JEE Main Maths · Determinants

Cramer's Rule in JEE Main

Name: Cramer's Rule: JEE Main previous year questions
Creator: Lumi

Cramer's Rule (Maths, Determinants) came 31 times in 30 of the 42 JEE Main shifts Lumi analysed, across 9 distinct ideas. 16 of them came in 2024–26; it was last asked in 2026.

Questions: 31; in 30 shifts
Ideas asked: 9; 5 asked more than once
Numerical answer: 3; 10% of its questions
Pattern: Asked most years; last asked 2026

Questions each year

In the shifts Lumi analysed for each year.

Difficulty and format

Easy 5Medium 24Hard 2

Format

Single correct28 Q
Numerical value3 Q

Ideas inside the topic

9 ideas

Condition for Infinite Solutions10 Q
Condition for No Solution6 Q
Parameter Evaluation in Homogeneous Systems5 Q
Evaluating Parameters for Consistency4 Q
Homogeneous System Solutions2 Q
Conditions for Integer Solutions1 Q
Solving Column Vector Matrix Equations1 Q
Trigonometric Coefficients and Solution Counting1 Q
Condition for Unique Solution1 Q

Where it sits

Part of Determinants, which had 59 questions in all. Cramer's Rule accounts for 53% of them. In Lumi's JEE taxonomy it belongs to Algebra.

Some questions sit in other chapters too: Matrices, Straight Lines.

Every question

All 31 Cramer's Rule questions

Newest first, each with its options and official answer.

