Learn

Friday, 9 October

JEE Main Maths · Class 12

Determinants: JEE Main previous year questions

Determinants had 59 questions in the 42 JEE Main shifts Lumi analysed, about 1.4 a shift, asked in 38 of 42 shifts. It ranks 7 of 22 Maths chapters by questions; 19% of its questions were hard.

Questions
59
in 38 of 42 shifts
A shift, on average
1.4
of 25 Maths questions
Since 2024
-0.3
1.5 a shift in 2017–23, 1.2 in 2024–26
Numerical answer
8
14% of its questions

Year by year

How often it came

Questions in the analysed shifts of each year. Years differ in how many shifts Lumi analysed, so read the bars with the shift count.

Questions each year
06123’176’208’215’224’2312’249’2512’26

2017: 1 shifts · 2020: 4 shifts · 2021: 4 shifts · 2022: 4 shifts · 2023: 4 shifts · 2024: 8 shifts · 2025: 8 shifts · 2026: 9 shifts

Difficulty by year
  • 20173
  • 20206
  • 20218
  • 20225
  • 20234
  • 202412
  • 20259
  • 202612
  • Easy
  • Medium
  • Hard

Inside the chapter

Topics and the ideas that repeat

5 topics and 16 distinct ideas; 9 ideas were asked more than once. Most questions are single correct and multi-step.

Topics, by questions

9 questions had no close topic in our taxonomy and are counted for the chapter only.

Ideas asked most
9 repeat

Study it on Lumi

Determinants: the interactive lesson

Every question

All 59 Determinants questions

Newest first. Each opens with its options and the official answer.

2026 12 questions

  1. 2 Apr 2026, Shift 1 · Q3Let α,β∈R\alpha, \beta \in \mathbf{R} be such that the system of linear equations x+2y+z=5x+2y+z=5 2x+y+αz=52x+y+\alpha z=5 8x+4y+βz=188x+4y+\beta z=18 has no…MediumSingle correct
  2. 4 Apr 2026, Shift 1 · Q6Let A=[112−201135]A=\begin{bmatrix}1&1&2\\-2&0&1\\1&3&5\end{bmatrix}. Then the sum of all elements of the matrix…MediumSingle correct
  3. 4 Apr 2026, Shift 2 · Q3If the system of equations: x+y+z=5x+y+z=5 x+2y+3z=9x+2y+3z=9 x+3y+λz=μx+3y+\lambda z=\mu has infinitely many solutions, then the value of λ+μ\lambda+\mu is:EasySingle correct
  4. 4 Apr 2026, Shift 2 · Q6Let A=[1274−2838−7]A=\begin{bmatrix}1&2&7\\4&-2&8\\3&8&-7\end{bmatrix} and det⁡(A−αI)=0\det(A-\alpha I)=0, where α\alpha is a real number. If the largest…HardSingle correct
  5. 5 Apr 2026, Shift 1 · Q3Let A be a 3×33 \times 3 matrix such that AT[101]=[522]A^T\begin{bmatrix}1\\0\\1\end{bmatrix}=\begin{bmatrix}5\\2\\2\end{bmatrix},…HardSingle correct
  6. 5 Apr 2026, Shift 1 · Q4Consider the system of linear equations in x,y,zx, y, z: x+2y+tz=0x + 2y + tz = 0, 6x+y+5tz=06x + y + 5tz = 0, 3x+t2y+f(t) z=03x + t^2y + f(t)\,z = 0, where…MediumSingle correct
  7. 5 Apr 2026, Shift 2 · Q3If f:N→Zf: \mathbf{N} \to \mathbf{Z} is defined by…HardSingle correct
  8. 6 Apr 2026, Shift 1 · Q21Let A=[−11−1101001]A=\begin{bmatrix}-1&1&-1\\1&0&1\\0&0&1\end{bmatrix} satisfy…MediumNumerical value
  9. 6 Apr 2026, Shift 2 · Q4The sum of all possible values of θ∈[0,2π]\theta\in[0,2\pi], for which the system of equations : xcos⁡3θ−8y−12z=0x\cos 3\theta-8y-12z=0…MediumSingle correct
  10. 6 Apr 2026, Shift 2 · Q17Let A=[13−121α01−1]A=\begin{bmatrix}1&3&-1\\2&1&\alpha\\0&1&-1\end{bmatrix} be a singular matrix. Let f(x)=∫0x(t2+2t+3)dtf(x)=\int_0^x\left(t^2+2t+3\right)dt,…MediumSingle correct
  11. 8 Apr 2026, Shift 2 · Q3If the system of linear equations : x+y+z=6x + y + z = 6, x+2y+5z=10x + 2y + 5z = 10, 2x+3y+λz=μ2x + 3y + \lambda z = \mu has infinitely many solutions, then…EasySingle correct
  12. 8 Apr 2026, Shift 2 · Q4Let A=[α12230045]A = \begin{bmatrix} \alpha & 1 & 2 \\ 2 & 3 & 0 \\ 0 & 4 & 5 \end{bmatrix} and…HardSingle correct

