question_answer

Directions: Each of these questions contains two statements: Assertion [A] and Reason [R]. Each of these questions also has four alternative choices, any one of which is the correct answer. You have to select one of the codes [a], [b], [c] and [d] given below.

Assertion [A] The graphical representation of 2x + y = 6 and 2x - y +2=0 will be a pair of parallel lines.

Reason [R] When k = -1, then linear equations 5x + ky = 4 and 15x + 3y = 12 have infinitely many solutions.

A) A is true, R is true; R is a correct explanation for A.

B) A is true, R is true; R is not a correct explanation for A.

C) A is true; R is False.

D) A is false; R is true.

Correct Answer: D

Solution :

Assertion We have,

\[{{l}_{1}}\,:\,2x+y-6=0;\,{{l}_{2}}:\,2x-y+2=0\]

\[{{l}_{1}}:\,y=6-2x;\,{{l}_{2}}:\,y=2x+2\]

From graph, it is clear that the given lines are not parallel lines.

Reason The linear equations

\[5x+ky-4=0\] and  \[15x+3y-12=0\] have infinitely many solutions.

\[\therefore \,\,\,\frac{5}{15}=\frac{k}{3}=\frac{-4}{-12}\Rightarrow \frac{1}{3}=\frac{k}{3}=\frac{1}{3}\Rightarrow k=1\]

Assertion [A] is false but Reason [R] is true.