JEE MAIN Determinants Previous Year Question Paper and Solution with PDF

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Previous Year Questions
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JEE MAIN Previous Year Questions (PYQs)

JEE MAIN Determinants PYQ

Qus : 1 JEE MAIN PYQ

The number of values of $\theta \in (0, \pi)$ for which the system of linear equations

$x + 3y + 7z = 0$

$-x + 4y + 7z = 0$

$(\sin 3\theta)x + (\cos 2\theta)y + 2z = 0$

has a non-trivial solution, is -

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

Solution

Qus : 2 JEE MAIN PYQ

Let $f(x)=\begin{vmatrix} 1+\sin^{2}x & \cos^{2}x & \sin 2x\\ \sin^{2}x & 1+\cos^{2}x & \sin 2x\\ \sin^{2}x & \cos^{2}x & 1+\sin 2x \end{vmatrix},\ x\in\left[\dfrac{\pi}{6},\dfrac{\pi}{3}\right].$ If $\alpha$ and $\beta$ respectively are the maximum and the minimum values of $f$, then

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

Solution

Qus : 3 JEE MAIN PYQ

If $A,B$ and $\big(\operatorname{adj}(A^{-1})+\operatorname{adj}(B^{-1})\big)$ are non-singular matrices of the same order, then the inverse of $A\Big(\operatorname{adj}(A^{-1})+\operatorname{adj}(B^{-1})\Big)^{-1}B$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (23 January Morning Shift) PYQ

Solution

Qus : 4 JEE MAIN PYQ

Let $A = \begin{bmatrix} 2 & b & 1 \\ b & b^2 + 1 & b \\ 1 & b & 2 \end{bmatrix}$ where $b > 0$. Then the minimum value of $\dfrac{\det(A)}{b}$ is –

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

Solution

Qus : 5 JEE MAIN PYQ

If $g$ is the inverse of a function $f$ and $f'(x)=\dfrac{1}{1+x^{5}}$, then $g'(x)$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2014 (Offline) PYQ

Solution

Qus : 6 JEE MAIN PYQ

Let $a_1,a_2,\dots,a_{10}$ be in G.P. with $a_i>0$ for $i=1,2,\dots,10$ and $S$ be the set of pairs $(r,k)$, $r,k\in\mathbb{N}$, for which $ \begin{vmatrix} \log_e(a_1^{\,r}a_2^{\,k}) & \log_e(a_2^{\,r}a_3^{\,k}) & \log_e(a_3^{\,r}a_4^{\,k})\\ \log_e(a_4^{\,r}a_5^{\,k}) & \log_e(a_5^{\,r}a_6^{\,k}) & \log_e(a_6^{\,r}a_7^{\,k})\\ \log_e(a_7^{\,r}a_8^{\,k}) & \log_e(a_8^{\,r}a_9^{\,k}) & \log_e(a_9^{\,r}a_{10}^{\,k}) \end{vmatrix} =0. $ Then the number of elements in $S$, is –

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

Solution

Qus : 7 JEE MAIN PYQ

Let $S$ be the set of all real values of $k$ for which the system of linear equations

$x + y + z = 2$

$2x + y - z = 3$

$3x + 2y + kz = 4$

has a unique solution. Then $S$ is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Morning Shift) PYQ

Solution

Qus : 8 JEE MAIN PYQ

Let $A$ and $B$ be two square matrices of order $3$ such that $|A|=3$ and $|B|=2$. Then $\left|,A^{T}A,( \operatorname{adj}(2A))^{-1},(\operatorname{adj}(4B)),(\operatorname{adj}(AB))^{-1},A A^{T}\right|$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (5 April Morning Shift) PYQ

Solution

Qus : 9 JEE MAIN PYQ

Let $A$ be a $3 \times 3$ matrix such that $|\operatorname{adj}(\operatorname{adj}(\operatorname{adj} \mathrm{A}))|=81$.

