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Day 431: MHT-CET Maths

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

  1. Question 1

    Applications of Derivative. Asked once: 15 May 2026 S2

    78
    A right circular cone is melting such that its volume is decreasing at the rate of 12π cm3/sec12\pi\ \mathrm{cm^3/sec}. The radius of the base is always equal to half of its height. Then the rate of change of the radius when the radius is 22 cm is:

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  2. Question 2

    Binomial Distribution. Asked once: 9 May 2024 S1

    129
    The probability mass function of random variable X is given by P[X=r]=(nr)(32)nP[X=r]=\binom{n}{r}\left(\frac{3}{2}\right)^n, n,r∈N0n,r\in\mathbb{N}_0, otherwise 0, then P[X≤2]=P[X\leq2]=

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  3. Question 3

    Circle. Asked once: 20 Apr 2026 S2

    57
    The equation of a circle whose center lies on x+2y=0x + 2y = 0 and touching the lines 3x−4y+8=03x - 4y + 8 = 0 and 3x−4y−28=03x - 4y - 28 = 0 is

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  4. Question 4

    Complex Numbers. Asked once: 25 Apr 2025 S2

    103
    A particle PP starts from the point Z0=1+2iZ_{0}= 1 + 2i where i=−1i =\sqrt{- 1}. It moves first horizontally away from the origin by 5 units and then vertically upwards parallel to positive Y -axis by 3 units to reach a point Z1Z_{1}. From Z1Z_{1} the particle moves 2\sqrt{2} units in the direction of vector i^+j^\widehat{i}+\widehat{j} and then it moves through an angle π2\frac{\pi}{2} in anticlockwise direction on a circle with centre at origin to reach at point Z2Z_{2}, then Z2=Z_{2}=

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  5. Question 5

    Conic Sections. Asked once: 14 May 2026 S2

    61
    If the tangent to the curve y2=4xy^2 = 4x at (4,4)(4, 4) touches the circle x2+y2−c=0x^2 + y^2 - c = 0 then the value of 5c5c is

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