2 Apr 2026, Shift 1 · Q3Let $\alpha, \beta \in \mathbf{R}$ be such that the system of linear equations $x+2y+z=5$ $2x+y+\alpha z=5$ $8x+4y+\beta z=18$ has no…MediumSingle correct
2 Apr 2026, Shift 2 · Q3If the system of equations $x + 5y + 6z = 4,$ $2x + 3y + 4z = 7,$ $x + 6y + az = b$ has infinitely many solutions, then the point $(a, b)$ …MediumSingle correct
4 Apr 2026, Shift 2 · Q3If the system of equations: $x+y+z=5$ $x+2y+3z=9$ $x+3y+\lambda z=\mu$ has infinitely many solutions, then the value of $\lambda+\mu$ is:EasySingle correct
5 Apr 2026, Shift 1 · Q4Consider the system of linear equations in $x, y, z$ : $x + 2y + tz = 0$ , $6x + y + 5tz = 0$ , $3x + t^2y + f(t)\,z = 0$ , where…MediumSingle correct
6 Apr 2026, Shift 2 · Q4The sum of all possible values of $\theta\in[0,2\pi]$ , for which the system of equations : $x\cos 3\theta-8y-12z=0$ …MediumSingle correct
8 Apr 2026, Shift 2 · Q3If the system of linear equations : $x + y + z = 6$ , $x + 2y + 5z = 10$ , $2x + 3y + \lambda z = \mu$ has infinitely many solutions, then…EasySingle correct
2 Apr 2025, Shift 1 · Q20If the system of linear equations $3x+y+\beta z=3$ $2x+\alpha y-z=-3$ $x+2y+z=4$ has infinitely many solutions, then the value of…MediumSingle correct
2 Apr 2025, Shift 2 · Q4If the system of equations $2x + \lambda y + 3z = 5$ $3x + 2y - z = 7$ $4x + 5y + \mu z = 9$ has infinitely many solutions, then…MediumSingle correct
7 Apr 2025, Shift 1 · Q4Let the system of equations : $2x + 3y + 5z = 9$ , $7x + 3y - 2z = 8$ , $12x + 3y - (4+\lambda)z = 16 - \mu$ , have infinitely many…MediumSingle correct
7 Apr 2025, Shift 2 · Q5Let the system of equations $x+5y-z=1$ $4x+3y-3z=7$ $24x+y+\lambda z=\mu$ $\lambda,\mu\in\mathbf{R}$ , have infinitely many solutions. Then…HardSingle correct
6 Apr 2024, Shift 2 · Q22If the system of equations $2x+7y+\lambda z=3$ $3x+2y+5z=4$ $x+\mu y+32z=-1$ has infinitely many solutions, then $(\lambda-\mu)$ is equal…MediumNumerical value
9 Apr 2024, Shift 1 · Q3Let $\lambda,\mu\in\mathbf{R}$ . If the system of equations $3x+5y+\lambda z=3$ $7x+11y-9z=2$ $97x+155y-189z=\mu$ has infinitely many…MediumSingle correct
9 Apr 2024, Shift 2 · Q22Consider the matrices : $A=\begin{bmatrix}2&-5\\3&m\end{bmatrix},\ B=\begin{bmatrix}20\\m\end{bmatrix}$ and…MediumNumerical value
30 Jan 2024, Shift 2 · Q4Consider the system of linear equations $x + y + z = 5$ , $x + 2y + \lambda^2 z = 9$ , $x + 3y + \lambda z = \mu$ , where…MediumSingle correct
31 Jan 2024, Shift 1 · Q4If the system of linear equations $x-2y+z=-4$ $2x+\alpha y+3z=5$ $3x-y+\beta z=3$ has infinitely many solutions, then $12\alpha+13\beta$ …MediumSingle correct
31 Jan 2024, Shift 2 · Q4Let $A$ be a $3\times3$ real matrix such that $A\begin{pmatrix}1\\0\\1\end{pmatrix}=2\begin{pmatrix}1\\0\\1\end{pmatrix}$ ,…MediumSingle correct
6 Apr 2023, Shift 1 · Q4If the system of equations $x+y+az=b$ $2x+5y+2z=6$ $x+2y+3z=3$ has infinitely many solutions, then $2a+3b$ is equal toMediumSingle correct
8 Apr 2023, Shift 2 · Q3Let S be the set of all values of $\theta \in [-\pi, \pi]$ for which the system of linear equations $x + y + \sqrt{3}z = 0$ …MediumSingle correct
13 Apr 2023, Shift 2 · Q4If the system of equations $2x+y-z=5$ $2x-5y+\lambda z=\mu$ $x+2y-5z=7$ has infinitely many solutions, then…MediumSingle correct
25 Jul 2022, Shift 1 · Q4The number of $\theta\in(0,4\pi)$ for which the system of linear equations $3(\sin 3\theta)x-y+z=2$ $3(\cos 2\theta)x+4y+3z=3$ …MediumSingle correct
24 Jun 2022, Shift 1 · Q6The 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…MediumSingle correct
29 Jun 2022, Shift 1 · Q7If the system of linear equations $2x + y - z = 7$ $x - 3y + 2z = 1$ $x + 4y + \delta z = k$ , where $\delta, k \in \mathbf{R}$ has…EasySingle correct
3 Aug 2021, Shift 2 · Q65For the system of linear equations $(k-3)x + y + z = 0$ $x + (k-3)y + z = 0$ $x + y + (k-3)z = 0$ the number of distinct values of $k$ ,…MediumSingle correct
25 Jul 2021, Shift 1 · Q79The values of a and b, for which the system of equations $2x+3y+6z=8$ $x+2y+az=5$ $3x+5y+9z=b$ has no solution, are :EasySingle correct
18 Mar 2021, Shift 1 · Q64Let $\alpha,\beta,\gamma$ be the real roots of the equation, $x^3+ax^2+bx+c=0$ , ( $a,b,c\in\mathbf{R}$ and $a,b\ne0$ ). If the system of…HardSingle correct
18 Mar 2021, Shift 1 · Q77The number of integral values of m so that the abscissa of point of intersection of lines $3x+4y=9$ and $y=mx+1$ is also an integer, is :MediumSingle correct
8 Jan 2020, Shift 1 · Q53For which of the following ordered pairs $(\mu, \delta)$ , the system of linear equations $x+2y+3z=1$ $3x+4y+5z=\mu$ $4x+4y+4z=\delta$ is…MediumSingle correct
9 Jan 2020, Shift 2 · Q55The following system of linear equations $7x+6y-2z=0$ $3x+4y+2z=0$ $x-2y-6z=0$ , hasEasySingle correct
2 Sep 2020, Shift 1 · Q55Let $S$ be the set of all $\lambda\in\mathbf{R}$ for which the system of linear equations $2x-y+2z=2$ $x-2y+\lambda z=-4$ …MediumSingle correct
6 Sep 2020, Shift 2 · Q71The sum of distinct values of $\lambda$ for which the system of equations $(\lambda-1)x+(3\lambda+1)y+2\lambda z=0$ …MediumNumerical value
2 Apr 2017 (offline) · Q65If 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…MediumSingle correct