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Day 485: MHT-CET Maths

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

  1. Question 1

    Line and Plane. Asked once: 16 Apr 2026 S2

    95
    If dd is the distance of point (2, 5, 10) from the plane containing the lines rˉ=(4j^−k^)+λ(i^+2j^−2k^)\bar{r} = (4\hat{j} - \hat{k}) + \lambda(\hat{i} + 2\hat{j} - 2\hat{k}) and rˉ=(2i^+j^)+μ(i^+2j^−2k^)\bar{r} = (2\hat{i} + \hat{j}) + \mu(\hat{i} + 2\hat{j} - 2\hat{k}), then d2=d^2 =

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  2. Question 2

    Permutations and Combinations. Asked once: 10 May 2023 S1

    149
    Words of length 10 are formed by using the letters A, B, C, D, E, F, G, H, I, J. Let x be number of such words where no letter is repeated and y be number of such words where exactly two letters are repeated twice and no other letter is repeated, then the value of yx\frac{y}{x} is

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  3. Question 3

    Probability Distribution. Asked once: 19 Apr 2025 S2

    113
    Let XX be a discrete random variable. The probability distribution of X is given below
    XX3010−10-10
    P(X)P(X)15\frac{1}{5}AABB
    and E(X)=4E(X) = 4, then the value of ABAB is equal to

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  4. Question 4

    Sets, Relations and Functions. Asked once: 11 May 2023 S2

    106
    If f:[1,∞)→[2,∞)f:[1,\infty)\to[2,\infty) is given by f(x)=x+1xf(x) = x+\frac{1}{x} then f−1(x)f^{-1}(x) equals

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  5. Question 5

    Straight Line. Asked once: 13 May 2024 S2

    149
    PS is the median of the triangle with vertices at P(2,2),Q(6,−1)P(2,2), Q(6,-1) and R(7,3)R(7,3), then the intercepts on the co-ordinate axes of the line passing through point (1,−1)(1,-1) and parallel to PS are respectively

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