If $S=\left\{n \in \mathbb{Z}:(|\operatorname{adj}(\operatorname{adj} A)|)^{\frac{(n-1)^2}{2}}=|A|^{\left(3 n^2-5 n-4\right)}\right\}$, then $\sum_\limits{n \in S}\left|A^{\left(n^2+n\right)}\right|$ is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (7 April Morning Shift) PYQ

Solution

Qus : 10 JEE MAIN PYQ

If the system $11x+y+\lambda z=-5,\quad 2x+3y+5z=3,\quad 8x-19y-39z=\mu$ has infinitely many solutions, then $\lambda^{4}-\mu$ equals:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (5 April Morning Shift) PYQ

Solution

Qus : 11 JEE MAIN PYQ

The number of values of $\alpha$ for which the system of equations :

x + y + z = $\alpha$

$\alpha$x + 2$\alpha$y + 3z = $-$1

x + 3$\alpha$y + 5z = 4

is inconsistent, is

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

Solution

Qus : 12 JEE MAIN PYQ

$ \text{Let } A = \begin{bmatrix} 2 & 1 & 0 \ 1 & 2 & -1 \ 0 & -1 & 2 \end{bmatrix}. \text{ If } \left| \operatorname{adj} \big( \operatorname{adj} (\operatorname{adj}(2A)) \big) \right| = (16)^n, \text{ then } n \text{ is equal to:} $

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (8 April Morning Shift) PYQ

Solution

Qus : 13 JEE MAIN PYQ

The values of $m, n$, for which the system of equations

$\begin{aligned} & x+y+z=4, \\ & 2 x+5 y+5 z=17, \\ & x+2 y+\mathrm{m} z=\mathrm{n} \end{aligned}$

has infinitely many solutions, satisfy the equation :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (5 April Evening Shift) PYQ

Solution

Qus : 14 JEE MAIN PYQ

If \[ \begin{vmatrix} a-b-c & 2a & 2a\\ 2b & b-c-a & 2b\\ 2c & 2c & c-a-b \end{vmatrix} =(a+b+c)\,(x+a+b+c)^{2},\ x\ne 0, \] then $x$ is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (11 January Evening Shift) PYQ

Solution

Qus : 15 JEE MAIN PYQ

If the system of linear equations

$x + ky + 3z = 0$

$3x + ky - 2z = 0$

$2x + 4y - 3z = 0$

has a non-zero solution $(x, y, z)$, then $\dfrac{xz}{y^{2}}$ is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (Offline) PYQ

Solution

Qus : 16 JEE MAIN PYQ

If $\left|\begin{bmatrix} x-4 & 2x & 2x \\ 2x & x-4 & 2x \\ 2x & 2x & x-4 \end{bmatrix}\right| = (A+Bx)(x-A)^{2}$ then the ordered pair $(A,B)$ is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (Offline) PYQ

Solution

Qus : 17 JEE MAIN PYQ

The values of $\alpha$ for which $\begin{vmatrix} 1 & \dfrac{3}{2} & \alpha+\dfrac{3}{2}\\[4pt] 1 & \dfrac{1}{3} & \alpha+\dfrac{1}{3}\\[4pt] 2\alpha+3 & 3\alpha+1 & 0 \end{vmatrix}=0$ lie in the interval:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (27 January Evening Shift) PYQ

Solution

Qus : 18 JEE MAIN PYQ

Let $A = \left( {\matrix{ {[x + 1]} & {[x + 2]} & {[x + 3]} \cr {[x]} & {[x + 3]} & {[x + 3]} \cr {[x]} & {[x + 2]} & {[x + 4]} \cr } } \right)$, where [t] denotes the greatest integer less than or equal to t. If det(A) = 192, then the set of values of x is the interval :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (27 August Evening Shift) PYQ

Solution

Qus : 19 JEE MAIN PYQ

The set $S$ is all values of $\theta\in[-\pi,\pi]$ for which the system $x+y+\sqrt{3},z=0,\quad -x+(\tan\theta),y+\sqrt{7},z=0,\quad x+y+(\tan\theta),z=0$ has a non-trivial solution. Then $\dfrac{120}{\pi}\displaystyle\sum_{\theta\in S}\theta$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (8 April Evening Shift) PYQ

Solution

Qus : 20 JEE MAIN PYQ

The value of $\left| {\matrix{ {(a + 1)(a + 2)} & {a + 2} & 1 \cr {(a + 2)(a + 3)} & {a + 3} & 1 \cr {(a + 3)(a + 4)} & {a + 4} & 1 \cr } } \right|$ is :

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

Solution

Qus : 21 JEE MAIN PYQ

Let $A=\begin{bmatrix} 1&0&0\\ 0&\alpha&\beta\\ 0&\beta&\alpha \end{bmatrix}$ and $\;|2A|^{3}=2^{21}$ where $\alpha,\beta\in\mathbb{Z}$. Then a value of $\alpha$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (29 January Morning Shift) PYQ

Solution

Qus : 22 JEE MAIN PYQ

For $\alpha, \beta \in \mathbb{R}$ and a natural number $n$, let $A_r=\left|\begin{array}{ccc}r & 1 & \frac{n^2}{2}+\alpha \\ 2 r & 2 & n^2-\beta \\ 3 r-2 & 3 & \frac{n(3 n-1)}{2}\end{array}\right|$. Then $2 A_{10}-A_8$ is

