Cramer's Rule and Consistency of Linear Equations

JEE Main Mathematics · Matrices and Determinants · 47 questions, latest first

• If the system of linear equations: x+y+z=6, x+2 y+5 z=10, 2 x+3 y+λ z=μ has infinitely many solutions, then the value of λ+μ…20268 April, Shift 2 · Q3
• If the system of equations: x+y+z=5; x+2 y+3 z=9; x+3 y+λ z=μ has infinitely many solutions, then the value of λ+μ is:20264 April, Shift 2 · Q3
• If the system of equations x+5 y+6 z=4, 2 x+3 y+4 z=7, x+6 y+a z=b has infinitely many solutions, then the point (a, b) lies on…20262 April, Shift 2 · Q3
• Let α, β ∈ R be such that the system of linear equations x+2 y+z=5; 2 x+y+α z=5; 8 x+4 y+β z=18 has no solution. Then (β)/(α) is…20262 April, Shift 1 · Q3
• The system of linear equations x+y+z=6; 2 x+5 y+a z=36; x+2 y+3 z=b has202623 January, Shift 2 · Q5
• Let n be the number obtained on rolling a fair die. If the probability that the system x-ny+z=6; x+(n-2) y+(n+1) z=8; (n-1) y+z=1…202622 January, Shift 2 · Q7
• 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:202621 January, Shift 2 · Q6
• Let the system of equations x+5 y-z=1; 4 x+3 y-3 z=7; 24 x+y+λ z=μ λ, μ ∈ R, have infinitely many solutions. Then the number of…20257 April, Shift 2 · Q5
• Let the system of equations: 2 x+3 y+5 z=9; 7 x+3 y-2 z=8; 12 x+3 y-(4+λ) z=16-μ have infinitely many solutions. Then the radius…20257 April, Shift 1 · Q4
• If the system of equations 2 x+λ y+3 z=5; 3 x+2 y-z=7; 4 x+5 y+μ z=9 has infinitely many solutions, then (λ^2+μ^2) is equal to:20252 April, Shift 2 · Q4
• If the system of linear equations 3 x+y+β z=3; 2 x+α y-z=-3; x+2 y+z=4 has infinitely many solutions, then the value of 22 β-9 α…20252 April, Shift 1 · Q20
• 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…202529 January, Shift 2 · Q5
• If the system of equations x+2 y-3 z=2; 2 x+λ y+5 z=5; 14 x+3 y+μ z=33 has infinitely many solutions, then λ+μ is equal to:202524 January, Shift 2 · Q5
• If the system of equations 2 x-y+z=4; 5 x+λ y+3 z=12; 100 x-47 y+μ z=212, has infinitely many solutions, then μ-2 λ is equal to202524 January, Shift 1 · Q4
• The system of equations x+y+z=6; x+2 y+5 z=9; x+5 y+λ z=μ has no solution if202523 January, Shift 2 · Q4
• If the system of equations (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 has infinitely many solutions,…202523 January, Shift 1 · Q4
• If the system of linear equations: x+y+2 z=6; 2 x+3 y+a z=a+1; -x-3 y+b z=2 b where a, b ∈ R, has infinitely many solutions, then…202522 January, Shift 2 · Q4
• Consider the matrices: A= [2, -5; 3, m], B= [20; m] and X= [x; y]. Let the set of all m, for which the system of equations A X=B…20249 April, Shift 2 · Q22
• Let λ, μ ∈ R. If the system of equations 3 x+5 y+λ z=3; 7 x+11 y-9 z=2; 97 x+155 y-189 z=μ has infinitely many solutions, then…20249 April, Shift 1 · Q3
• 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:20248 April, Shift 2 · Q3
• If the system of equations 2 x+7 y+λ z=3; 3 x+2 y+5 z=4; x+μ y+32 z=-1 has infinitely many solutions, then (λ-μ) is equal to ____:20246 April, Shift 2 · Q22
• The values of m, n, for which the system of equations x+y+z=4; 2 x+5 y+5 z=17, x+2 y+m z=n has infinitely many solutions, satisfy…20245 April, Shift 2 · Q4
• If the system of equations 11 x+y+λ z=-5; 2 x+3 y+5 z=3; 8 x-19 y-39 z=μ has infinitely many solutions, then λ^4-μ is equal to:20245 April, Shift 1 · Q4
• 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:20241 February, Shift 2 · Q5
• 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 ____.20241 February, Shift 1 · Q5
• 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…202431 January, Shift 2 · Q4
• 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 to202431 January, Shift 1 · Q4
• Consider the system of linear equations x+y+z=5, x+2 y+λ^2 z=9, x+3 y+λ z=μ, where λ, μ ∈ R. Then, which of the following…202430 January, Shift 2 · Q4
• Consider the system of linear equations 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…202430 January, Shift 1 · Q3
• 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…202429 January, Shift 2 · Q23
• 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=γ.…202315 April, Shift 1 · Q5
• 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 equal to202313 April, Shift 2 · Q4
• 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?202313 April, Shift 1 · Q4
• 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…202311 April, Shift 2 · Q4
• 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, 3 x+2 y+3 λ z=λ has no…202310 April, Shift 2 · Q22
• 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?202310 April, Shift 1 · Q3
• 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?20236 April, Shift 2 · Q5
• 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 to20236 April, Shift 1 · Q4
• For the system of linear equations α x+y+z=1, x+α y+z=1, x+y+α z=β, which one of the following statements is NOT correct?20231 February, Shift 2 · Q65
• 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,…20231 February, Shift 1 · Q66
• 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?202331 January, Shift 1 · Q65
• 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 α…202330 January, Shift 2 · Q63
• 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)…202330 January, Shift 1 · Q62
• Consider the following system of equations 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 the…202329 January, Shift 1 · Q65
• 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)…202325 January, Shift 1 · Q62
• If the system of equations x+2 y+3 z=3; 4 x+3 y-4 z=4; 8 x+4 y-λ z=9+μ has infinitely many solutions, then the ordered pair (λ,…202324 January, Shift 2 · Q64
• 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…202324 January, Shift 1 · Q64