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JEE Determinants PYQs with Solutions

508 previous year questions from Determinants (JEE Main & Advanced Mathematics) with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

508 questionsMathematics2002–2026Answers + solutions

About Determinants PYQs

Determinants has 508 previous year questions in the Quantrex Academy JEE Main & Advanced Mathematics bank. The 220 questions in this list come from JEE Main (198) and JEE Advanced (22), spanning 2002 to 2026. Each question opens on its own page with the options, the correct answer and the worked solution where available.

Questions by year (this list)

  • 2026: 11
  • 2025: 13
  • 2024: 21
  • 2023: 23
  • 2022: 17
  • 2021: 30
  • 2020: 21
  • 2019: 25
  • 2018: 10
  • 2017: 6
  • 2016: 4
  • 2015: 4

Determinants questions with solutions

1

If the system of linear equations: x+y+z=6 , x+2y+5z=10 , 2x+3y+λ z=μ has infinitely many solutions, then the value of λ+μ equals:

JEE Main 2026 Solution View → 2

The sum of all possible values of θ ∈ [0, 2π] , for which the system of equations : x 3θ - 8y - 12z = 0 x 2θ + 3y + 3z = 0 x + y + 3z = 0 has a non-trivial solution, is equal to :

JEE Main 2026 Solution View → 3

If f: N arrow Z is defined by f(n) = vmatrix n & -1 & -5 -2n^2 & 3(2k+1) & 2k+1 -3n^3 & 3k(2k+1) & 3k(k+2)+1 vmatrix , k ∈ N , and ∑_ n=1 ^ k f(n) = 98 , then k is equal to :

JEE Main 2026 Solution View → 4

Consider the system of linear equations in x, y, z : x + 2y + tz = 0 , 6x + y + 5tz = 0 , 3x + t^2 y + f(t) z = 0 , where f: ℝ arrow ℝ is a differentiable function. If this system

JEE Main 2026 Solution View → 5

If the system of equations: x+y+z=5 x+2y+3z=9 x+3y+λ z=μ has infinitely many solutions, then the value of λ+μ is:

JEE Main 2026 Solution View → 6

If 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) lies on the line

JEE Main 2026 Solution View → 7

Let α, β ∈ ℝ be such that the system of linear equations x + 2y + z = 5 2x + y + α z = 5 8x + 4y + β z = 18 has no solution. Then (β)/(α) is equal to :

JEE Main 2026 Solution View → 8

The system of linear equations x+y+z=6 2 x+5 y+a z=36 x+2 y+3 z=b has

JEE Main 2026 Solution View → 9

Among the statements : I: If | array ccc 1 & α & β α & 1 & γ β & γ & 1 array |=| array ccc 0 & α & β α & 0 & γ β & γ & 0 array | , then ^ 2 α+ ^ 2 β+ ^ 2 γ=(3)/(2) , and II : If |

JEE Main 2026 Solution View → 10

Let n be the number obtained on rolling a fair die. If the probability that the system x-n y+z=6 x+(n-2) y+(n+1) z=8 (n-1) y+z=1 has a unique solution is (k)/(6) , then the sum of

JEE Main 2026 Solution View → 11

If the system of equations 3 x+y+4 z=3 2 x+α y-z=-3 x+2 y+z=4 has no solution, then the value of α is equal to :

JEE Main 2026 Solution View → 12

Let the system of equations aligned & x+5 y-z=1 & 4 x+3 y-3 z=7 & 24 x+y+λ z=μ aligned λ, μ ∈ R , have infinitely many solutions. Then the number of the solutions of this system

JEE Main 2025 Solution View → 13

Let the system of equations : aligned & 2 x+3 y+5 z=9 & 7 x+3 y-2 z=8 & 12 x+3 y-(4+λ) z=16-μ aligned have infinitely many solutions. Then the radius of the circle centred at (λ

JEE Main 2025 Solution View → 14

If y(x)=| array ccc x & x & x+ x+1 27 & 28 & 27 1 & 1 & 1 array |, x ∈ ℝ , then (d^2 y)/(d x^2)+y is equal to

JEE Main 2025 Solution View → 15

If the system of equation aligned & 2 x+λ y+3 z=5 & 3 x+2 y-z=7 & 4 x+5 y+μ z=9 aligned has infinitely many solutions, then (λ^2+μ^2) is equal to :

JEE Main 2025 Solution View → 16

If the system of linear equations aligned & 3 x+y+β z=3 & 2 x+α y-z=-3 & x+2 y+z=4 aligned has infinitely many solutions, then the value of 22 β-9 α is :

JEE Main 2025 Solution View → 17

Let α, β(α ≠ β) be the values of m , for which the equations x+y+z=1 ; x+2 y+4 z=m and x+4 y+10 z=m^2 have infinitely many solutions. Then the value of ∑_ n=1 ^ 10 (n^α+n^β) is

JEE Main 2025 Solution View → 18

Let M and m respectively be the maximum and the minimum values of \(f(x)=| array ccc 1+ ^2 x & ^2 x & 4 4 x ^2 x & 1+ ^2 x & 4 4 x ^2 x & ^2 x & 1+4 4 x array |, x ∈ R\) Then

JEE Main 2025 Solution View → 19

If the system of equations aligned & x+2 y-3 z=2 & 2 x+λ y+5 z=5 & 14 x+3 y+μ z=33 aligned has infinitely many solutions, then λ+μ is equal to :

JEE Main 2025 Solution View → 20

For some a, b , let f(x)=| array ccc a+( x)/(x) & 1 & ~b a & 1+( x)/(x) & ~b a & 1 & ~b+( x)/(x) array |, x ≠ 0, _ x arrow 0 f(x)=λ+μ a+ν b . Then (λ+μ+ν)^2 is equal to :

JEE Main 2025 Solution View → 21

If the system of equations aligned & 2 x-y+z=4 & 5 x+λ y+3 z=12 & 100 x-47 y+μ z=212 aligned has infinitely many solutions, then μ-2 λ is equal to

JEE Main 2025 Solution View → 22

The system of equations aligned & x+y+z=6 & x+2 y+5 z=9, & x+5 y+λ z=μ, aligned has no solution if