2025 9 questions

  1. 2 Apr 2025, Shift 1 · Q15Let a∈Ra\in\mathbf{R} and A be a matrix of order 3×33\times3 such that det⁡(A)=−4\det(A)=-4 and…MediumSingle correct
  2. 2 Apr 2025, Shift 1 · Q20If the system of linear equations 3x+y+βz=33x+y+\beta z=3 2x+αy−z=−32x+\alpha y-z=-3 x+2y+z=4x+2y+z=4 has infinitely many solutions, then the value of…MediumSingle correct
  3. 2 Apr 2025, Shift 2 · Q4If the system of equations 2x+λy+3z=52x + \lambda y + 3z = 5 3x+2y−z=73x + 2y - z = 7 4x+5y+μz=94x + 5y + \mu z = 9 has infinitely many solutions, then…MediumSingle correct
  4. 3 Apr 2025, Shift 1 · Q5Let AA be a matrix of order 3×33 \times 3 and ∣A∣=5|A| = 5. If ∣2 adj(3A adj(2A))∣=2α⋅3β⋅5γ|2\,adj(3A\,adj(2A))| = 2^{\alpha}\cdot 3^{\beta}\cdot 5^{\gamma},…MediumSingle correct
  5. 3 Apr 2025, Shift 1 · Q16If y(x)=∣sin⁡xcos⁡xsin⁡x+cos⁡x+1272827111∣y(x) = \begin{vmatrix} \sin x & \cos x & \sin x + \cos x + 1 \\ 27 & 28 & 27 \\ 1 & 1 & 1 \end{vmatrix}, x∈Rx \in \mathbb{R}, then…MediumSingle correct
  6. 3 Apr 2025, Shift 2 · Q22Let I be the identity matrix of order 3×33 \times 3 and for the matrix…HardNumerical value
  7. 7 Apr 2025, Shift 1 · Q4Let the system of equations : 2x+3y+5z=92x + 3y + 5z = 9, 7x+3y−2z=87x + 3y - 2z = 8, 12x+3y−(4+λ)z=16−μ12x + 3y - (4+\lambda)z = 16 - \mu, have infinitely many…MediumSingle correct
  8. 7 Apr 2025, Shift 2 · Q5Let the system of equations x+5y−z=1x+5y-z=1 4x+3y−3z=74x+3y-3z=7 24x+y+λz=μ24x+y+\lambda z=\mu λ,μ∈R\lambda,\mu\in\mathbf{R}, have infinitely many solutions. Then…HardSingle correct
  9. 8 Apr 2025, Shift 2 · Q4Let A=[22+p2+p+q46+2p8+3p+2q612+3p20+6p+3q]A = \begin{bmatrix} 2 & 2+p & 2+p+q \\ 4 & 6+2p & 8+3p+2q \\ 6 & 12+3p & 20+6p+3q \end{bmatrix}. If…MediumSingle correct