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (6 April Morning Shift) PYQ

Solution

Qus : 23 JEE MAIN PYQ

Let $S$ be the set of all $\lambda \in \mathbb{R}$ for which the system of linear equations \[ 2x - y + 2z = 2 \] \[ x - 2y + \lambda z = -4 \] \[ x + \lambda y + z = 4 \] has no solution. Then the set $S$ :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2 September 2020 (Morning) PYQ

Solution

Qus : 24 JEE MAIN PYQ

If A = $\left[ {\matrix{ 1 & {\sin \theta } & 1 \cr { - \sin \theta } & 1 & {\sin \theta } \cr { - 1} & { - \sin \theta } & 1 \cr } } \right]$;

then for all $\theta $ $ \in $ $\left( {{{3\pi } \over 4},{{5\pi } \over 4}} \right)$, det (A) lies in the interval :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (12 January Evening Shift) PYQ

Solution

Qus : 25 JEE MAIN PYQ

If $S$ is the set of distinct values of $b$ for which the following system of linear equations

$x + y + z = 1$

$x + ay + z = 1$

$ax + by + z = 0$

has no solution, then $S$ is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2017 (Offline) PYQ

Solution

Qus : 26 JEE MAIN PYQ

Let $\omega$ be a complex number such that $2\omega + 1 = z$ where $z = \sqrt{-3}$. If $\begin{vmatrix} 1 & 1 & 1 \\ 1 & -\omega^{2}-1 & \omega^{2} \\ 1 & \omega^{2} & \omega^{7} \end{vmatrix} = 3k$, then $k$ is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2017 (Offline) PYQ

Solution

Qus : 27 JEE MAIN PYQ

If \[ f(x)= \begin{vmatrix} 2\cos^{4}x & 2\sin^{4}x & 3+\sin^{2}2x\\ 3+2\cos^{4}x & 2\sin^{4}x & \sin^{2}2x\\ 2\cos^{4}x & 3+2\sin^{4}x & \sin^{2}2x \end{vmatrix}, \] then $\dfrac{1}{5}\,f'(0)$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (30 January Morning Shift) PYQ

Solution

Qus : 28 JEE MAIN PYQ

The greatest value of $c\in\mathbb{R}$ for which the system of linear equations

$x-cy-cz=0$

$cx-y+cz=0$

$cx+cy-z=0$

has a non-trivial solution, is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (8 April Morning Shift) PYQ

Solution

Qus : 29 JEE MAIN PYQ

$\text { Let } A=\left[\begin{array}{lll} 1 & 0 & 0 \\ 0 & \alpha & \beta \\ 0 & \beta & \alpha \end{array}\right] \text { and }|2 \mathrm{~A}|^3=2^{21} \text { where } \alpha, \beta \in Z \text {, Then a value of } \alpha \text { is }$

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (29 January Morning Shift) PYQ

Solution

Qus : 30 JEE MAIN PYQ

Let the numbers $2, b, c$ be in an A.P. and $ A = \begin{bmatrix} 1 & 1 & 1 \\ 2 & b & c \\ 4 & b^2 & c^2 \end{bmatrix}. $ If $\det(A) \in [2, 16]$, then $c$ lies in the interval:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (8 April Evening Shift) PYQ

Solution

Qus : 31 JEE MAIN PYQ

If $\Delta $ = $\left| {\matrix{ {x - 2} & {2x - 3} & {3x - 4} \cr {2x - 3} & {3x - 4} & {4x - 5} \cr {3x - 5} & {5x - 8} & {10x - 17} \cr } } \right|$ = Ax³ + Bx² + Cx + D, then B + C is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 3 September 2020 (Morning) PYQ

Solution

Qus : 32 JEE MAIN PYQ

If

$S = \left\{ {x \in \left[ {0,2\pi } \right]:\left| {\matrix{ 0 & {\cos x} & { - \sin x} \cr {\sin x} & 0 & {\cos x} \cr {\cos x} & {\sin x} & 0 \cr } } \right| = 0} \right\},$

then $\sum\limits_{x \in S} {\tan \left( {{\pi \over 3} + x} \right)} $ is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2017 (8 April Morning Shift) PYQ