JEE Main 2025 Solution View → 23

If the system of equations aligned & (λ-1) x+(λ-4) y+λ z=5 & λ x+(λ-1) y+(λ-4) z=7 & (λ+1) x+(λ+2) y-(λ+2) z=9 aligned has infinitely many solutions, then λ^2+λ is equal to

JEE Main 2025 Solution View → 24

If the system of linear equations : aligned & x+y+2 z=6 & 2 x+3 y+a z=a+1 & -x-3 y+b z=2 ~b aligned where a, b ∈ R , has infinitely many solutions, then 7 a+3 b is equal to :

JEE Main 2025 Solution View → 25

Let S=\ A=( array lll 0 & 1 & c 1 & a & d 1 & b & e array ): a, b, c, d, e ∈\ 0,1\ . and .|A| ∈\ -1,1\ \ , where |A| denotes the determinant of A . Then the number of elements in

JEE Advanced 2024 Solution View → 26

Consider the matrices : A=[ array ll 2 & -5 3 & m array ], B=[ array l 20 m array ] and X=[ array l x y array ] . Let the set of all m , for which the system of equations A X=B

JEE Main 2024 Solution View → 27

Let λ, μ ∈ R . If the system of equations aligned & 3 x+5 y+λ z=3 & 7 x+11 y-9 z=2 & 97 x+155 y-189 z=μ aligned has infinitely many solutions, then μ+2 λ is equal to :

JEE Main 2024 Solution View → 28

If α ≠ a, β ≠ b, γ ≠ c and | array lll α & b & c a & β & c a & b & γ array |=0 , then a α-a + b β-b + γ γ-c is equal to:

JEE Main 2024 Solution View → 29

If the system of equations x+4 y-z=λ, 7 x+9 y+μ z=-3,5 x+y+2 z=-1 has infinitely many solutions, then (2 μ+3 λ) is equal to :

JEE Main 2024 Solution View → 30

If the system of equations aligned & 2 x+7 y+λ z=3 & 3 x+2 y+5 z=4 & x+μ y+32 z=-1 aligned has infinitely many solutions, then (λ-μ) is equal to________

JEE Main 2024 Solution View → 31

For α, β ∈ ℝ and a natural number n , let A_r=| array ccc r & 1 & (n^2)/(2)+α 2 r & 2 & n^2-β 3 r-2 & 3 & (n(3 n-1))/(2) array | . Then

JEE Main 2024 Solution View → 32

Let α β γ=45 ; α, β, γ ∈ ℝ . If x(α, 1,2)+y(1, β, 2)+z(2,3, γ)=(0,0,0) for some x, y, z ∈ ℝ, x y z ≠ 0 , then 6 α+4 β+γ is equal to _______

JEE Main 2024 Solution View → 33

The values of m, n , for which the system of equations aligned & x+y+z=4, & 2 x+5 y+5 z=17, & x+2 y+m z=n aligned has infinitely many solutions, satisfy the equation:

JEE Main 2024 Solution View → 34

If the system of equations array r 11 x+y+λ z=-5 2 x+3 y+5 z=3 8 x-19 y-39 z=μ array has infinitely many solutions, then λ^4-μ is equal to :

JEE Main 2024 Solution View → 35

If the system of equations aligned & x+( 2 α) y+( 2 α) z=0 & x+( α) y+( α) z=0 & x+( α) y-( α) z=0 aligned has a non-trivial solution, then α ∈(0, (π)/(2)) is equal to :

JEE Main 2024 Solution View → 36

Let the system of equations x + 2y + 3z = 5, 2x + 3y + z = 9, 4x + 3y + = μ have infinite number of solutions. Then λ + 2μ is equal to:

JEE Main 2024 Solution View → 37

If the system of equations 2x + 3y - z = 5 x + + 3z = - 4 3x - y + = 7 has infinitely many solutions, then 13αβ is equal to

JEE Main 2024 Solution View → 38

Let A be a 3 × 3 real matrix such that A( array ll 1 0 1 array ) = 2( array ll 1 0 1 array ), A( array ll - 1 0 1 array ) = 4( array ll - 1 0 1 array ), A( array ll 0 1 0 array )

JEE Main 2024 Solution View → 39

If f(x) = | cases x ^ 3 & 2 x ^ 2 + 1 & 1 + 3x 3 x ^ 2 + 2 & 2x & x ^ 3 + 6 x ^ 3 - x & 4 & x ^ 2 - 2 cases | for all x ∈ ℝ , then 2f(0) + f ^ ' (0) is equal to

JEE Main 2024 Solution View → 40

If the system of linear equations x - 2y + z = - 4 2x + + 3z = 5 3x - y + = 3 has infinitely many solutions, then 12α + 13β is equal to

JEE Main 2024 Solution View → 41

Consider the system of linear equations x + y + z = 5, x + 2y + λ ^ 2 z = 9 and x + 3y + = μ , where λ, μ ∈ R . Then, which of the following statement is NOT correct ?

JEE Main 2024 Solution View → 42

If f(x) = | cases 2 ^ 4 x & 2 ^ 4 x & 3 + ^ 2 2x 3 + 2 ^ 4 x & 2 ^ 4 x & ^ 2 2x 2 ^ 4 x & 3 + 2 ^ 4 x & ^ 2 2x cases | then (1)/(5) f ^ ' ( 0 ) is equal to ________.

JEE Main 2024 Solution View → 43

Consider the system of linear equation x + y + z = 4μ, x + 2y + 2 = 10μ, x + 3y + 4 λ ^ 2 z = μ ^ 2 + 15 , where λ, μ ∈ R . Which one of the following statements is NOT correct?

