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Day 141: JEE Mains Maths

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

  1. Question 1

    Statistics. Asked once: 29 Jan 2025 (same type asked 6 times) See all 6 of this type

    68
    Let x1,x2,……x10x_{1},x_{2},\ldots\ldots x_{10} be ten observations such that ∑i=110(xi−2)=30,∑i=110(xi−β)2=98,β>2\sum_{i = 1}^{10} \left( x_{i}- 2 \right)= 30,\sum_{i = 1}^{10} \left( x_{i}- \beta \right)^{2}= 98,\beta > 2 and their variance is 45\frac{4}{5}. If μ\mu and σ2\sigma^{2} are respectively the mean and the variance of 2(x1−1)+4β,2(x2−1)+2\left( x_{1}- 1 \right)+ 4\beta,2\left( x_{2}- 1 \right)+ 4β,….,2(x10−1)+4β4\beta,\ldots.,2\left( x_{10}- 1 \right)+ 4\beta, then βμσ2\frac{\beta\mu}{\sigma^{2}} is equal to :

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  2. Question 2

    Matrices. Asked once: 5 Apr 2026 S1 (same type asked 6 times) See all 6 of this type

    53
    Let A be a 3×33 \times 3 matrix such that AT[101]=[522], AT[001]=[311], A[101]=[344]A^{T}\begin{bmatrix} 1 \\ 0 \\ 1 \end{bmatrix}=\begin{bmatrix} 5 \\ 2 \\ 2 \end{bmatrix},\ A^{T}\begin{bmatrix} 0 \\ 0 \\ 1 \end{bmatrix}=\begin{bmatrix} 3 \\ 1 \\ 1 \end{bmatrix},\ A\begin{bmatrix} 1 \\ 0 \\ 1 \end{bmatrix}=\begin{bmatrix} 3 \\ 4 \\ 4 \end{bmatrix} and A[001]=[131]A\begin{bmatrix} 0 \\ 0 \\ 1 \end{bmatrix}=\begin{bmatrix} 1 \\ 3 \\ 1 \end{bmatrix} If det(A)=1det(A) = 1, then det⁡(adj(A2+A))\det\left( adj\left( A^{2}+ A \right) \right) is equal to :

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  3. Question 3

    Three Dimensional Geometry. Asked once: 24 Jan 2025 (same type asked 6 times) See all 6 of this type

    68
    Let the line passing through the points (−1,2,1)( - 1,2,1) and parallel to the line x−12=y+13=z4\frac{x - 1}{2}=\frac{y + 1}{3}=\frac{z}{4} intersect the line x+23=y−32=z−41\frac{x + 2}{3}=\frac{y - 3}{2}=\frac{z - 4}{1} at the point PP. Then the distance of P from the point Q(4,−5,1)Q(4, - 5,1) is :

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  4. Question 4

    Binomial Theorem. Asked once: 8 Apr 2024 (same type asked 6 times) See all 6 of this type

    170
    If the term independent of xx in the expansion of (ax 2+12x3)10\left( \sqrt{ax}\ ^{2}+\frac{1}{2x^{3}} \right)^{10} is 105, then a2a^{2} is equal to :

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  5. Question 5

    Differentiation. Asked once: 1 Feb 2024 (same type asked 6 times) See all 6 of this type

    151
    Let f(x)=∣2x2+5∣x∣−3∣,x∈Rf(x) =\left| 2x^{2}+ 5 \right|x| - 3|,x \in R. If mm and nn denote the number of points where ff is not continuous and not differentiable respectively, then m+nm + n is equal to:

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