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JEE Advanced 2023 · Paper 1

JEE Advanced 2023 Mathematics question on Matrices and Determinants

Let α,β\alpha, \beta and γ\gamma be real numbers. Consider the following system of linear equations
x+2y+z=7x + 2y + z = 7
x+αz=11x + \alpha z = 11
2x−3y+βz=γ2x - 3y + \beta z = \gamma

Match each entry in List-I to the correct entries in List-II.
List-I
(P) If β=12(7α−3)\beta = \dfrac{1}{2}(7\alpha - 3) and γ=28\gamma = 28, then the system has
(Q) If β=12(7α−3)\beta = \dfrac{1}{2}(7\alpha - 3) and γ≠28\gamma \neq 28, then the system has
(R) If β≠12(7α−3)\beta \neq \dfrac{1}{2}(7\alpha - 3) where α=1\alpha = 1 and γ≠28\gamma \neq 28, then the system has
(S) If β≠12(7α−3)\beta \neq \dfrac{1}{2}(7\alpha - 3) where α=1\alpha = 1 and γ=28\gamma = 28, then the system has
List-II
(1) a unique solution
(2) no solution
(3) infinitely many solutions
(4) x=11x = 11, y=−2y = -2 and z=0z = 0 as a solution
(5) x=−15x = -15, y=4y = 4 and z=0z = 0 as a solution
  1. A.
    (P)→(3)(Q)→(2)(R)→(1)(S)→(4)(P) \rightarrow (3) \quad (Q) \rightarrow (2) \quad (R) \rightarrow (1) \quad (S) \rightarrow (4)
  2. B.
    (P)→(3)(Q)→(2)(R)→(5)(S)→(4)(P) \rightarrow (3) \quad (Q) \rightarrow (2) \quad (R) \rightarrow (5) \quad (S) \rightarrow (4)
  3. C.
    (P)→(2)(Q)→(1)(R)→(4)(S)→(5)(P) \rightarrow (2) \quad (Q) \rightarrow (1) \quad (R) \rightarrow (4) \quad (S) \rightarrow (5)
  4. D.
    (P)→(2)(Q)→(1)(R)→(1)(S)→(3)(P) \rightarrow (2) \quad (Q) \rightarrow (1) \quad (R) \rightarrow (1) \quad (S) \rightarrow (3)
Show answer

Correct option: A

[JEE Advanced 2023 · Paper 1]

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