JEE Main 2024 Solution View → 44

Let for any three distinct consecutive terms a, b, c of an A.P, the lines ax + by + c = 0 be concurrent at the point P and Q ( α, β ) be a point such that the system of equations

JEE Main 2024 Solution View → 45

The values of α , for which | cases 1 & (3)/(2) & α + (3)/(2) 1 & (1)/(3) & α + (1)/(3) 2α + 3 & 3α + 1 & 0 cases | = 0 , lie in the interval

JEE Main 2024 Solution View → 46

Let α, β and γ be real numbers. Consider the following system of linear equations x + 2y + z = 7 x + = 11 2x - 3y + = γ Match each entry in List-I to the correct entries in

JEE Advanced 2023 Solution View → 47

Let the system of linear equations – x + 2y - 9z = 7 - x + 3y + 7z = 9 - 2x + y + 5z = 8 - 3x + y + 13z = λ has a unique solution x = α, y = β, z = γ . Then the distance of the

JEE Main 2023 Solution View → 48

If the system of equations 2x + y - z = 5 2x - 5y + = μ x + 2y - 5z = 7 has infinitely many solutions, then ( λ + μ ) ^ 2 + ( λ - μ ) ^ 2 is equal to

JEE Main 2023 Solution View → 49

For the system of linear equations 2x + 4y + 2az = b x + 2y + 3z = 4 2x + 5y + 2z = 8 which of the following is NOT correct?

JEE Main 2023 Solution View → 50

Let D _ k = | array ll 1 2k 2k - 1 n & n ^ 2 + n + 2 & n ^ 2 n & n ^ 2 + n & n ^ 2 + n + 2 array | . If ∑ _ k = 1 ^ n D _ k = 96 , then n is equal to _________.

JEE Main 2023 Solution View → 51

If the system of linear equations 7x + 11y + = 13 5x + 4y + 7z = β 175x + 194y + 57z = 361 has infinitely many solutions, then α + β + 2 is equal to

JEE Main 2023 Solution View → 52

If | cases x + 1 & x & x x & x + λ & x x & x & x + λ ^ 2 cases | = (9)/(8)(103x + 81), then λ, (λ)/(3) are the roots of the equation

JEE Main 2023 Solution View → 53

Let S be the set of values of λ , for which the system of equations 6 - 3y + 3z = 4 λ ^ 2 , 2x + 6 + 4z = 1 and 3x + 2y + 3 = λ has no solution. Then, 12 ∑ _ λ ∈ S |λ| is equal to

JEE Main 2023 Solution View → 54

For the system of linear equations 2x - y + 3z = 5 3x + 2y - z = 7 4x + 5y + = β , which of the following is NOT correct?

JEE Main 2023 Solution View → 55

Let S be the set of all values of θ ∈ [ - π, π ] for which the system of linear equations x + y + 3 z = 0 - x + ( tanθ ) y + 7 z = 0 x + y + ( tanθ ) z = 0 has non-trivial

JEE Main 2023 Solution View → 56

For the system of equations x + y + z = 6 x + 2y + = 10 x + 3y + 5z = β , which one of the following is NOT true?

JEE Main 2023 Solution View → 57

If 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 to

JEE Main 2023 Solution View → 58

For the system of linear equations ax + y + z = 1 , x + ay + z = 1, x + y + az = β , which one of the following statements is NOT correct?

JEE Main 2023 Solution View → 59

Let S denote the set of all real values of λ such that the system of equations + y + z = 1 x + + z = 1 x + y + = 1 is inconsistent, then ∑ _ λ ∈ S ( |λ| ^ 2 + |λ|) is equal to

JEE Main 2023 Solution View → 60

If a point P(α, β, γ) satisfying ( cases α & β & γ cases )( cases 2 & 10 & 8 9 & 3 & 8 8 & 4 & 8 cases ) = ( cases 0 & 0 & 0 cases ) lies on the plane 2x + 4y + 3z = 5 , then 6α +

JEE Main 2023 Solution View → 61

For the system of linear equations x + y + z = 6 + + 7z = 3 x + 2y + 3z = 14 which of the following is NOT true ?

JEE Main 2023 Solution View → 62

For α, β ∈ ℝ , suppose the system of linear equations x - y + z = 5 2x + 2y + = 8 3x - y + 4z = β has infinitely many solutions. Then α and β are the roots of

JEE Main 2023 Solution View → 63

Let the system of linear equations x + y + kz = 2 2x + 3y - z = 1 3x + 4y + 2z = k have infinitely many solutions. Then the system (k + 1)x + (2k - 1)y = 7 (2k + 1)x + |k + 5|y =

JEE Main 2023 Solution View → 64

Consider the following system of questions + 2y + z = 1 2 + 3y + z = 1 3x + + 2z = β For some α, β ∈ ℝ . Then which of the following is NOT correct.

JEE Main 2023 Solution View → 65

Let S _ 1 and S _ 2 be respectively the sets of all a ∈ R - \ 0\ for which the system of linear equations ax + 2ay - 3az = 1 (2a + 1)x + (2a + 3)y + (a + 1)z = 2 (3a + 5) x + (a +

JEE Main 2023 Solution View → 66

If the system of equations x + 2y + 3z = 3 , 4x + 3y - 4z = 4 and 8x + 4y - = 9 + μ has infinitely many solutions, then the ordered pair (λ, μ) is equal to

JEE Main 2023 Solution View → 67

Let N denote the number that turns up when a fair die is rolled. If the probability that the system of equations x + y + z = 12x + Ny + 2z = 23x + 3y + Nz = 3 has unique solution

JEE Main 2023 Solution View → 68

Let α be a root of the equation (a - c) x ^ 2 + (b - a)x + (c - b) = 0 where a, b, c are distinct real numbers such that the matrix [ cases α ^ 2 & α & 1 1 & 1 & 1 a & b & c cases

JEE Main 2023 Solution View → 69

Let p, q, r be non-zero real numbers that are, respectively, the 10 ^ th , 100 ^ th and 1000 ^ th terms of a harmonic progression. Consider the system of linear equations x + y +

JEE Advanced 2022 Solution View → 70

If the system of equations x + y + z = 6 2x + 5y + = β x + 2y + 3z = 14 has infinitely many solutions, then α + β is equal to

JEE Main 2022 Solution View → 71

Let p and p + 2 be prime numbers and let Δ = | cases p ! & (p + 1) ! & (p + 2) ! (p + 1) ! & (p + 2) ! & (p + 3) ! (p + 2) ! & (p + 3) ! & (p + 4) ! cases | Then the sum of the

JEE Main 2022 Solution View → 72

If the system of linear equations. 8x + y + 4z = - 2 x + y + z = 0 - 3y = μ has infinitely many solutions, then the distance of the point (λ, μ, - (1)/(2)) from the plane 8x + y +

JEE Main 2022 Solution View → 73

The number of real values of λ , such that the system of linear equations 2x - 3y + 5z = 9 x + 3y - z = - 18 3x - y + ( λ ^ 2 - |λ|)z = 16 has no solutions, is

JEE Main 2022 Solution View → 74

The number of θ ∈ (0, 4π) for which the system of linear equations 3(sin3θ)x - y + z = 2 3(cos2θ)x + 4y + 3z = 3 6x + 7y + 7z = 9 has no solution is

JEE Main 2022 Solution View → 75

If the system of linear equations 2x + y - z = 7 x - 3y + 2z = 1 x + 4y + = k , where δ, k ∈ R has infinitely many solutions, then δ + k is equal to

JEE Main 2022 Solution View → 76

If the system of linear equations 2x - 3y = γ + 5 + 5y = β + 1 , where α, β, γ ∈ R has infinitely many solutions, then the value of |9α + 3β + 5γ| is equal to

JEE Main 2022 Solution View → 77

If the system of linear equations 2x + 3y - z = - 2 x + y + z = 4 x - y + |λ|z = 4λ - 4 where λ ∈ ℝ , has no solution, then

JEE Main 2022 Solution View → 78

Let f(x) = | cases a & - 1 & 0 ax & a & - 1 a x ^ 2 & ax & a cases |, a ∈ R . Then the sum of the squares of all the values of a for 2 f ^ ' (10) - f ^ ' (5) + 100 = 0 is

JEE Main 2022 Solution View → 79

Let the system of linear equations x + 2y + z = 2 , + 3y - z = α, - + y + 2z = - α be inconsistent. Then α is equal to

JEE Main 2022 Solution View → 80

If the system of equations + y + z = 5, x + 2y + 3z = 4, x + 3y + 5z = β . Has infinitely many solutions, then the ordered pair (α, β) is equal to

JEE Main 2022 Solution View → 81

The ordered pair (a, b) , for which the system of linear equations 3x - 2y + z = b 5x - 8y + 9z = 3 2x + y + az = - 1 has no solution, is

JEE Main 2022 Solution View → 82

The system of equations - kx + 3y - 14z = 25 - 15x + 4y - kz = 3 - 4x + y + 3z = 4 Question: is consistent for all k in the set

JEE Main 2022 Solution View → 83

Let A be a 3 × 3 real matrix such that A( array ll 1 1 0 array ) = ( array ll 1 1 0 array ); A( array ll 1 0 1 array ) = ( array ll - 1 0 1 array ) and A( array ll 0 0 1 array ) =

JEE Main 2022 Solution View → 84

Let the system of linear equations x + y + az = 2 3x + y + z = 4 x + 2z = 1 have a unique solution (x, y, z) . If (α, x), (y, α) and (x, - y) are collinear points, then the sum of

JEE Main 2022 Solution View → 85

The number of values of α for which the system of equations x + y + z = α + 2 + 3z = - 1 x + 3 + 5z = 4 is inconsistent, is

JEE Main 2022 Solution View → 86

Let α, β and γ be real numbers such that the system of linear equations array c x+2 y+3 z= α 4 x+5 y+6 z= β 7 x+8 y+9 z= γ- 1 array is consistent. Let |M| represent the

JEE Advanced 2021 Solution View → 87

Let α, β and γ be real numbers such that the system of linear equations array c x+2 y+3 z= α 4 x+5 y+6 z= β 7 x+8 y+9 z= γ- 1 array is consistent. Let |M| represent the

JEE Advanced 2021 Solution View → 88

Consider the system of linear equations - x + y + 2z = 0 3x - ay + 5z = 1 2x - 2y - az = 7 Let S _ 1 be the set of all a ∈ R for which the system is inconsistent and S _ 2 be the

JEE Main 2021 Solution View → 89

If α + β + γ = 2π, then the system of equations x + (cosγ)y + (cosβ)z = 0 (cosγ)x + y + (cosα)z = 0 (cosβ)x + (cosα)y + z = 0 has :

JEE Main 2021 Solution View → 90

If a _ r = cos(2rπ)/(9) + isin(2rπ)/(9), r = 1, 2, 3, … , i = - 1 , then the determinant | cases a _ 1 & a _ 2 & a _ 3 a _ 4 & a _ 5 & a _ 6 a _ 7 & a _ 8 & a _ 9 cases | is equal

JEE Main 2021 Solution View → 91

If the following system of linear equations 2x + y + z = 5 x - y + z = 3 x + y + az = b has no solution, then :

JEE Main 2021 Solution View → 92

Let [ λ ] be the greatest integer less than or equal to λ . The set of all values of λ for which the system of linear equations x + y + z = 4, 3x + 2y + 5z = 3, 9x + 4y + ( 28 + [

JEE Main 2021 Solution View → 93

Let A = [ cases [ x + 1 ] & [ x + 2 ] & [ x + 3 ] [ x ] & [ x + 3 ] & [ x + 3 ] [ x ] & [ x + 2 ] & [ x + 4 ] cases ] , where [ x ] denotes the greatest integer less than or equal

JEE Main 2021 Solution View → 94

If the system of linear equations 2x + y - z = 3 x - y - z = α 3x + 3y + = 3 has infinitely many solutions, then |α + β - αβ| is equal to __________.

JEE Main 2021 Solution View → 95

Two fair dice are thrown. The numbers on them are taken as λ and μ, and a system of linear equations x + y + z = 5 x + 2y + 3z = μ x + 3y + = 1 is constructed. If p is the

JEE Main 2021 Solution View → 96

Let θ ∈ (0, (π)/(2)) . If the system of linear equations (1 + ^ 2 ⁡ θ)x + ^ 2 ⁡ + 4sin ⁡ 3 = 0 ^ 2 ⁡ + (1 + ^ 2 ⁡ θ)y + 4sin ⁡ 3 = 0 ^ 2 ⁡ + ^ 2 ⁡ + ( 1 + 4sin ⁡ 3θ ) z = 0 has a

JEE Main 2021 Solution View → 97

For real numbers α and β, consider the following system of linear equations: x + y - z = 2, x + 2y + = 1 and 2x - y + z = β . If the system has infinite solutions, then α + β is

JEE Main 2021 Solution View → 98

Let f(x) = | cases ^ 2 x & - 2 + ^ 2 x & cos2x 2 + ^ 2 x & ^ 2 x & cos2x ^ 2 x & ^ 2 x & 1 + cos2x cases |, x ∈ [0, π] . Then the maximum value of f(x) is equal to

JEE Main 2021 Solution View → 99

The 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 :

JEE Main 2021 Solution View → 100

The values of λ and μ such that the system of equations x + y + z = 6, 3x + 5y + 5z = 26 and x + 2y + = μ has no solution, are:

JEE Main 2021 Solution View → 101

The value of k ∈ R, for which the following system of linear equations 3x - y + 4z = 3 x + 2y - 3z = - 2 6x + 5y + kz = - 3 has infinitely many solutions, is:

JEE Main 2021 Solution View → 102

Let a, b, c, d be in arithmetic progression with common difference λ . If | cases x + a - c & x + b & x + a x - 1 & x + c & x + b x - b + d & x + d & x + c cases | = 2 , then

JEE Main 2021 Solution View → 103

Let the system of linear equations 4x + + 2z = 0 2x - y + z = 0 + 2y + 3z = 0, λ, μ ∈ R has a non-trivial solution. Then which of the following is true?

JEE Main 2021 Solution View → 104

Let α, β, γ be the real roots of the equation, x ^ 3 + a x ^ 2 + bx + c = 0, ( a, b, c ∈ R and a, b ≠ 0 ). If the system of equations (in, u, v, w ) given by + + = 0, + + = 0, + +

JEE Main 2021 Solution View → 105

If x, y, z are in arithmetic progression with common difference d, x ≠ 3d, and the determinant of the matrix [ cases 3 & 4 2 & x 4 & 5 2 & y 5 & k & z cases ] is zero, then the

JEE Main 2021 Solution View → 106

The system of equations kx + y + z = 1, x + ky + z = k and x + y + zk = k ^ 2 has no solution if k is equal to:

JEE Main 2021 Solution View → 107

The maximum value of f(x) = | cases ^ 2 x & 1 + ^ 2 x & cos2x 1 + ^ 2 x & ^ 2 x & cos2x ^ 2 x & ^ 2 x & sin2x cases |, x ∈ R is

JEE Main 2021 Solution View → 108

Consider the following system of equations: x + 2y - 3z = a 2x + 6y - 11z = b x - 2y + 7z = c where a, b and c are real constants. Then the system of equations :

JEE Main 2021 Solution View → 109

The value of | cases (a + 1)(a + 2) & a + 2 & 1 (a + 2)(a + 3) & a + 3 & 1 (a + 3)(a + 4) & a + 4 & 1 cases | is

JEE Main 2021 Solution View → 110

Let A be a 3 × 3 matrix with det (A) = 4 . Let R _ i denote the i ^ th row of A . If a matrix B is obtained by performing the operation R _ 2 → 2 R _ 2 + 5 R _ 3 on 2A , then det

JEE Main 2021 Solution View → 111

The following system of linear equations 2x + 3y + 2z = 9 3x + 2y + 2z = 9 x - y + 4z = 8

JEE Main 2021 Solution View → 112

If the system of equations kx + y + 2z = 1 3x - y - 2z = 2 - 2x - 2y - 4z = 3 has infinitely many solutions, then k is equal to ______ .

JEE Main 2021 Solution View → 113

For the system of linear equations: x - 2y = 1, x - y + kz = - 2, ky + 4z = 6, k ∈ R Consider the following statements: (A) The system has unique solution if k ≠ 2, k ≠ - 2 . (B)

JEE Main 2021 Solution View → 114

Let A and B be 3 × 3 real matrices such that A is a symmetric matrix and B is a skew-symmetric matrix. Then the system of linear equations ( A ^ 2 B ^ 2 - B ^ 2 A ^ 2 )X = O

JEE Main 2021 Solution View → 115

The system of linear equations 3x - 2y - kz = 10 2x - 4y - 2z = 6 x + 2y - z = 5m is inconsistent if :

JEE Main 2021 Solution View → 116

The sum of distinct values of λ for which the system of equations : (λ - 1)x + (3λ + 1)y + 2 = 0 (λ - 1)x + (4λ - 2)y + (λ + 3)z = 0 2x + (3λ + 1)y + 3(λ - 1)z = 0 , Has non-zero

JEE Main 2020 Solution View → 117

Let m and M be respectively the minimum and maximum value values of | cases ^ 2 x & 1 + ^ 2 x & sin2x 1 + ^ 2 x & ^ 2 x & sin2x ^ 2 x & ^ 2 x & 1 + sin2x cases | Then the ordered

JEE Main 2020 Solution View → 118

The values of λ and μ for which the system of linear equations x + y + z = 2 , x + 2y + 3z = 5 , x + 3y + = μ has infinitely many solutions, are respectively

JEE Main 2020 Solution View → 119

If the system of linear equations x + y + 3z = 0 x + 3y + k ^ 2 z = 0 3x + y + 3z = 0 has a non-zero solution ( x, y, z ) for some k ∈ R, then x + ((y)/(z)) is equal to :

JEE Main 2020 Solution View → 120

If a + x = b + y = c + z + 1, where a, b, c, x, y, z are non-zero distinct real numbers, then | cases x & a + y & x + a y & b + y & y + b z & c + y & z + c cases | is equal to :

JEE Main 2020 Solution View → 121

If the minimum and the maximum values of the function f: [(π)/(4), (π)/(2)] → R, defined by f(θ) = | cases - ^ 2 θ & - 1 - ^ 2 θ & 1 - ^ 2 θ & - 1 - ^ 2 θ & 1 12 & 10 & - 2 cases

JEE Main 2020 Solution View → 122

Let λ ∈ R . The system of linear equations 2 x _ 1 - 4 x _ 2 + λ x _ 3 = 1 x _ 1 - 6 x _ 2 + x _ 3 = 2 λ x _ 1 - 10 x _ 2 + 4 x _ 3 = 3 is inconsistent for :

JEE Main 2020 Solution View → 123

If the system of equations x + y + z = 2 2x + 4y - z = 6 3x + 2y + = μ has infinitely many solutions, then :

JEE Main 2020 Solution View → 124

Suppose the vectors x _ 1 , x _ 2 and x _ 3 are the solutions of the system of linear equations, Ax = b when the vector b on the right side is equal to b _ 1 , b _ 2 and b _ 3

JEE Main 2020 Solution View → 125

If the system of equations x - 2y + 3z = 9 2x + y + z = b x - 7y + az = 24, has infinitely many solutions, then a - b is equal to ______

JEE Main 2020 Solution View → 126

Let S be the set of all integer solutions (x, y, z) of the system of equations x - 2y + 5z = 0 - 2x + 4y + z = 0 - 7x + 14y + 9z = 0 such that 15 ≤ x ^ 2 + y ^ 2 + z ^ 2 ≤ 150 .

