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Day 239: JEE Mains Maths

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

  1. Question 1

    Probability. Asked once: 26 Jun 2022 (same type asked 7 times) See all 7 of this type

    77
    Let a biased coin be tossed 5 times. If the probability of getting 4 heads is equal to the probability of getting 5 heads, then the probability of getting atmost two heads is:

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  2. Question 2

    Binomial Theorem. Asked once: 22 Jan 2026 S2 (same type asked 6 times) See all 6 of this type

    70
    Let CrC_{r} denote the coefficient of xrx^{r} in the binomial expansion of (1+x)n,n∈N,0≤r≤n(1 + x)^{n},n \in N,0 \leq r \leq n. If Pn=C0−C1+223C2−234C3+…..+(−2)nn+1CnP_{n}=C_{0}-C_{1}+\frac{2^{2}}{3}C_{2}-\frac{2^{3}}{4}C_{3}+ \ldots.. +\frac{( - 2)^{n}}{n + 1}C_{n}, then the value of ∑n=1251P2n\sum_{n = 1}^{25} \frac{1}{P_{2n}} equals.

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  3. Question 3

    Statistics. Asked once: 29 Jul 2022 (same type asked 6 times) See all 6 of this type

    82
    Let the mean and the variance of 20 observations x1,x2,…x20x_{1},x_{2},\ldots x_{20} be 15 and 9 , respectively. For α∈R\alpha \in R, if the mean of (x1+α)2,(x2+α)2,…,(x20+α)2\left( x_{1}+ \alpha \right)^{2},\left( x_{2}+ \alpha \right)^{2},\ldots,\left( x_{20}+ \alpha \right)^{2} is 178 , then the square of the maximum value of α\alpha is equal to

  4. Question 4

    Matrices. Asked once: 23 Jan 2025 (same type asked 6 times) See all 6 of this type

    141
    Let A=[aij]A =\left\lbrack a_{ij} \right\rbrack be a 3×33 \times 3 matrix such that A[010]=[001],A[413]=[010]A\begin{bmatrix} 0 \\ 1 \\ 0 \end{bmatrix}=\begin{bmatrix} 0 \\ 0 \\ 1 \end{bmatrix},A\begin{bmatrix} 4 \\ 1 \\ 3 \end{bmatrix}=\begin{bmatrix} 0 \\ 1 \\ 0 \end{bmatrix} and A[212]=[100]A\begin{bmatrix} 2 \\ 1 \\ 2 \end{bmatrix}=\begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix}, then a23a_{23} equals:

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  5. Question 5

    Three Dimensional Geometry. Asked once: 5 Apr 2024 (same type asked 6 times) See all 6 of this type

    61
    Let dd be the distance of the point of intersection of the lines x+63=y2=z+11\frac{x + 6}{3}=\frac{y}{2}=\frac{z + 1}{1} and x−74=y−93=z−42\frac{x- 7}{4}=\frac{y- 9}{3}=\frac{z- 4}{2} from the point (7,8,9)(7,8,9). Then d2+6d^{2}+ 6 is equal to:

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