Q12. (λ −1)x + (λ −4)y + λz = 5 If the system of equations λx + (λ −1)y + (λ −4)z = 7 has infinitely many solutions, then λ2 + λ is (λ + 1)x + (λ + 2)y −(λ + 2)z = 9 equal to (1) 6 (2) 10 (3) 20 (4) 12
What This Question Tests
This question requires applying the conditions for a system of linear equations to have infinitely many solutions, specifically setting the determinant of the coefficient matrix and related determinants to zero.
Concepts Tested
Formulas Used
For infinitely many solutions: D=0, D1=0, D2=0, D3=0
📚 NCERT Sections This Tests
12.5 — A Hydrogen Atom Initially In The Ground Level Absorbs A Photon,
Physics Class 12 · Chapter 12
12.5 A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level. Determine the wavelength and frequency of photon.
1.27 — If The Solubility Product Of Cus Is 6 × 10–16, Calculate The Maximum Molarity Of
Chemistry Class 11 · Chapter 1
1.27 If the solubility product of CuS is 6 × 10–16, calculate the maximum molarity of CuS in aqueous solution.
5.28 — How Many Ions Are Produced From The Complex Co(Nh3)6Cl2 In Solution?
Chemistry Class 11 · Chapter 5
5.28 How many ions are produced from the complex Co(NH3)6Cl2 in solution? (i) 6 (ii) 4 (iii) 3 (iv) 2 139 Coordination Compounds Reprint 2025-26
📋 Question Details
- Chapter
- Determinants
- Topic
- System of Linear Equations
- Year
- 2025
- Shift
- 23 Jan Shift 1
- Q Number
- Q12
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 4: Determinants
More from this Chapter
Q89.Let a, b, c be any real numbers. Suppose that there are real numbers x, y, z not all zero such that x = cy + bz, y = az + cx and z = bx + ay. Then a2 + b2 + c2 + 2abc is equal to (1) 2 (2) −1 (3) 0 (4) 1
Q75. a a + 1 a −1 a + 1 b + 1 c −1 Let a, b, c be such that b(a + c) ≠0. If −b b + 1 b −1 + a −1 b −1 c + 1 = 0, then the c c −1 c + 1 (−1)n+2a (−1)n+1b (−1)nc value of ' n ' is (1) zero (2) any even integer (3) any odd integer (4) any integer JEE Main 2009 JEE Main Previous Year Paper
Q78.If the system of equations x + y + z = 6 x + 2y + 3z = 10 x + 2y + λz = 0 has a unique solution, then λ is not equal to (1) 1 (2) 0 (3) 2 (4) 3
Q77.If a, b, c, are non zero complex numbers satisfying a2 + b2 + c2 = 0 and b2 + c2 ab ac ab c2 + a2 bc = ka2b2c2 , then k is equal to ac bc a2 + b2 (1) 1 (2) 3 (3) 4 (4) 2 is 3