Question

Match the two columns .

Column I		Column II
(A)	$x=a$ is a line	(p)	parallel to $x$-axis
(B)	$y=b$ is a line	(q)	$\left(0,0\right)$
(C)	$y=x$ is a straight line which passes through solutions	(r)	infinitely many solutions
(D)	A linear equation in two variables $ax+by=c$ has	(s)	parallel to $y$-axis

Choose the correct options:

• A. $\left(A\right)\to s;\left(B\right)\to p;\left(C\right)\to r;\left(D\right)\to q$
• B. $\left(A\right)\to s;\left(B\right)\to p;\left(C\right)\to q;\left(D\right)\to r$
• C. $\left(A\right)\to p;\left(B\right)\to s;\left(C\right)\to q;\left(D\right)\to r$
• D. $\left(A\right)\to r;\left(B\right)\to p;\left(C\right)\to q;\left(D\right)\to s$

Answer 1

The correct option is B

$\left(A\right)\to s;\left(B\right)\to p;\left(C\right)\to q;\left(D\right)\to r$

Explanation for (A)

Any equation of $x=a$ form is always a straight line parallel to $y$-axis therefore correct match for (A)→ s

Explanation for (B)

Any equation of $y=b$ form is always a straight line parallel to $\mathrm{x}$-axis therefore correct match for (B)→p.

Explanation for (C)

Any equation of $y=x$ form is always satisfied by the point $\left(0,0\right)$ , Hence $y=x$ passes through origin therefore correct match for (C)→ q.

Explanation for (D)

The graph of a linear equation $ax+by=c$ is always a straight line

On a straight line, there are infinitely many abscissa for infinitely many ordinates and vice versa respectively. So we get infinitely many solutions therefore correct match for (D)→r.

We conclude the correct match for given equations are $\left(A\right)\to s;\left(B\right)\to p;\left(C\right)\to q;\left(D\right)\to r$

Hence, the correct answer is option B.