1. Tardigrade
  2. Question
  3. Mathematics
  4. Given the system of equations x+y-z=2 ; 2 x-y+4 z=1 and x+α y+z=β. Where α, β ∈ 0,1,2,3,4 then Column I Column II A The number of ordered pairs (α, β) such that the system has unique solution is P 1 B The number of ordered pairs (α, β) such that the system has no solution is Q 4 C The number of ordered pairs (α, β) such that the system has infinitely many solution is R 20 D The number of ordered pairs (α, β) such that the system is consistent S 21 T 24

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Given the system of equations $x+y-z=2 ; 2 x-y+4 z=1$ and $x+\alpha y+z=\beta$. Where $\alpha, \beta \in\{0,1,2,3,4\}$, then
Column I Column II
A The number of ordered pairs $(\alpha, \beta)$ such that the system has unique solution is P 1
B The number of ordered pairs $(\alpha, \beta)$ such that the system has no solution is Q 4
C The number of ordered pairs $(\alpha, \beta)$ such that the system has infinitely many solution is R 20
D The number of ordered pairs $(\alpha, \beta)$ such that the system is consistent S 21
T 24

Determinants

Solution:

Correct answer is (d) $A \rightarrow R ; B \rightarrow Q ; C \rightarrow P ; D \rightarrow S$