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Day 196: MHT-CET Maths

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

  1. Question 1

    Line and Plane. Asked once: 20 Apr 2025 S2 (same type asked 6 times) See all 6 of this type

    131
    The co-ordinates of the point where the line joining the points ( 2,−3,12, - 3,1 ) and ( 3,−4,−53, - 4, - 5 ) and intersects the plane 2x+y+z=72x+y+z= 7 are

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  2. Question 2

    Measures of Dispersion. Asked once: 11 May 2024 S1 (same type asked 6 times) See all 6 of this type

    140
    If variance of x1,x2,…,xnx_1, x_2, \ldots, x_n is σx2\sigma_x^2, then the variance of λx1,λx2,…,λxn\lambda x_1, \lambda x_2, \ldots, \lambda x_n (λ≠0)(\lambda \neq 0) is

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  3. Question 3

    Permutations and Combinations. Asked once: 10 May 2024 S1 (same type asked 6 times) See all 6 of this type

    132
    A group consists of 8 boys and 5 girls, then the number of committees of 5 persons that can be formed, if the committee consists of at least 2 girls and at most 2 boys, is

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  4. Question 4

    Applications of Derivative. Asked once: 4 May 2023 S2 (same type asked 6 times) See all 6 of this type

    133
    A ladder 5 m long rests against a vertical wall. If its top slides downwards at the rate of 10 cm/sec, then the foot of the ladder is sliding at the rate of ___ m/sec, when it is 4 m away from the wall.

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  5. Question 5

    Differential Equations. Asked once: 12 May 2026 S2 (same type asked 5 times) See all 5 of this type

    86
    If g(x)g(x) denotes the integrating factor of the differential equation xlog⁡xdydx+y=2log⁡xx\log x\dfrac{dy}{dx} + y = 2\log x and ∫g(x) dx=h(x)[g(x)−1]+c\displaystyle\int g(x)\,dx = h(x)[g(x) - 1] + c, then h(x)=h(x) =........

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