NIMCET 2010 — Mathematics PYQ

Solution

The correct option is (d) $\frac{17\sqrt{5}}{15}$.

1. Standardize the Equations:

To find the distance between two parallel lines, we first write them in the general form $Ax+By+C=0$.

• Line 1: $y=2x+4$

  Rearranging: $2x-y+4=0$

• Line 2: $6x=3y+5$

  Rearranging: $6x-3y-5=0$

  To make the coefficients of $x$ and $y$ same as Line 1, divide the entire equation by $3$:

  $2x-y-\frac{5}{3}=0$

2. Identify the Constants:

Now we have:

• Line 1: $2x-y+4=0⟹A=2,B=-1,C_1=4$

• Line 2: $2x-y-\frac{5}{3}=0⟹A=2,B=-1,C_2=-\frac{5}{3}$

3. Use the Distance Formula:

The distance $d$ between two parallel lines $Ax+By+C_1=0$ and $Ax+By+C_2=0$ is given by:

4. Calculation:

Substitute the values into the formula:

To match the options, rationalize the denominator by multiplying the numerator and denominator by $\sqrt{5}$: