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

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 (A) A arrow R ; B arrow Q ; C arrow P ; D arrow P (B) A arrow R ; B arrow Q ; C arrow P ; D arrow Q (C) A arrow R ; B arrow Q ; C arrow P ; D arrow R (D) A arrow R ; B arrow Q ; C arrow P ; D arrow S

Tardigrade Admin · Accepted Answer

Correct answer is (d) A arrow R ; B arrow Q ; C arrow P ; D arrow S

$A \to R; B \to Q; C \to P; D \to P$

$A \to R; B \to Q; C \to P; D \to Q$

$A \to R; B \to Q; C \to P; D \to R$

$A \to R; B \to Q; C \to P; D \to S$

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

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

A→R;B→Q;C→P;D→P

A→R;B→Q;C→P;D→Q

A→R;B→Q;C→P;D→R

A→R;B→Q;C→P;D→S

Correct answer is (d) A→R;B→Q;C→P;D→S

$A \to R; B \to Q; C \to P; D \to P$

$A \to R; B \to Q; C \to P; D \to Q$

$A \to R; B \to Q; C \to P; D \to R$

$A \to R; B \to Q; C \to P; D \to S$

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