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Determinants — JEE Main & Advanced Mathematics PYQs

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

508 questionsMathematicsSolutions on every page
1

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

JEE Main 2026 Solution View → 2

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

JEE Main 2026 Solution View → 3

If f: N 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 R is a differentiable function. If this system has in

JEE Main 2026 Solution View → 5

If the system of equations: x+y+z=5 x+2y+3z=9 x+3y+ z= has infinitely many solutions, then the value of + 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 , R be such that the system of linear equations x + 2y + z = 5 2x + y + z = 5 8x + 4y + z = 18 has no solution. Then 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 & & & 1 & & & 1 array |= | array ccc 0 & & & 0 & & & 0 array | , then ² + ² + ² = 3 2 , and II : If | array ccc x²+x & x+1 & x-2 2 x²+3 x

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

JEE Main 2026 Solution View → 11

If the system of equations 3 x+y+4 z=3 2 x+ y-z=-3 x+2 y+z=4 has no solution, then the value of 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+ z= aligned , R , have infinitely many solutions. Then the number of the solutions of this system, If x, y,

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+ ) z=16- aligned have infinitely many solutions. Then the radius of the circle centred at ( , )

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+ y+3 z=5 & 3 x+2 y-z=7 & 4 x+5 y+ z=9 aligned has infinitely many solutions, then ( ^2+ ^2 ) is equal to :

JEE Main 2025 Solution View → 16

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

JEE Main 2025 Solution View → 17

Let , ( ) 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^ +n^ ) is equal to :

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 (M^4-m^

JEE Main 2025 Solution View → 19

If the system of equations aligned & x+2 y-3 z=2 & 2 x+ y+5 z=5 & 14 x+3 y+ z=33 aligned has infinitely many solutions, then + 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 0 f(x)= + a + b . Then ( + + )^2 is equal to :

JEE Main 2025 Solution View → 21

If the system of equations aligned & 2 x-y+z=4 & 5 x+ y+3 z=12 & 100 x-47 y+ z=212 aligned has infinitely many solutions, then -2 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+ z= , aligned has no solution if

JEE Main 2025 Solution View → 23

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

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

JEE Main 2024 Solution View → 28

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

JEE Main 2024 Solution View → 29

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

JEE Main 2024 Solution View → 30

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

JEE Main 2024 Solution View → 31

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

JEE Main 2024 Solution View → 32

Let =45 ; , , R . If x( , 1,2)+y(1, , 2)+z(2,3, )=(0,0,0) for some x, y, z R , x y z 0 , then 6 +4 + 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+ z=-5 2 x+3 y+5 z=3 8 x-19 y-39 z= array has infinitely many solutions, then ^4- is equal to :

JEE Main 2024 Solution View → 35

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

JEE Main 2024 Solution View → 36

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

JEE Main 2024 Solution View → 37

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

JEE Main 2024 Solution View → 38

Let A be a 3 × 3 real matrix such that A 1 0 1 = 2 1 0 1 , A − 1 0 1 = 4 − 1 0 1 , A 0 1 0 = 2 0 1 0 . Then, the system A − 3 I x y z = 1 2 3 has

JEE Main 2024 Solution View → 39

If f x = x 3 2 x 2 + 1 1 + 3 x 3 x 2 + 2 2 x x 3 + 6 x 3 − x 4 x 2 − 2 for all x ∈ ℝ , then 2 f 0 + f ' 0 is equal to

JEE Main 2024 Solution View → 40

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

JEE Main 2024 Solution View → 41

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

JEE Main 2024 Solution View → 42

If f x = 2 cos 4 x 2 sin 4 x 3 + sin 2 2 x 3 + 2 cos 4 x 2 sin 4 x sin 2 2 x 2 cos 4 x 3 + 2 sin 4 x sin 2 2 x then 1 5 f ' ( 0 ) is equal to ________.

JEE Main 2024 Solution View → 43

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

JEE Main 2024 Solution View → 44

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

JEE Main 2024 Solution View → 45

The values of α , for which 1 3 2 α + 3 2 1 1 3 α + 1 3 2 α + 3 3 α + 1 0 = 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 + 2 y + z = 7 x + α z = 11 2 x - 3 y + β z = γ Match each entry i

JEE Advanced 2023 Solution View → 47

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

JEE Main 2023 Solution View → 48

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

JEE Main 2023 Solution View → 49

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

JEE Main 2023 Solution View → 50

Let D k = 1 2 k 2 k - 1 n n 2 + n + 2 n 2 n n 2 + n n 2 + n + 2 . If ∑ k = 1 n D k = 96 , then n is equal to _________.