JEE Main 2020 Solution View → 127

If Δ = | cases x - 2 & 2x - 3 & 3x - 4 2x - 3 & 3x - 4 & 4x - 5 3x - 5 & 5x - 8 & 10x - 17 cases | = A x ^ 3 + B x ^ 2 + Cx + D , then B + C is equal to :

JEE Main 2020 Solution View → 128

Let S be the set of all λ ∈ R for which the system of linear equations 2x - y + 2z = 2 x - 2y + = - 4 x + + z = 4 has no solution. Then the set S

JEE Main 2020 Solution View → 129

The following system of linear equations 7x + 6y - 2z = 0 3x + 4y + 2z = 0 x - 2y - 6z = 0, has

JEE Main 2020 Solution View → 130

Let a - 2b + c = 1 . If f(x) = | cases x + a & x + 2 & x + 1 x + b & x + 3 & x + 2 x + c & x + 4 & x + 3 cases |, then:

JEE Main 2020 Solution View → 131

If for some α and β in R , the intersection of the following three planes x + 4y - 2z = 1 x + 7y - 5z = β x + 5y + = 5 is a line in R ^ 3 , then α + β is equal to:

JEE Main 2020 Solution View → 132

The system of linear equations + 2y + 2z = 5 2 + 3y + 5z = 8 4x + + 6z = 10 has

JEE Main 2020 Solution View → 133

For which of the following ordered pairs (μ, δ), the system of linear equations x + 2y + 3z = 1 3x + 4y + 5z = μ 4x + 4y + 4z = δ is inconsistent?

JEE Main 2020 Solution View → 134

If the system of linear equations, x + y + z = 6 x + 2y + 3z = 10 3x + 2y + = μ has more than two solutions, then μ - λ ^ 2 , is equal to.

JEE Main 2020 Solution View → 135

Let A = [ a _ ij ] and B = [ b _ ij ] be two 3 × 3 real matrices such that b _ ij = (3) ^ (i + j - 2) a _ ij , where i, j = 1,2, 3 . If the determinant of B is 81 , then

JEE Main 2020 Solution View → 136

If the system of linear equations 2x + 2ay + az = 0 2x + 3by + bz = 0 2x + 4cy + cz = 0, where a, b, c ∈ R are non-zero and distinct; has a non-zero solution, then

JEE Main 2020 Solution View → 137

Let x ∈ R and let P = [ cases 1 & 1 & 1 0 & 2 & 2 0 & 0 & 3 cases ], Q = [ cases 2 & x & x 0 & 4 & 0 x & x & 6 cases ] and R = PQ P ^ - 1 . Then which of the following options

JEE Advanced 2019 Solution View → 138

A value of θ ∈ (0, (π)/(3)), for which | cases 1 + ^ 2 θ & ^ 2 θ & 4cos6θ ^ 2 θ & 1 + ^ 2 θ & 4cos6θ ^ 2 θ & ^ 2 θ & 1 + 4cos6θ cases | = 0, is

JEE Main 2019 Solution View → 139

If [ x ] denotes the greatest integer ≤ x, then the system of linear equations [ sinθ ] x + [ - cosθ ] y = 0 , [ cotθ ] x + y = 0

JEE Main 2019 Solution View → 140

The sum of the real roots of the equation | cases x & - 6 & - 1 2 & - 3x & x - 3 - 3 & 2x & x + 2 cases | = 0, is equal to:

JEE Main 2019 Solution View → 141

Let λ be a real number for which the system of linear equations x + y + z = 6, 4x + - = λ - 2 and 3x + 2y - 4z = - 5 has infinitely many solutions. Then λ is a root of the

JEE Main 2019 Solution View → 142

If the system of linear equations x + y + z = 5 , x + 2y + 2z = 6 , x + 3y + = µ, ( λ, µ ∈ R ) , has infinitely many solutions, then the value of λ + µ is:

JEE Main 2019 Solution View → 143

If Δ _ 1 = | cases x & sinθ & cosθ - sinθ & - x & 1 cosθ & 1 & x cases | and Δ _ 2 = | cases x & sin2θ & cos2θ - sin2θ & - x & 1 cos2θ & 1 & x cases |, x ≠ 0; then for all θ ∈ (0

JEE Main 2019 Solution View → 144

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 (x)/(y) + (y)/(z) + (z)/(x) + k is equal to

JEE Main 2019 Solution View → 145

Let α and β be the roots of the equation x ^ 2 + x + 1 = 0 . Then for y ≠ 0 in R, | cases y + 1 & α & β α & y + β & 1 β & 1 & y + α cases | is equal to

JEE Main 2019 Solution View → 146

Let the numbers 2, b, c be in an A.P. and A = [ cases 1 & 1 & 1 2 & b & c 4 & b ^ 2 & c ^ 2 cases ] . If det ( A ) ∈ [ 2,16 ] , then c lies in the interval:

JEE Main 2019 Solution View → 147

If the system of linear equations x - 2y + kz = 1 2x + y + z = 2 3x - y - kz = 3 has a solution (x, y, z), z ≠ 0, then (x, y) lies on the straight line whose equation is:

JEE Main 2019 Solution View → 148

The greatest value of c ∈ 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

JEE Main 2019 Solution View → 149

If A = [ cases 1 & sinθ & 1 - sinθ & 1 & sinθ - 1 & - sinθ & 1 cases ] , then for all θ ∈ ((3π)/(4), (5π)/(4)) , det(A) lies in the interval :

JEE Main 2019 Solution View → 150

The set of all values of λ for which the system of linear equations x - 2y - 2z = x + 2y + z = - x - y = has a non-trivial solution :