2024 12 questions

  1. 6 Apr 2024, Shift 2 · Q4If AA is a square matrix of order 3 such that det⁡(A)=3\det(A)=3 and…MediumSingle correct
  2. 6 Apr 2024, Shift 2 · Q22If the system of equations 2x+7y+λz=32x+7y+\lambda z=3 3x+2y+5z=43x+2y+5z=4 x+μy+32z=−1x+\mu y+32z=-1 has infinitely many solutions, then (λ−μ)(\lambda-\mu) is equal…MediumNumerical value
  3. 9 Apr 2024, Shift 1 · Q3Let λ,μ∈R\lambda,\mu\in\mathbf{R}. If the system of equations 3x+5y+λz=33x+5y+\lambda z=3 7x+11y−9z=27x+11y-9z=2 97x+155y−189z=μ97x+155y-189z=\mu has infinitely many…MediumSingle correct
  4. 9 Apr 2024, Shift 1 · Q23Let A be a non-singular matrix of order 3. If det⁡(3 adj(2 adj((det⁡A)A)))=3−13⋅2−10\det(3\,\mathrm{adj}(2\,\mathrm{adj}((\det A)A)))=3^{-13}\cdot2^{-10} and…HardNumerical value
  5. 9 Apr 2024, Shift 2 · Q22Consider the matrices : A=[2−53m], B=[20m]A=\begin{bmatrix}2&-5\\3&m\end{bmatrix},\ B=\begin{bmatrix}20\\m\end{bmatrix} and…MediumNumerical value
  6. 29 Jan 2024, Shift 1 · Q5Let A=[1000αβ0βα]A=\begin{bmatrix}1&0&0\\0&\alpha&\beta\\0&\beta&\alpha\end{bmatrix} and ∣2A∣3=221|2A|^3=2^{21} where α,β∈Z\alpha,\beta\in\mathbb{Z}, Then a…EasySingle correct
  7. 30 Jan 2024, Shift 2 · Q3Let R=(x000y000z)R = \begin{pmatrix} x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z \end{pmatrix} be a non-zero 3×33\times 3 matrix, where…HardOther
  8. 30 Jan 2024, Shift 2 · Q4Consider the system of linear equations x+y+z=5x + y + z = 5, x+2y+λ2z=9x + 2y + \lambda^2 z = 9, x+3y+λz=μx + 3y + \lambda z = \mu, where…MediumSingle correct
  9. 31 Jan 2024, Shift 1 · Q3If f(x)=∣x32x2+11+3x3x2+22xx3+6x3−x4x2−2∣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} for all x∈Rx\in\mathbb{R}, then…MediumSingle correct
  10. 31 Jan 2024, Shift 1 · Q4If the system of linear equations x−2y+z=−4x-2y+z=-4 2x+αy+3z=52x+\alpha y+3z=5 3x−y+βz=33x-y+\beta z=3 has infinitely many solutions, then 12α+13β12\alpha+13\beta…MediumSingle correct
  11. 31 Jan 2024, Shift 2 · Q4Let AA be a 3×33\times3 real matrix such that A(101)=2(101)A\begin{pmatrix}1\\0\\1\end{pmatrix}=2\begin{pmatrix}1\\0\\1\end{pmatrix},…MediumSingle correct
  12. 31 Jan 2024, Shift 2 · Q22Let A be a 3×33\times3 matrix and det⁡(A)=2\det(A)=2. If…MediumNumerical value

2023 4 questions

  1. 6 Apr 2023, Shift 1 · Q4If the system of equations x+y+az=bx+y+az=b 2x+5y+2z=62x+5y+2z=6 x+2y+3z=3x+2y+3z=3 has infinitely many solutions, then 2a+3b2a+3b is equal toMediumSingle correct
  2. 8 Apr 2023, Shift 2 · Q3Let S be the set of all values of θ∈[−π,π]\theta \in [-\pi, \pi] for which the system of linear equations x+y+3z=0x + y + \sqrt{3}z = 0…MediumSingle correct
  3. 13 Apr 2023, Shift 2 · Q4If the system of equations 2x+y−z=52x+y-z=5 2x−5y+λz=μ2x-5y+\lambda z=\mu x+2y−5z=7x+2y-5z=7 has infinitely many solutions, then…MediumSingle correct
  4. 13 Apr 2023, Shift 2 · Q5Let for A=[123α31112]A=\begin{bmatrix}1&2&3\\ \alpha&3&1\\ 1&1&2\end{bmatrix}, ∣A∣=2|A|=2. If ∣2 adj(2 adj(2A))∣=32n|2\,\mathrm{adj}(2\,\mathrm{adj}(2A))|=32^n, then…MediumSingle correct

2022 5 questions

  1. 25 Jul 2022, Shift 1 · Q4The number of θ∈(0,4π)\theta\in(0,4\pi) for which the system of linear equations 3(sin⁡3θ)x−y+z=23(\sin 3\theta)x-y+z=2 3(cos⁡2θ)x+4y+3z=33(\cos 2\theta)x+4y+3z=3…MediumSingle correct
  2. 28 Jul 2022, Shift 1 · Q14Let the matrix A=[010001100]A=\begin{bmatrix}0&1&0\\0&0&1\\1&0&0\end{bmatrix} and the matrix B0=A49+2A98B_0=A^{49}+2A^{98}. If Bn=Adj(Bn−1)B_n=\mathrm{Adj}(B_{n-1}) for…HardSingle correct
  3. 24 Jun 2022, Shift 1 · Q6The number of values of α\alpha for which the system of equations : x+y+z=αx+y+z=\alpha αx+2αy+3z=−1\alpha x+2\alpha y+3z=-1 x+3αy+5z=4x+3\alpha y+5z=4 is…MediumSingle correct
  4. 24 Jun 2022, Shift 1 · Q9Let S={n:1≤n≤50S = \{\sqrt{n} : 1 \le n \le 50 and n is odd}\}. Let a∈Sa \in S and…MediumSingle correct
  5. 29 Jun 2022, Shift 1 · Q7If the system of linear equations 2x+y−z=72x + y - z = 7 x−3y+2z=1x - 3y + 2z = 1 x+4y+δz=kx + 4y + \delta z = k, where δ,k∈R\delta, k \in \mathbf{R} has…EasySingle correct

