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Day 343: JEE Mains Maths

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

  1. Question 1

    Probability. Asked once: 29 Jan 2023 (same type asked 7 times) See all 7 of this type

    80
    Three rotten apples are mixed accidently with seven good apples and four apples are drawn one by one without replacement. Let the random variable XX denote the number of rotten apples. If μ\mu and σ2\sigma^{2} represent mean and variance of XX, respectively, then 10(μ2+σ2)10\left( \mu^{2}+\sigma^{2} \right) is equal to

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  2. Question 2

    Quadratic Equations. Asked once: 14 Jun 2022 (same type asked 7 times) See all 7 of this type

    67
    If the sum of the squares of the reciprocals of the roots α\alpha and β\beta of the equation 3x2+λx−1=03x^{2}+\lambda x- 1 = 0 is 15 , then 6(α3+β3)26\left( \alpha^{3}+\beta^{3} \right)^{2} is equal to:

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  3. Question 3

    Binomial Theorem. Asked once: 2021 Paper 19 (same type asked 7 times) See all 7 of this type

    86
    Let (nk)\begin{pmatrix} n \\ k \end{pmatrix} denote  nCk\ ^{n}C_{k} and [nk]={(nk),if 0≤k≤n0,otherwise\begin{bmatrix} n \\ k \end{bmatrix}=\left\{ \begin{matrix} \begin{pmatrix} n \\ k \end{pmatrix}, & \text{if } 0 \leq k \leq n \\ 0, & \text{otherwise} \end{matrix} \right. If Ak=∑i=09(9i)[1212−k+i]+∑i=08(8i)[1313−k+i]A_{k}=\sum_{i = 0}^{9} \begin{pmatrix} 9 \\ i \end{pmatrix}\begin{bmatrix} 12 \\ 12 - k + i \end{bmatrix}+\sum_{i = 0}^{8} \begin{pmatrix} 8 \\ i \end{pmatrix}\begin{bmatrix} 13 \\ 13 - k + i \end{bmatrix} and A4−A3=190pA_{4}-A_{3}= 190p, then pp is equal to:

  4. Question 4

    Application of Derivatives. Asked once: 14 Jun 2022 (same type asked 7 times) See all 7 of this type

    161
    The number of distinct real roots of the equation x7−7x−2=0x^{7}- 7x - 2 = 0 is

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  5. Question 5

    Three Dimensional Geometry. Asked once: 2021 Paper 6 (same type asked 7 times) See all 7 of this type

    81
    If the distance of the point (1,−2,3)(1, - 2,3) from the plane x+2y−3z+10=0x+ 2y- 3z+ 10 = 0 measured parallel to the line, x−13=2−ym=z+31\frac{x- 1}{3}=\frac{2 -y}{m}=\frac{z+ 3}{1} is 72\sqrt{\frac{7}{2}}, then the value of ∣m∣|m| is equal to