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JEE MAIN Previous Year Questions (PYQs)

JEE MAIN Linear Programming PYQ

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





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (24 February Evening Shift) PYQ

Solution

JEE MAIN PYQ
Let $\theta \in \left( {0,{\pi \over 2}} \right)$. If the system of linear equations $(1 + {\cos ^2}\theta )x + {\sin ^2}\theta y + 4\sin 3\,\theta z = 0$, ${\cos ^2}\theta x + (1 + {\sin ^2}\theta )y + 4\sin 3\,\theta z = 0$, ${\cos ^2}\theta x + {\sin ^2}\theta y + (1 + 4\sin 3\,\theta )z = 0,$ has a non-trivial solution, then the value of $\theta$ is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (26 August Morning Shift) PYQ

Solution

JEE MAIN PYQ
Let the system of linear equations $x + y + \alpha z = 2$, $3x + y + z = 4$, $x + 2z = 1$ have a unique solution $(x^*, y^*, z^*)$. If $(\alpha, x^*)$, $(y^*, \alpha)$ and $(x^*, -y^*)$ are collinear points, then the sum of absolute values of all possible values of $\alpha$ is ?





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (24 June Evening Shift) PYQ

Solution

JEE MAIN PYQ
If the system of equations $x+4y-z=\lambda,; 7x+9y+\mu z=-3,; 5x+y+2z=-1$ has infinitely many solutions, then $(2\mu+3\lambda)$ is equal to:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (8 April Evening Shift) PYQ

Solution

JEE MAIN PYQ
If the system of linear equations

$2x + 3y - z = - 2$

$x + y + z = 4$

$x - y + |\lambda |z = 4\lambda - 4$

where, $\lambda$ $\in$ R, has no solution, then






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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (28 June Morning Shift) PYQ

Solution

JEE MAIN PYQ
The shortest distance between the lines $\dfrac{x - 3}{4} = \dfrac{y + 7}{-11} = \dfrac{z - 1}{5}$ and $\dfrac{x - 5}{3} = \dfrac{y - 9}{-6} = \dfrac{z + 2}{1}$ is:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (9 April Morning Shift) PYQ

Solution

JEE MAIN PYQ
Let $\lambda,\mu\in\mathbb{R}$. If the system of equations $3x+5y+\lambda z=3$ $7x+11y-9z=2$ $97x+155y-189z=\mu$ has infinitely many solutions, then $\mu+2\lambda$ is equal to:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (9 April Morning Shift) PYQ

Solution

JEE MAIN PYQ
Let the line $L$ intersect the lines $x-2=-y=z-1$, $2(x+1)=2(y-1)=z+1$ and be parallel to the line $\dfrac{x-2}{3}=\dfrac{y-1}{1}=\dfrac{z-2}{2}$. Then which of the following points lies on $L$?





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (9 April Morning Shift) PYQ

Solution

JEE MAIN PYQ
If the system of equations $2x+y-z=5$ $2x-5y+\lambda z=\mu$ $x+2y-5z=7$ has infinitely many solutions, then $(\lambda+\mu)^2+(\lambda-\mu)^2$ is equal to:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (13 April Evening Shift) PYQ

Solution

JEE MAIN PYQ
If the system of linear equations

$ \begin{aligned} & 3 x+y+\beta z=3 \\ & 2 x+\alpha y-z=-3 \\ & x+2 y+z=4 \end{aligned} $

has infinitely many solutions, then the value of $22 \beta-9 \alpha$ is





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (2 April Morning Shift) PYQ

Solution

JEE MAIN PYQ
If the system of equations $ \begin{aligned} 2x + 3y - z &= 5, \\ x + \alpha y + 3z &= -4, \\ 3x - y + \beta z &= 7 \end{aligned} $ has infinitely many solutions, then $13\alpha\beta$ is equal to:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (1 February Morning Shift) PYQ

Solution

JEE MAIN PYQ
Let $\lambda \in $ R . The system of linear equations
2x1- 4x2 + $\lambda $x3 = 1
x1 - 6x2 + x3 = 2
$\lambda $x1 - 10x2 + 4x3 = 3
is inconsistent for:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 5 September 2020 (Morning) PYQ

Solution

JEE MAIN PYQ
Let $\lambda $ be a real number for which the system of linear equations x + y + z = 6, 4x + $\lambda $y – $\lambda $z = $\lambda $ – 2, 3x + 2y – 4z = – 5 has infinitely many solutions. Then $\lambda $ is a root of the quadratic equation





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (10 April Evening Shift) PYQ

Solution

JEE MAIN PYQ
If the system of linear equations $8x + y + 4z = -2$ $x + y + z = 0$ $\lambda x - 3y = \mu$ has infinitely many solutions, then the distance of the point $(\lambda, \mu, -\tfrac{1}{2})$ from the plane $8x + y + 4z + 2 = 0$ is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (26 July Morning Shift) PYQ

Solution

JEE MAIN PYQ
Let $S$ denote the set of all real values of $\lambda$ such that the system of equations $\lambda x + y + z = 1$ $x + \lambda y + z = 1$ $x + y + \lambda z = 1$ is inconsistent, then $\displaystyle \sum_{\lambda \in S}\big(|\lambda|^{2}+|\lambda|\big)$ is equal to:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (1 February Morning Shift) PYQ

Solution


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