JEE Main 2023 Solution View → 51

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

JEE Main 2023 Solution View → 52

If x + 1 x x x x + λ x x x x + λ 2 = 9 8 103 x + 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 λ x - 3 y + 3 z = 4 λ 2 , 2 x + 6 λ y + 4 z = 1 and 3 x + 2 y + 3 λ z = λ has no

JEE Main 2023 Solution View → 54

For the system of linear equations 2 x - y + 3 z = 5 3 x + 2 y - z = 7 4 x + 5 y + α z = 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 + ( tan θ ) y + 7 z = 0 x + y + ( tan &#952

JEE Main 2023 Solution View → 56

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

JEE Main 2023 Solution View → 57

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

JEE Main 2023 Solution View → 58

For the system of linear equations a x + y + z = 1 , x + a y + z = 1 , x + y + a z = 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 λ x + y + z = 1 x + λ y + z = 1 x + y + λ z = 1 is inconsistent, then ∑ &#9

JEE Main 2023 Solution View → 60

If a point P α , β , γ satisfying α β γ 2 10 8 9 3 8 8 4 8 = 0 0 0 lies on the plane 2 x + 4 y + 3 z = 5 , then 6 α + 9 β + 7 γ is equa

JEE Main 2023 Solution View → 61

For the system of linear equations x + y + z = 6 α x + β y + 7 z = 3 x + 2 y + 3 z = 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 2 x + 2 y + α z = 8 3 x - y + 4 z = β has infinitely many solutions. Then &#945

JEE Main 2023 Solution View → 63

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

JEE Main 2023 Solution View → 64

Consider the following system of questions α x + 2 y + z = 1 2 α x + 3 y + z = 1 3 x + α y + 2 z = β For some α , β ∈ ℝ . Then which of th

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 a x + 2 a y - 3 a z = 1 2 a + 1 x + 2 a + 3 y + a + 1 z = 2 3 a + 5 x + a +

JEE Main 2023 Solution View → 66

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

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 = 1 2 x + N y + 2 z = 2 3 x + 3 y + N z = 3 has unique so

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 α 2 α 1 1 1 1 a b c is singular. Then

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 + z = 1

JEE Advanced 2022 Solution View → 70

If the system of equations x + y + z = 6 2 x + 5 y + α z = β x + 2 y + 3 z = 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 = p ! p + 1 ! p + 2 ! p + 1 ! p + 2 ! p + 3 ! p + 2 ! p + 3 ! p + 4 ! Then the sum of the maximum values of α and β , such

JEE Main 2022 Solution View → 72

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

JEE Main 2022 Solution View → 73

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

JEE Main 2022 Solution View → 74

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

JEE Main 2022 Solution View → 75

If the system of linear equations 2 x + y - z = 7 x - 3 y + 2 z = 1 x + 4 y + δ z = 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 2 x - 3 y = γ + 5 α x + 5 y = β + 1 , where α , β , γ ∈ R has infinitely many solutions, then the value of 9 &

JEE Main 2022 Solution View → 77

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

JEE Main 2022 Solution View → 78

Let f x = a - 1 0 a x a - 1 a x 2 a x a , 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 + 2 y + z = 2 , α x + 3 y - z = α , - α x + y + 2 z = - α be inconsistent. Then α is equal to

JEE Main 2022 Solution View → 80

If the system of equations α x + y + z = 5 , x + 2 y + 3 z = 4 , x + 3 y + 5 z = 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 3 x - 2 y + z = b 5 x - 8 y + 9 z = 3 2 x + y + a z = - 1 has no solution, is

JEE Main 2022 Solution View → 82

The system of equations - k x + 3 y - 14 z = 25 - 15 x + 4 y - k z = 3 - 4 x + y + 3 z = 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 1 1 0 = 1 1 0 ; A 1 0 1 = - 1 0 1 and A 0 0 1 = 1 1 2 . If X = x 1 x 2 x 3 T and I is an identity matrix of order 3 , then the system

