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Day 86: JEE Mains Maths

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

  1. Question 1

    Three Dimensional Geometry. Asked 2 times: 27 Jan 2024*, 4 Apr 2024 (* = numbers or wording changed that year) See all 2 times it was asked

    170
    Let PP be the point of intersection of the lines x−21=y−45=z−21\frac{x - 2}{1}=\frac{y - 4}{5}=\frac{z - 2}{1} and  x−32=y−23=z−32\ \frac{x - 3}{2}=\frac{y - 2}{3}=\frac{z - 3}{2}. Then, the shortest distance of PP from the line 4x=2y=z4x = 2y = z is

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  2. Question 2

    Quadratic Equations. Asked 2 times: 1 Feb 2023*, 1 Feb 2024 (* = numbers or wording changed that year) See all 2 times it was asked

    69
    Let S={x∈R:(3+2)x+(3−2)x=10}S =\left\{ x\in R:(\sqrt{3}+\sqrt{2})^{x}+ (\sqrt{3}-\sqrt{2})^{x}= 10 \right\}. Then the number of elements in SS is :

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  3. Question 3

    Statistics. Asked 2 times: 2021 Paper 26*, 1 Feb 2024 (* = numbers or wording changed that year) See all 2 times it was asked

    168
    Consider 10 observation x1,x2,…,x10x_{1},x_{2},\ldots,x_{10} such that ∑i=110(xi−α)=2\sum_{i = 1}^{10} \left( x_{i}- \alpha \right)= 2 and ∑i=110(xi−β)2=40\sum_{i = 1}^{10} \left( x_{i}- \beta \right)^{2}= 40, where α,β\alpha,\beta are positive integers. Let the mean and the variance of the observations be 65\frac{6}{5} and 8425\frac{84}{25} respectively. Then βα\frac{\beta}{\alpha} is equal to:

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  4. Question 4

    Matrices. Asked 2 times: 25 Jun 2022*, 31 Jan 2024 (* = numbers or wording changed that year) See all 2 times it was asked

    169
    Let AA be a 33 real matrix such that A(101)=2(101),A(−101)=4(−101),A(010)=2(010)A\begin{pmatrix} 1 \\ 0 \\ 1 \end{pmatrix}= 2\begin{pmatrix} 1 \\ 0 \\ 1 \end{pmatrix},A\begin{pmatrix} - 1 \\ 0 \\ 1 \end{pmatrix}= 4\begin{pmatrix} - 1 \\ 0 \\ 1 \end{pmatrix},A\begin{pmatrix} 0 \\ 1 \\ 0 \end{pmatrix}= 2\begin{pmatrix} 0 \\ 1 \\ 0 \end{pmatrix}. Then, the system (A−3I)(xyz)=(123)(A- 3I)\begin{pmatrix} x \\ y \\ z \end{pmatrix}=\begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix} has

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  5. Question 5

    Binomial Theorem. Asked 2 times: 11 Apr 2023*, 30 Jan 2024 (* = numbers or wording changed that year) See all 2 times it was asked

    86
    Number of integral terms in the expansion of {7(12)+11(16)}824\left\{ 7^{\left( \frac{1}{2} \right)}+11^{\left( \frac{1}{6} \right)} \right\}^{824} is equal to