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Day 259: MHT-CET Maths

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

  1. Question 1

    Sequences and Series. Asked once: 9 May 2024 S2 (same type asked 2 times) See all 2 of this type

    128
    If log⁡2x+log⁡4x+log⁡8x+log⁡16x=2536\log_2 x + \log_4 x + \log_8 x + \log_{16} x = \dfrac{25}{36} and x=2kx = 2^k, then kk is

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  2. Question 2

    Complex Numbers. Asked once: 13 May 2024 S2 (same type asked 2 times) See all 2 of this type

    145
    If (3x+2)−(5y−3)i(3x+2)-(5y-3)i and (6x+3)+(2y−4)i(6x+3)+(2y-4)i are conjugates of each other, then the value of x−yx+y\frac{x-y}{x+y} is

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  3. Question 3

    Probability Distribution. Asked once: 9 May 2023 S1 (same type asked 2 times) See all 2 of this type

    108
    A random variable X takes values −1,0,1,2-1,0,1,2 with probabilities 1+3p4,1−p4,1+2p4,1−4p4\frac{1+3p}{4},\frac{1-p}{4},\frac{1+2p}{4},\frac{1-4p}{4} respectively, where pp varies over R\mathbb{R}. Then the minimum and maximum values of the mean of X are respectively.

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  4. Question 4

    Circle. Asked once: May 2022 S1 (same type asked 2 times) See all 2 of this type

    145
    If the lines 3x−4y−7=03x-4y-7=0 and 2x−3y−5=02x-3y-5=0 pass through diameters of a circle of area 49π49\pi square units, then the equation of the circle is

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  5. Question 5

    Indefinite Integration. Asked once: 15 May 2023 S1 (same type asked 2 times) See all 2 of this type

    122
    The value of ∫dx5+4sin⁡x\int \frac{dx}{5+4\sin x} is equal to

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