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Day 145: MHT-CET Maths

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

  1. Question 1

    Limits. Asked 2 times: May 2022 S1*, 4 May 2023 S2 (* = numbers or wording changed that year) See all 2 times it was asked

    132
    If lim⁡x→1x2−ax+bx−1=7\lim_{x\to1}\frac{x^2-ax+b}{x-1}=7, then a+ba+b is equal to

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  2. Question 2

    Binomial Distribution. Asked 2 times: 3 May 2023 S1, 3 May 2023 S2 See all 2 times it was asked

    115
    Two cards are drawn successively with replacement from a well-shuffled pack of 52 cards. Let x denote the random variable of number of kings obtained in the two drawn cards. Then P(x=1)+P(x=2)P(x=1)+P(x=2) equals

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  3. Question 3

    Applications of Derivative. Asked 2 times: 2 May 2023 S2, 3 May 2023 S1 See all 2 times it was asked

    135
    The equation of the normal to the curve x=θ+sin⁡θ, y=1+cos⁡θx=\theta+\sin\theta,\ y=1+\cos\theta at θ=π2\theta=\frac{\pi}{2} is

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  4. Question 4

    Trigonometric Functions. Asked 2 times: 2 May 2023 S1, 3 May 2023 S1 See all 2 times it was asked

    115
    The number of real solutions of tan⁡−1 ⁣x(x+1)+sin⁡−1 ⁣x2+x+1=π2\tan^{-1}\!\sqrt{x(x+1)}+\sin^{-1}\!\sqrt{x^2+x+1}=\frac{\pi}{2} is

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  5. Question 5

    Trigonometry - II. Asked 2 times: May 2021 S1*, 3 May 2023 S1 (* = numbers or wording changed that year) See all 2 times it was asked

    136
    If tan⁡x=34\tan x=\frac{3}{4} and π<x<3π2\pi<x<\frac{3\pi}{2}, then cos⁡x2=\cos\frac{x}{2}=

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