Question : $B_{1}$ is a point on the side AC of $\Delta ABC$ and $B_{1}B$ is joined. A line is drawn through A parallel to $B_{1}B$ meeting BC at $A_{1}$ and another line is drawn through C parallel to $B_{1}B$ meeting AB produced at $C_{1}$. Then:

Option 1: $\frac{1}{CC_{1}}-\frac{1}{AA_{1}}=\frac{1}{BB_{1}}$

Option 2: $\frac{1}{CC_{1}}+\frac{1}{AA_{1}}=\frac{1}{BB_{1}}$

Option 3: $\frac{1}{BB_{1}}-\frac{1}{AA_{1}}=\frac{2}{CC_1}$

Option 4: $\frac{1}{AA_1}-\frac{1}{CC_1}=\frac{2}{BB_1}$

Question : What is the slope of the line parallel to the line passing through the points (5, – 1) and (4, – 4)?

Option 1: $– 3$

Option 2: $\frac{–1}{3}$

Option 3: $3$

Option 4: $\frac{1}{3}$

Question : The graph of the equation $x=a(a \neq 0)$ is a_____.

Option 1: line parallel to the x-axis

Option 2: line parallel to the y-axis

Option 3: line at an angle of 45 degree to y-axis

Option 4: line at an angle of 45 degree to x-axis

Question : If $\frac{a^2}{b+c}=\frac{b^2}{c+a}=\frac{c^2}{a+b}=1$, then $\frac{1}{1+a}+\frac{1}{1+b}+\frac{1}{1+c}$ is:

Option 1: 1

Option 2: 2

Option 3: 3

Option 4: 4

Question : If $\frac{a^2}{b+c}=\frac{b^2}{c+a}=\frac{c^2}{a+b}=1$, then find the value of $\frac{2}{1+a}+\frac{2}{1+b}+\frac{2}{1+c}$.

Option 1: 0

Option 2: 1

Option 3: 2

Option 4: 3

Question : $3\left[\mathrm{a}-\frac{1}{\mathrm{a}}\right]+\left[\mathrm{a}-\frac{1}{\mathrm{a}}\right]^3=?$

Option 1: $a^2-\frac{1}{a^3}$

Option 2: $a^3-\frac{1}{a^3}$

Option 3: $a^3+\frac{1}{a^3}$

Option 4: $a^2-\frac{1}{a^2}$