2021 8 questions

  1. 3 Aug 2021, Shift 2 · Q63Let A=(aij)A = (a_{ij}) be a 3×33\times3 matrix, where aij=7max⁡{i,j}a_{ij} = 7^{\max\{i,j\}}. Then det⁡A\det A is equal toMediumSingle correct
  2. 3 Aug 2021, Shift 2 · Q64Let AA be a 3×33\times3 matrix and ∣A∣=−1|A| = -1. A matrix BB is obtained from the matrix AA by applying the following elementary row…EasySingle correct
  3. 3 Aug 2021, Shift 2 · Q65For the system of linear equations (k−3)x+y+z=0(k-3)x + y + z = 0 x+(k−3)y+z=0x + (k-3)y + z = 0 x+y+(k−3)z=0x + y + (k-3)z = 0 the number of distinct values of kk,…MediumSingle correct
  4. 25 Jul 2021, Shift 1 · Q79The values of a and b, for which the system of equations 2x+3y+6z=82x+3y+6z=8 x+2y+az=5x+2y+az=5 3x+5y+9z=b3x+5y+9z=b has no solution, are :EasySingle correct
  5. 25 Jul 2021, Shift 1 · Q88Let M={A=(abcd):a,b,c,d∈{±3,±2,±1,0}}M=\left\{A=\begin{pmatrix}a&b\\c&d\end{pmatrix}:a,b,c,d\in\{\pm3,\pm2,\pm1,0\}\right\}. Define f:M→Zf:M\to\mathbf{Z}, as…MediumNumerical value
  6. 16 Mar 2021, Shift 2 · Q77The maximum value of…MediumSingle correct
  7. 18 Mar 2021, Shift 1 · Q64Let α,β,γ\alpha,\beta,\gamma be the real roots of the equation, x3+ax2+bx+c=0x^3+ax^2+bx+c=0, (a,b,c∈Ra,b,c\in\mathbf{R} and a,b≠0a,b\ne0). If the system of…HardSingle correct
  8. 18 Mar 2021, Shift 1 · Q79The solutions of the equation…MediumSingle correct

2020 6 questions

  1. 8 Jan 2020, Shift 1 · Q53For which of the following ordered pairs (μ,δ)(\mu, \delta), the system of linear equations x+2y+3z=1x+2y+3z=1 3x+4y+5z=μ3x+4y+5z=\mu 4x+4y+4z=δ4x+4y+4z=\delta is…MediumSingle correct
  2. 9 Jan 2020, Shift 2 · Q54Let a−2b+c=1a-2b+c=1. If f(x)=∣x+ax+2x+1x+bx+3x+2x+cx+4x+3∣f(x)=\begin{vmatrix}x+a&x+2&x+1\\x+b&x+3&x+2\\x+c&x+4&x+3\end{vmatrix}, then :MediumSingle correct
  3. 9 Jan 2020, Shift 2 · Q55The following system of linear equations 7x+6y−2z=07x+6y-2z=0 3x+4y+2z=03x+4y+2z=0 x−2y−6z=0x-2y-6z=0, hasEasySingle correct
  4. 2 Sep 2020, Shift 1 · Q55Let SS be the set of all λ∈R\lambda\in\mathbf{R} for which the system of linear equations 2x−y+2z=22x-y+2z=2 x−2y+λz=−4x-2y+\lambda z=-4…MediumSingle correct
  5. 6 Sep 2020, Shift 2 · Q54Let θ=π5\theta=\frac{\pi}{5} and A=[cos⁡θsin⁡θ−sin⁡θcos⁡θ]A=\begin{bmatrix}\cos\theta&\sin\theta\\-\sin\theta&\cos\theta\end{bmatrix}. If B=A+A4B=A+A^4, then det⁡(B)\det(B) :HardSingle correct
  6. 6 Sep 2020, Shift 2 · Q71The sum of distinct values of λ\lambda for which the system of equations (λ−1)x+(3λ+1)y+2λz=0(\lambda-1)x+(3\lambda+1)y+2\lambda z=0…MediumNumerical value

2017 3 questions

  1. 2 Apr 2017 (offline) · Q63Let ω\omega be a complex number such that 2ω+1=z2\omega+1=z where z=−3z=\sqrt{-3}. If…MediumSingle correct
  2. 2 Apr 2017 (offline) · Q64If A=[2−3−41]A=\begin{bmatrix}2&-3\\-4&1\end{bmatrix}, then adj(3A2+12A)\mathrm{adj}(3A^2+12A) is equal to :MediumSingle correct
  3. 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=1x+y+z=1 x+ay+z=1x+ay+z=1 ax+by+z=0ax+by+z=0 has no…MediumSingle correct

Pattern: Asked most years.