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 \[x+2y-4=0\] and \[2x+4y-12=0\]will be a pair of parallel lines.

Reason [R] Let \[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\]and \[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\] be two linear equations and if\[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}\ne \frac{{{c}_{1}}}{{{c}_{2}}}\], then the pair of equations represent parallel lines and they have no solution.

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: A

Solution :

\[{{l}_{1}}:\,x+2y-4=0\] and \[{{l}_{2}}:2x+4y-12=0\]

so, the lines \[{{l}_{1}}\] and  \[{{l}_{2}}\] are parallel to each other.

Assertion : True; Reason : True and is the correct explanation of assertion.