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Day 407: JEE Mains Maths

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

  1. Question 1

    Determinants. Asked once: 2021 Paper 2 (same type asked 9 times) See all 9 of this type

    72
    For the system of linear equations:
    x−2y=1,x−y+kz=−2,ky+4z=6,k∈Rx- 2y= 1,x-y+kz= - 2,ky+ 4z= 6,k\in R
    consider the following statements: (A) The system has unique solution if k≠2,k≠−2k\neq 2,k\neq - 2. (B) The system has unique solution if k=−2k= - 2. (C) The system has unique solution if k=2k= 2. (D) The system has no-solution if k=2k= 2. (E) The system has infinite number of solutions if k≠−2k\neq - 2. Which of the following statements are correct?

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  2. Question 2

    Differential Equations. Asked once: 28 Jan 2025 (same type asked 41 times) See all 41 of this type

    150
    If y=y(x)y = y(x) is the solution of the differential equation, 4−x2dydx=((sin⁡−1(x2))2−y)sin⁡−1(x2)\sqrt{4 -x^{2}}\frac{dy}{dx}=\left( \left( \sin^{- 1}\left( \frac{x}{2} \right) \right)^{2}-y \right)\sin^{- 1}\left( \frac{x}{2} \right) −2≤x≤2,y(2)=(π2−84)- 2 \leq x\leq 2,y(2) =\left( \frac{\pi^{2}- 8}{4} \right), then y2(0)y^{2}(0) is equal to

  3. Question 3

    Three Dimensional Geometry. Asked once: 8 Apr 2024 (same type asked 33 times) See all 33 of this type

    69
    If the shortest distance between the lines
    L1:r→=(2+λ)i^+(1−3λ)j^+(3+4λ)k^,λ∈RL_{1}:\overrightarrow{r}= (2 +\lambda)\widehat{i}+ (1 - 3\lambda)\widehat{j}+ (3 + 4\lambda)\widehat{k},\lambda\in\mathbb{R}
    L2:r→=2(1+μ)i^+3(1+μ)j^+(5+μ)k^,μ∈RL_{2}:\overrightarrow{r}= 2(1 +\mu)\widehat{i}+ 3(1 +\mu)\widehat{j}+ (5 +\mu)\widehat{k},\mu\in\mathbb{R}
    is mn\frac{m}{\sqrt{n}}, where gcd(m,n)=1gcd(m,n) = 1, then the value of m+nm+n equals.

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  4. Question 4

    Determinants. Asked once: 22 Jan 2025 (same type asked 26 times) See all 26 of this type

    139
    If the system of linear equations :
    x+y+2z=62x+3y+az=a+1 −x−3y+bz=2b\begin{matrix} & x + y + 2z = 6 \\ & 2x + 3y + az = a + 1 \\ & \ - x - 3y + bz = 2b \end{matrix}
    where a,b∈Ra,b \in R, has infinitely many solutions, then 7a+3b7a + 3b is equal to :

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  5. Question 5

    Three Dimensional Geometry. Asked once: 1 Feb 2024 (same type asked 19 times) See all 19 of this type

    165
    If the mirror image of the point P(3,4,9)P(3,4,9) in the line x−13=y+12=z−21\frac{x - 1}{3}=\frac{y + 1}{2}=\frac{z - 2}{1} is (α,β,γ)(\alpha,\beta,\gamma), then 14(α+β+γ)14(\alpha + \beta + \gamma) is :

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