1}(-9) is

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  2. Question 2

    Applications of Derivative. Asked once: 14 May 2024 S1 (same type asked 2 times) See all 2 of this type

    126
    Let the curve be represented by x=2(cos⁡t+tsin⁡t)x=2(\cos t+t\sin t), y=2(sin⁡t−tcos⁡t)y=2(\sin t-t\cos t). Then normal at any point 'tt' of the curve is at a distance of units from the origin.

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  3. Question 3

    Trigonometry - II. Asked once: 19 Apr 2025 S1 (same type asked 2 times) See all 2 of this type

    110
    If 3sin⁡α=5sin⁡β3\sin\alpha = 5\sin\beta, then tan⁡(α+β2)tan⁡(α−β2)=\dfrac{\tan\left( \frac{\alpha+\beta}{2} \right)}{\tan\left( \frac{\alpha-\beta}{2} \right)}=

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  4. Question 4

    Applications of Derivative. Asked once: 11 May 2024 S2 (same type asked 2 times) See all 2 of this type

    143
    For all real x, the minimum value of 1−x+x21+x+x2\frac{1-x+x^2}{1+x+x^2} is

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  5. Question 5

    Definite Integration. Asked once: 10 May 2024 S2 (same type asked 2 times) See all 2 of this type

    106
    ∫0πxtan⁡xsec⁡x+cos⁡x dx=\displaystyle\int_0^\pi \frac{x\tan x}{\sec x+\cos x}\,dx =

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