Solution

Qus : 33 JEE MAIN PYQ

If $\alpha \neq \mathrm{a}, \beta \neq \mathrm{b}, \gamma \neq \mathrm{c}$ and $\left|\begin{array}{lll}\alpha & \mathrm{b} & \mathrm{c} \\ \mathrm{a} & \beta & \mathrm{c} \\ \mathrm{a} & \mathrm{b} & \gamma\end{array}\right|=0$, then $\frac{\mathrm{a}}{\alpha-\mathrm{a}}+\frac{\mathrm{b}}{\beta-\mathrm{b}}+\frac{\gamma}{\gamma-\mathrm{c}}$ is equal to :

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

Solution

Qus : 34 JEE MAIN PYQ

The system of equations kx + y + z = 1, x + ky + z = k and x + y + zk = k² has no solution if k is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (17 March Morning Shift) PYQ

Solution

Qus : 35 JEE MAIN PYQ

If x, y, z are in arithmetic progression with common difference d, x $\ne$ 3d, and the determinant of the matrix $\left[ {\matrix{ 3 & {4\sqrt 2 } & x \cr 4 & {5\sqrt 2 } & y \cr 5 & k & z \cr } } \right]$ is zero, then the value of k² is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (17 March Evening Shift) PYQ

Solution

Qus : 36 JEE MAIN PYQ

The solutions of the equation $\left| {\matrix{ {1 + {{\sin }^2}x} & {{{\sin }^2}x} & {{{\sin }^2}x} \cr {{{\cos }^2}x} & {1 + {{\cos }^2}x} & {{{\cos }^2}x} \cr {4\sin 2x} & {4\sin 2x} & {1 + 4\sin 2x} \cr } } \right| = 0,(0 < x < \pi )$, are
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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (18 March Morning Shift) PYQ

Solution

Qus : 37 JEE MAIN PYQ

Let $\alpha, \beta, \gamma$ be the real roots of the equation $x^3 + ax^2 + bx + c = 0$, $(a, b, c \in \mathbb{R} \text{ and } a, b \ne 0)$. If the system of equations (in $u, v, w$) given by $\alpha u + \beta v + \gamma w = 0$, $\beta u + \gamma v + \alpha w = 0$, $\gamma u + \alpha v + \beta w = 0$ has non-trivial solution, then the value of $\dfrac{a^2}{b}$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (18 March Morning Shift) PYQ

Solution

Qus : 38 JEE MAIN PYQ

Let $A=\left[\begin{array}{ccc}2 & 1 & 2 \\ 6 & 2 & 11 \\ 3 & 3 & 2\end{array}\right]$ and $P=\left[\begin{array}{lll}1 & 2 & 0 \\ 5 & 0 & 2 \\ 7 & 1 & 5\end{array}\right]$. The sum of the prime factors of $\left|P^{-1} A P-2 I\right|$ is equal to

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (29 January Evening Shift) PYQ

Solution

Qus : 39 JEE MAIN PYQ

Let $a \in R$ and $A$ be a matrix of order $3 \times 3$ such that $\operatorname{det}(A)=-4$ and $A+I=\left[\begin{array}{lll}1 & a & 1 \\ 2 & 1 & 0 \\ a & 1 & 2\end{array}\right]$, where $I$ is the identity matrix of order $3 \times 3$. If $\operatorname{det}((a+1) \operatorname{adj}((a-1) A))$ is $2^{\mathrm{m}} 3^{\mathrm{n}}, \mathrm{m}$, $\mathrm{n} \in\{0,1,2, \ldots, 20\}$, then $\mathrm{m}+\mathrm{n}$ is equal to :

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

Solution

Qus : 40 JEE MAIN PYQ

Let $\alpha $ and $\beta $ be the roots of the equation x² + x + 1 = 0. Then for y $ \ne $ 0 in R,
$\left| {\matrix{ {y + 1} & \alpha & \beta \cr \alpha & {y + \beta } & 1 \cr \beta & 1 & {y + \alpha } \cr } } \right|$

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (9 April Morning Shift) PYQ

Solution

Qus : 41 JEE MAIN PYQ

If $f(x)= \begin{vmatrix} x^{3} & 2x^{2}+1 & 1+3x\\ 3x^{2}+2 & 2x & x^{3}+6\\ x^{3}-x & 4 & x^{2}-2 \end{vmatrix} \ \text{for all } x\in\mathbb{R},\ \text{then } 2f(0)+f'(0)$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (31 January Morning Shift) PYQ

Solution

Qus : 42 JEE MAIN PYQ

If the system of equations

$ \begin{aligned} & 2 x+\lambda y+3 z=5 \\ & 3 x+2 y-z=7 \\ & 4 x+5 y+\mu z=9 \end{aligned} $

has infinitely many solutions, then $\left(\lambda^2+\mu^2\right)$ is equal to :