JEE Main 2019 Solution View → 151

An ordered pair (α, β) for which the system of linear equations (1 + α)x + + z = 2 + (1 + β)y + z = 3 + + 2z = 2 has a unique solution, is :

JEE Main 2019 Solution View → 152

If | array ccc a-b-c & 2 a & 2 a 2 b & b-c-a & 2 b 2 c & 2 c & c-a-b array | =(a+b+c)(x+a+b+c)^ 2 , x ≠ 0 and a+b+c ≠ 0, then x is equal to

JEE Main 2019 Solution View → 153

Let A and B be two invertible matrices of order 3 × 3 . If det(ABA^ T )=8 and det (AB^ -1 )=8 , then det (BA^ -1 ~B^ T ) is equal to

JEE Main 2019 Solution View → 154

If the system of linear equations 2 x+2 y+3 z=a 3 x-y+5 z=b x-3 y+2 z=c where, a, b, care non-zero real numbers, has more than onc solution, then

JEE Main 2019 Solution View → 155

Let A = [ cases 2 & b & 1 b & b ^ 2 + 1 & b 1 & b & 2 cases ], where b > 0 . Then the minimum value of (det(A))/(b) is:

JEE Main 2019 Solution View → 156

The number of values of θ ∈ (0, π) for which the system of linear equations x + 3y + 7z = 0 - x + 4y + 7z = 0 (sin ⁡ 3θ)x + (cos ⁡ 2θ)y + 2z = 0 has a non-trivial solution, is:

JEE Main 2019 Solution View → 157

Let a _ 1 , a _ 2 , a _ 3 … , a _ 10 be in G . P . with a _ i > 0 for i = 1, 2, … , 10 and S be the set of pairs (r, k), r, k ∈ N (the set of natural numbers) for which | cases _

JEE Main 2019 Solution View → 158

If the system of equations x + y + z = 5, x + 2y + 3z = 9, x + 3y + = β has inifinitely many solutions, then β - α equals

JEE Main 2019 Solution View → 159

Let d ∈ R, and A = [ cases - 2 & 4 + d & (sinθ) - 2 1 & (sinθ) + 2 & d 5 & (2sinθ) - d & (- sinθ) + 2 + 2d cases ], θ ∈ [0, 2π] . If the minimum value of det(A) is 8, then a value

JEE Main 2019 Solution View → 160

If the system of linear equations x - 4y + 7z = g ; 3y - 5z = h ; - 2x + 5y - 9z = k is consistent, then:

JEE Main 2019 Solution View → 161

The system of linear equations x + y + z = 2 2x + 3y + 2z = 5 2x + 3y + ( a ^ 2 - 1)z = a + 1

JEE Main 2019 Solution View → 162

Let S be the of all column matrices [ array ll b _ 1 b _ 2 b _ 3 array ] such that b _ 1 , b _ 2 , b _ 3 ∈ ℝ and the system of equations (in real variables) array ll - x + 2y + 5z

JEE Advanced 2018 Solution View → 163

Let P be a matrix of order 3 × 3 such that all the entries in P are from the set \ - 1, 0,1\ . Then, the maximum possible value of the determinant of P is _______.

JEE Advanced 2018 Solution View → 164

The number of values of k for which the system of linear equations (k + 2)x + 10y = k and kx + (k + 3)y = k - 1 has no solution is

JEE Main 2018 Solution View → 165

If the system of linear equations aligned &x+a y+z=3 &x+2 y+2 z=6 &x+5 y+3 z=b aligned has no solution, then

JEE Main 2018 Solution View → 166

If f(x)=| array ccc x & x & 1 2 x & x^2 & 2 x x & x & 1 array | , then _ x arrow 0 f^ (x) x

JEE Main 2018 Solution View → 167

Let S be the set of all real values of k for which the system of linear equations aligned &x+y+z=2 &2 x+y-z=3 &3 x+2 y+k z=4 aligned has a unique solution. Then S is

JEE Main 2018 Solution View → 168

If f(x) = | cases cosx & x & 1 2sinx & x ^ 2 & 2x tanx & x & 1 cases | , then _ x → 0 ⁡ f ^ ′ (x) x

JEE Main 2018 Solution View → 169

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 :

JEE Main 2018 Solution View → 170

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 xz y ^ 2 is equal to:

JEE Main 2018 Solution View → 171

If | cases x - 4 & 2x & 2x 2x & x - 4 & 2x 2x & 2x & x - 4 cases | = (A + Bx) (x - A) ^ 2 , then the ordered pair ( A, B ) is equal to

JEE Main 2018 Solution View → 172

Which of the following is (are) NOT the square of a 3 × 3 matrix with real entries?

JEE Advanced 2017 Solution View → 173

For a real number α, if the system [ cases 1 & α & α ^ 2 α & 1 & α α ^ 2 & α & 1 cases ][ array ll x y z array ] = [ array ll 1 - 1 1 array ] of linear equations, has infinitely

JEE Advanced 2017 Solution View → 174

If x = a, y = b, z = c is a solution of the system of linear equations x + 8y + 7z = 0 9x + 2y + 3z = 0 x + y + z = 0 Such that the point (a, b, c) lies on the plane x + 2y + z =

JEE Main 2017 Solution View → 175

The number of real values of λ for which the system of linear equations, 2x + 4y - = 0 , 4x + + 2z = 0 and + 2y + 2z = 0 , has infinitely many solutions, is:

JEE Main 2017 Solution View → 176

If S = \ x ∈ [0, 2π]: | cases 0 & cos ⁡ x & - sin ⁡ x sin ⁡ x & 0 & cos ⁡ x cos ⁡ x & sin ⁡ x & 0 cases | = 0\ , then ∑ _ x ∈ S tan((π)/(3) + x) is equal to:

JEE Main 2017 Solution View → 177

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:

JEE Main 2017 Solution View → 178

Let a, λ, u ∈ ℝ . Consider the system of linear equations ax + 2y = λ 3x - 2y = μ Which of the following statement(s) is (are) correct ?