JEE Main 2022 Solution View → 84

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

JEE Main 2022 Solution View → 85

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

JEE Main 2022 Solution View → 86

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

JEE Advanced 2021 Solution View → 87

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

JEE Advanced 2021 Solution View → 88

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

JEE Main 2021 Solution View → 89

If α + β + γ = 2 π , then the system of equations x + cos γ y + cos β z = 0 cos γ x + y + cos α z = 0 cos β x + cos α y + z = 0 ha

JEE Main 2021 Solution View → 90

If a r = cos 2 r π 9 + i sin 2 r π 9 , r = 1 , 2 , 3 , … , i = - 1 , then the determinant a 1 a 2 a 3 a 4 a 5 a 6 a 7 a 8 a 9 is equal to :

JEE Main 2021 Solution View → 91

If the following system of linear equations 2 x + y + z = 5 x - y + z = 3 x + y + a z = 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 , 3 x + 2 y + 5 z = 3 ,

JEE Main 2021 Solution View → 93

Let A = [ x + 1 ] [ x + 2 ] [ x + 3 ] [ x ] [ x + 3 ] [ x + 3 ] [ x ] [ x + 2 ] [ x + 4 ] , where [ x ] denotes the greatest integer less than or equal to x . If det ( A ) = 192 ,

JEE Main 2021 Solution View → 94

If the system of linear equations 2 x + y - z = 3 x - y - z = α 3 x + 3 y + β z = 3 has infinitely many solutions, then α + β - α β 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 + 2 y + 3 z = μ x + 3 y + λ z = 1 is const

JEE Main 2021 Solution View → 96

Let θ ∈ 0 , π 2 . If the system of linear equations 1 + cos 2 ⁡ θ x + sin 2 ⁡ θ y + 4 sin ⁡ 3 θ z = 0 cos 2 ⁡ θ x + 1 +

JEE Main 2021 Solution View → 97

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

JEE Main 2021 Solution View → 98

Let f x = sin 2 x - 2 + cos 2 x cos 2 x 2 + sin 2 x cos 2 x cos 2 x sin 2 x cos 2 x 1 + cos 2 x , 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 2 x + 3 y + 6 z = 8 x + 2 y + a z = 5 3 x + 5 y + 9 z = 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 , 3 x + 5 y + 5 z = 26 and x + 2 y + λ z = μ has no solution, are:

JEE Main 2021 Solution View → 101

The value of k ∈ R , for which the following system of linear equations 3 x - y + 4 z = 3 x + 2 y - 3 z = - 2 6 x + 5 y + k z = - 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 x + a - c x + b x + a x - 1 x + c x + b x - b + d x + d x + c = 2 , then value of λ 2 is equa

JEE Main 2021 Solution View → 103

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

JEE Main 2021 Solution View → 104

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

JEE Main 2021 Solution View → 105

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

JEE Main 2021 Solution View → 106

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

JEE Main 2021 Solution View → 107

The maximum value of f x = sin 2 x 1 + cos 2 x cos 2 x 1 + sin 2 x cos 2 x cos 2 x sin 2 x cos 2 x sin 2 x , x ∈ R is

JEE Main 2021 Solution View → 108

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

JEE Main 2021 Solution View → 109

The value of a + 1 a + 2 a + 2 1 a + 2 a + 3 a + 3 1 a + 3 a + 4 a + 4 1 is

JEE Main 2021 Solution View → 110

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

JEE Main 2021 Solution View → 111

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

JEE Main 2021 Solution View → 112

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

JEE Main 2021 Solution View → 113

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

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 , where X is

JEE Main 2021 Solution View → 115

The system of linear equations 3 x - 2 y - k z = 10 2 x - 4 y - 2 z = 6 x + 2 y - z = 5 m 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 + 3 λ + 1   y + 2 λ z = 0 λ - 1   x + 4 λ - 2   y +

JEE Main 2020 Solution View → 117

Let m and M be respectively the minimum and maximum value values of cos 2 x 1 + sin 2 x sin 2 x 1 + cos 2 x sin 2 x sin 2 x cos 2 x sin 2 x 1 + sin 2 x Then the ordered pair (m, M)

JEE Main 2020 Solution View → 118

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

JEE Main 2020 Solution View → 119

If the system of linear equations x + y + 3 z = 0 x + 3 y + k 2 z = 0 3 x + y + 3 z = 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 x a + y x + a y b + y y + b z c + y z + c is equal to :

JEE Main 2020 Solution View →
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