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

Solution

Qus : 43 JEE MAIN PYQ

The number of distinct real roots of the equation $ \begin{vmatrix} \cos x & \sin x & \sin x \\ \sin x & \cos x & \sin x \\ \sin x & \sin x & \cos x \end{vmatrix} = 0 $ in the interval $ \left[ -\frac{\pi}{4}, \frac{\pi}{4} \right] $ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (9 April Morning Shift) PYQ

Solution

Qus : 44 JEE MAIN PYQ

If the system of equations $2x+3y-z=0,\ x+ky-2z=0$ and $2x-y+z=0$ has a non-trivial solution $(x,y,z)$, then $\dfrac{x}{y}+\dfrac{y}{z}+\dfrac{z}{x}+k$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (9 April Evening Shift) PYQ

Solution

Qus : 45 JEE MAIN PYQ

If ${\Delta _1} = \left| {\matrix{ x & {\sin \theta } & {\cos \theta } \cr { - \sin \theta } & { - x} & 1 \cr {\cos \theta } & 1 & x \cr } } \right|$ and
${\Delta _2} = \left| {\matrix{ x & {\sin 2\theta } & {\cos 2\theta } \cr { - \sin 2\theta } & { - x} & 1 \cr {\cos 2\theta } & 1 & x \cr } } \right|$, $x \ne 0$ ;

then for all $\theta \in \left( {0,{\pi \over 2}} \right)$ :

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

Solution

Qus : 46 JEE MAIN PYQ

Let $A = \left[ {\matrix{ 1 & { - 2} & \alpha \cr \alpha & 2 & { - 1} \cr } } \right]$ and $B = \left[ {\matrix{ 2 & \alpha \cr { - 1} & 2 \cr 4 & { - 5} \cr } } \right],\,\alpha \in C$. Then the absolute value of the sum of all values of $\alpha$ for which det(AB) = 0 is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (30 June Morning Shift) PYQ

Solution

Qus : 47 JEE MAIN PYQ

Let $A$ be a matrix of order $3\times 3$ and $|A|=5$. If $\left|,2,\operatorname{adj}\left(3A,\operatorname{adj}(2A)\right)\right|=2^{\alpha}\cdot 3^{\beta}\cdot 5^{\gamma}$, $\alpha,\beta,\gamma\in\mathbb{N}$, then $\alpha+\beta+\gamma$ is equal to

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (3 April Morning Shift) PYQ

Solution

Qus : 48 JEE MAIN PYQ

If the minimum and the maximum values of the function $f:\left[ {{\pi \over 4},{\pi \over 2}} \right] \to R$, defined by$f\left( \theta \right) = \left| {\matrix{ { - {{\sin }^2}\theta } & { - 1 - {{\sin }^2}\theta } & 1 \cr { - {{\cos }^2}\theta } & { - 1 - {{\cos }^2}\theta } & 1 \cr {12} & {10} & { - 2} \cr } } \right|$ are m and M respectively, then the ordered pair (m,M) isequal to :

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

Solution

Qus : 49 JEE MAIN PYQ

The sum of the real roots of the equation
$\left| {\matrix{ x & { - 6} & { - 1} \cr 2 & { - 3x} & {x - 3} \cr { - 3} & {2x} & {x + 2} \cr } } \right| = 0$, is equal to :

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

Solution

Qus : 50 JEE MAIN PYQ

If a + x = b + y = c + z + 1, where a, b, c, x, y, z are non-zero distinct real numbers, then
$\left| {\matrix{ x & {a + y} & {x + a} \cr y & {b + y} & {y + b} \cr z & {c + y} & {z + c} \cr } } \right|$ is equal to :

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

Solution

Qus : 51 JEE MAIN PYQ

Let $d\in\mathbb{R}$, and $A=\begin{bmatrix} -2 & 4+d & \sin\theta-2\\ 1 & \sin\theta+2 & d\\ 5 & 2\sin\theta-d & -\sin\theta+2+2d \end{bmatrix},\ \theta\in[0,2\pi].$ If the minimum value of $\det(A)$ is $8$, then a value of $d$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (10 January Morning Shift) PYQ

Solution

Qus : 52 JEE MAIN PYQ

The set of all values of $\lambda$ for which the system of linear equations

$2x_{1}-2x_{2}+x_{3}=\lambda x_{1}$

$2x_{1}-3x_{2}+2x_{3}=\lambda x_{2}$

$-x_{1}+2x_{2}=\lambda x_{3}$

has a non-trivial solution

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2015 (Offline) PYQ

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