JEE Advanced 2016 Solution View → 179

The total number of distinct x ∈ R for which | cases x & x ^ 2 & 1 + x ^ 3 2x & 4 x ^ 2 & 1 + 8 x ^ 3 3x & 9 x ^ 2 & 1 + 27 x ^ 3 cases | = 10 is

JEE Advanced 2016 Solution View → 180

The number of distinct real roots of the equation, | cases cosx & sinx & sinx sinx & cosx & sinx sinx & sinx & cosx cases | = 0 in the interval [- (π)/(4), (π)/(4)] is :

JEE Main 2016 Solution View → 181

The system of linear equations x + - z = 0 - y - z = 0 x + y - = 0 has a non -trivial solution for

JEE Main 2016 Solution View → 182

Which of the following values of α satisfy the equation | cases (1 + α) ^ 2 & (1 + 2α) ^ 2 & (1 + 3α) ^ 2 (2 + α) ^ 2 & (2 + 2α) ^ 2 & (2 + 3α) ^ 2 (3 + α) ^ 2 & (3 + 2α) ^ 2 & (3

JEE Advanced 2015 Solution View → 183

If | cases x ^ 2 + x & x + 1 & x - 2 2 x ^ 2 + 3x - 1 & 3x & 3x - 3 x ^ 2 + 2x + 3 & 2x - 1 & 2x - 1 cases | = ax - 12 , then a is equal to:

JEE Main 2015 Solution View → 184

The least value of the product xyz (such that x, yandz are positive real numbers) for which the determinant | array ll x 1 1 array array ll 1 y 1 array array ll 1 1 z array | is

JEE Main 2015 Solution View → 185

The set of all values of λ for which the system of linear equations: 2 x _ 1 - 2 x _ 2 + x _ 3 = λ x _ 1 2 x _ 1 - 3 x _ 2 + 2 x _ 3 = λ x _ 2 - x _ 1 + 2 x _ 2 = λ x _ 3 has a

JEE Main 2015 Solution View → 186

If Δ _ r = | cases r & 2r - 1 & 3r - 2 (n)/(2) & n - 1 & a (1)/(2)n(n - 1) & (n - 1) ^ 2 & (1)/(2)(n - 1)(3n + 4) cases | , then the value of ∑ _ r = 1 ^ n - 1 Δ _ r

JEE Main 2014 Solution View → 187

If aligned &. array ccc a^2 & b^2 & c^2 (a+λ)^2 & (b+λ)^2 & (c+λ^2) (a-λ)^2 & (b-λ^2) & (-λ^2. array ) &=k λ| array ccc a^2 & b^2 & c^2 a & b & c 1 & 1 & 1 array |, λ ≠ 0 aligned

JEE Main 2014 Solution View → 188

If f(θ)=| array ccc 1 & θ & 1 - θ & 1 & - θ -1 & θ & 1 array | and A and B are respectively the maximum and the minimum values of f(θ) , then (A, B) is equal to:

JEE Main 2014 Solution View → 189

If a, b, c are non - zero real numbers and if the system of equations (a - 1)x = y + z (b - 1)y = x + z (c - 1)z = x + y has a non - trivial solution, then ab + bc + ca equals :

JEE Main 2014 Solution View → 190

If α, β ≠ 0 , f(n) = α ^ n + β ^ n and | cases 3 & 1 + f(1) & 1 + f(2) 1 + f(1) & 1 + f(2) & 1 + f(3) 1 + f(2) & 1 + f(3) & 1 + f(4) cases | = K (1 - α) ^ 2 (1 - β) ^ 2 (α - β) ^

JEE Main 2014 Solution View → 191

Statement-1: The system of linear equations aligned & x+( α) y+( α) z=0 & x+( α) y+( α) z=0 & x-( α) y-( α) z=0 aligned has a non-trivial solution for only one value ofα lying in

JEE Main 2013 Solution View → 192

If the system of linear equations : aligned & x_1+2 x_2+3 x_3=6 & x_1+3 x_2+5 x_3=9 & 2 x_1+5 x_2+a x_3=b aligned is consistent and has infinite number of solutions, then :

JEE Main 2013 Solution View → 193

If a, b, c are sides of a scalene triangle, then the value of | array lll a & b & c b & c & a c & a & b array | is :

JEE Main 2013 Solution View → 194

The number of values of k , for which the system of equations : (k + 1)x + 8y = 4k kx + (k + 3)y = 3k - 1 has no solution, is :

JEE Main 2013 Solution View → 195

Let P=[a_ i j ] be a 3 × 3 matrix and let Q=[b_ i j ] , where b_ i j =2^ i+j a_ i j for 1 ≤ i, j ≤ 3 . If the determinant of P is 2 , then the determinant of the matrix Q is

JEE Advanced 2012 Solution View → 196

Statement 1: If the system of equations x+k y+ 3 z=0,3 x+k y-2 z=0,2 x+3 y-4 z=0 has a nontrivial solution, then the value of k is (31)/(2) . Statement 2: A system of three

JEE Main 2012 Solution View → 197

If a, b, c , are non zero complex numbers satisfying a^2+b^2+c^2=0 and | array ccc b^2+c^2 & a b & a c a b & c^2+a^2 & b c a c & b c & a^2+b^2 array |=k a^2 b^2 c^2 , then k is

JEE Main 2012 Solution View → 198

If | array ccc -2 a & a+b & a+c b+a & -2 b & b+c c+a & b+c & -2 c array | = α( a+b() b+c() c+a) ≠ 0 then α is equal to

JEE Main 2012 Solution View → 199

If the system of equations aligned & x+y+z=6 & x+2 y+3 z=10 & x+2 y+λ z=0 aligned has a unique solution, then λ is not equal to

JEE Main 2012 Solution View → 200

The number of values of k for which the linear equations 4 x+k y+2 z=0 ; k x+4 y+z=0 ; 2 x+2 y+z=0 possess a non-zero solution is

JEE Main 2011 Solution View →
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Related JEE Mathematics chapters

Application of Derivatives (795)Three Dimensional Geometry (756)Sequences and Series (748)Functions (700)Definite Integration (692)Vector Algebra (616)Differential Equations (586)Continuity and Differentiability (576)Probability (561)Complex Number (551)Binomial Theorem (550)Quadratic Equation (517)

Determinants in other exams

NDA Determinants (130)BITSAT Determinants (20)