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Day 546: MHT-CET Maths

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

  1. Question 1

    Trigonometric Functions. Asked once: 3 May 2023 S2

    114
    The number of all values of θ\theta in the interval (−π2,π2)\left(-\frac{\pi}{2},\frac{\pi}{2}\right) satisfying the equation (1−tan⁡θ)(1+tan⁡θ)sec⁡2θ+2tan⁡2θ=0(1-\tan\theta)(1+\tan\theta)\sec^{2}\theta+2\tan^{2}\theta=0 is

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  2. Question 2

    Indefinite Integration. Asked once: 10 May 2023 S1

    116
    If ∫dθcos⁡2θ(tan⁡2θ+sec⁡2θ)=λtan⁡θ+2log⁡e∣f(θ)∣+c\int\frac{d\theta}{\cos^2\theta(\tan 2\theta+\sec 2\theta)}=\lambda\tan\theta+2\log_e|f(\theta)|+c (where c is a constant of integration), then the ordered pair (λ,∣f(θ)∣)(\lambda,|f(\theta)|) is equal to

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  3. Question 3

    Trigonometric Functions. Asked once: 3 May 2023 S2

    107
    The equation (cos⁡p−1)x2+(cos⁡p)x+sin⁡p=0(\cos p-1)x^{2}+(\cos p)x+\sin p=0 in the variable xx, has real roots. Then pp can take any value in the interval

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  4. Question 4

    Indefinite Integration. Asked once: 10 May 2023 S1

    133
    ∫1+sin⁡(log⁡x)1+cos⁡(log⁡x) dx=\int\frac{1+\sin(\log x)}{1+\cos(\log x)}\,dx=

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  5. Question 5

    Trigonometric Functions. Asked once: 3 May 2023 S1

    116
    Let S={x∈(−π,π)∣x≠0,±π2}S=\{x\in(-\pi,\pi)\mid x\neq0,\pm\frac{\pi}{2}\}. The sum of all distinct solutions of 3sec⁡x+cosec x+2(tan⁡x−cot⁡x)=0\sqrt{3}\sec x+\text{cosec}\,x+2(\tan x-\cot x)=0 in S is equal to

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