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Day 425: JEE Mains Maths

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

  1. Question 1

    Three Dimensional Geometry. Asked once: 27 Jan 2024 (same type asked 33 times) See all 33 of this type

    68
    If the shortest distance between the lines x−41=y+12=z−3\frac{x - 4}{1}=\frac{y + 1}{2}=\frac{z}{- 3} and x−λ2=y+14=z−2−5\frac{x - \lambda}{2}=\frac{y + 1}{4}=\frac{z - 2}{- 5} is 65\frac{6}{\sqrt{5}}, then the sum of all possible values of λ\lambda is :

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  2. Question 2

    Determinants. Asked once: 31 Jan 2024 (same type asked 26 times) See all 26 of this type

    68
    If the system of linear equations
    x−2y+z=−4x- 2y+z= - 4
    2x+αy+3z=52x+\alpha y+ 3z= 5
    3x−y+βz=33x-y+\beta z= 3
    has infinitely many solutions, then 12α+13β12\alpha+ 13\beta is equal to

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  3. Question 3

    Determinants. Asked once: 2021 Paper 4 (same type asked 19 times) See all 19 of this type

    76
    Let AA be a 3×33 \times 3 matrix with det(A)=4det(A) = 4. Let RiR_{i} denote the ith i^{\text{th~}} row of AA. If a matrix BB is obtained by performing the operation R2→2R2+5R3R_{2}\rightarrow 2R_{2}+ 5R_{3} on 2A2A, then det(B)det(B) is equal to:

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  4. Question 4

    Vector Algebra. Asked once: 2021 Paper 7 (same type asked 18 times) See all 18 of this type

    62
    Let a→=2i^−3j^+4k^\overrightarrow{a}= 2\widehat{i}- 3\widehat{j}+ 4\widehat{k} and b→=7i^+j^−6k^\overrightarrow{b}= 7\widehat{i}+\widehat{j}- 6\widehat{k}. If r→×a→=r→×b→,r→⋅(i^+2j^+k^)=−3\overrightarrow{r}\times\overrightarrow{a}=\overrightarrow{r}\times\overrightarrow{b},\overrightarrow{r}\cdot (\widehat{i}+ 2\widehat{j}+\widehat{k}) = - 3, then r→⋅(2i^−3j^+k^)\overrightarrow{r}\cdot (2\widehat{i}- 3\widehat{j}+\widehat{k}) is equal to :

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  5. Question 5

    Differential Equations. Asked once: 30 Jan 2024 (same type asked 41 times) See all 41 of this type

    87
    Let y=y(x)y = y(x) be the solution of the differential equation (1−x2)dy=[xy+(x3+2)3(1−x2)]dx\left( 1 -x^{2} \right)dy=\left\lbrack xy+\left( x^{3}+ 2 \right)\sqrt{3\left( 1 -x^{2} \right)} \right\rbrack dx, −1<x<1,y(0)=0- 1 <x< 1,y(0) = 0. If y(12)=mn,my\left( \frac{1}{2} \right)=\frac{m}{n},m and nn are coprime numbers, then m+nm + n is equal to