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Day 325: JEE Mains Maths

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

  1. Question 1

    Definite Integration. Asked once: 10 Apr 2023 (same type asked 4 times) See all 4 of this type

    65
    Let ff be a differentiable function such that x2f(x)−x=4∫0xtf(t)dt,f(1)=23x^{2}f(x) - x = 4\int_{0}^{x} tf(t)dt,f(1) =\frac{2}{3}. Then 18f(3)18f(3) is equal to

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  2. Question 2

    Matrices. Asked once: 29 Jun 2022 (same type asked 4 times) See all 4 of this type

    70
    Let A=[aij]A =\left\lbrack a_{ij} \right\rbrack be a square matrix of order 3 such that aij=2j−ia_{ij}=2^{j - i}, for all i,j=1,2,3i,j = 1,2,3. Then, the matrix A2+A3+…+A10A^{2}+A^{3}+ \ldots +A^{10} is equal to:

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  3. Question 3

    Vector Algebra. Asked once: 2021 Paper 14 (same type asked 4 times) See all 4 of this type

    60
    p→=(3i^+2j^+k^),q→=(2i^+j^+k^),r→\overrightarrow{p}= (3\widehat{i}+ 2\widehat{j}+\widehat{k}),\overrightarrow{q}= (2\widehat{i}+\widehat{j}+\widehat{k}),\overrightarrow{r} is perpendicular to both p→+q→\overrightarrow{p}+\overrightarrow{q} and (p→−q→),∣r→∣=3,r→=ai^+bj^+ck^(\overrightarrow{p}-\overrightarrow{q}),|\overrightarrow{r}| =\sqrt{3},\overrightarrow{r}=a\widehat{i}+b\widehat{j}+c\widehat{k}. Find ∣a∣+∣b∣+∣c∣|a| + |b| + |c|.

  4. Question 4

    Application of Integrals. Asked once: 29 Jul 2022 (same type asked 4 times) See all 4 of this type

    76
    The area of the region {(x,y):∣x−1∣≤y≤5−x2}\left\{ (x,y):|x - 1| \leq y \leq\sqrt{5 -x^{2}} \right\} is equal to :

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  5. Question 5

    Application of Integrals. Asked once: 2021 Paper 5 (same type asked 4 times) See all 4 of this type

    88
    Let the curve y=y(x)y=y(x) be the solution of the differential equation, dydx=2(x+1)\frac{dy}{dx}= 2(x+ 1). If the numerical value of area bounded by the curve y=y(x)y=y(x) and xx-axis is 483\frac{4\sqrt{8}}{3}, then the value of y(1)y(1) is equal to