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Day 426: JEE Mains Maths

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

  1. Question 1

    Three Dimensional Geometry. Asked once: 15 Apr 2023 (same type asked 33 times) See all 33 of this type

    62
    Let SS be the set of all values of λ\lambda, for which the shortest distance between the lines x−λ0=y−34=z+61\frac{x - \lambda}{0}=\frac{y - 3}{4}=\frac{z + 6}{1} and x+λ3=y−4=z−60\frac{x + \lambda}{3}=\frac{y}{- 4}=\frac{z - 6}{0} is 13 . Then 8∣∑λ∈Sλ∣8\left| \sum_{\lambda \in S} \lambda \right| is equal to

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  2. Question 2

    Determinants. Asked once: 29 Jan 2024 (same type asked 26 times) See all 26 of this type

    172
    Let for any three distinct consecutive terms a,b,ca,b,c of an A.P, the lines ax+by+c=0ax + by + c = 0 be concurrent at the point PP and Q(α,β)Q(\alpha,\beta) be a point such that the system of equations x+y+z=6x + y + z = 6, 2x+5y+αz=β2x + 5y + \alpha z = \beta and x+2y+3z=4x + 2y + 3z = 4, has infinitely many solutions. Then (PQ)2(PQ)^{2} is equal to

  3. Question 3

    Vector Algebra. Asked once: 2021 Paper 6 (same type asked 18 times) See all 18 of this type

    80
    Let a→=i^+2j^−3k^\overrightarrow{a}=\widehat{i}+ 2\widehat{j}- 3\widehat{k} and b→=2i^−3j^+5k^\overrightarrow{b}= 2\widehat{i}- 3\widehat{j}+ 5\widehat{k}. If r→×a→=b→×r→,r→⋅(αi^+2j^+k^)=3\overrightarrow{r}\times\overrightarrow{a}=\overrightarrow{b}\times\overrightarrow{r},\overrightarrow{r}\cdot (\alpha\widehat{i}+ 2\widehat{j}+\widehat{k}) = 3 and r→⋅(2i^+5j^−αk^)=−1,α∈R\overrightarrow{r}\cdot (2\widehat{i}+ 5\widehat{j}-\alpha\widehat{k}) = - 1,\alpha\in R, then the value of α+∣r→∣2\alpha+ |\overrightarrow{r}|^{2} is equal to:

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  4. Question 4

    Differential Equations. Asked once: 29 Jan 2024 (same type asked 41 times) See all 41 of this type

    72
    A function y=f(x)y = f(x) satisfies f(x)sin⁡2x+sin⁡x−(1+cos⁡2x)f′(x)=0f(x)\sin2x + \sin x -\left( 1 +\cos^{2}x \right)f^{'}(x) = 0 with condition f(0)=0f(0) = 0. Then f(π2)f\left( \frac{\pi}{2} \right) is equal to

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  5. Question 5

    Three Dimensional Geometry. Asked once: 10 Apr 2023 (same type asked 33 times) See all 33 of this type

    77
    The shortest distance between the lines x+21=y−2=z−52\frac{x + 2}{1}=\frac{y}{- 2}=\frac{z - 5}{2} and x−41=y−12=z+30\frac{x - 4}{1}=\frac{y - 1}{2}=\frac{z + 3}{0} is

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