Question : Successive discounts of $p$% and $q$% on a catalogue price of an article is equivalent to a single discount of:

Option 1: $\left(p -q + \frac{pq}{100} \right )$%

Option 2: $\left(p - q - \frac{pq}{100} \right )$%

Option 3: $\left(p + q - \frac{pq}{100} \right )$%

Option 4: $\left(p + q + \frac{pq}{100} \right )$%

Question : If $\tan ^2 \alpha=3+Q^2$, then $\sec \alpha+\tan ^3 \alpha \operatorname{cosec} \alpha=?$

Option 1: $\left(3+Q^2\right)^{\frac{3}{2}}$

Option 2: $\left(7+Q^2\right)^{\frac{3}{2}}$

Option 3: $\left(5-Q^2\right)^{\frac{3}{2}}$

Option 4: $\left(4+Q^2\right)^{\frac{3}{2}}$

Question : If $M =\left ( \frac{3}{7} \right ) ÷ \left ( \frac{6}{5} \right ) ×\left ( \frac{2}{3} \right ) + \left ( \frac{1}{5} \right ) ×\left ( \frac{3}{2} \right )$ and $N = \left ( \frac{2}{5} \right ) × \left ( \frac{5}{6} \right ) ÷ \left ( \frac{1}{3} \right ) + \left ( \frac{3}{5} \right ) × \left ( \frac{2}{3} \right ) ÷ \left ( \frac{3}{5} \right )$,
then what is the value of $\frac{M}{N}$?

Option 1: $\frac{207}{560}$

Option 2: $\frac{339}{1120}$

Option 3: $\frac{113}{350}$

Option 4: $\frac{69}{175}$

Question : If $x_{1}x_{2}x_{3}=4(4+x_{1}+x_{2}+x_{3})$, then what is the value of $\left [ \frac{1}{(2+x_{1})} \right ]+\left [ \frac{1}{(2+x_{2})} \right ]+\left [ \frac{1}{(2+x_{3})} \right ]?$

Option 1: $1$

Option 2: $\frac{1}{2}$

Option 3: $2$

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

Question : If $\left (4x+\frac{1}{x} \right)=5,x\neq 0,$ then the value of $\frac{5x}{4x^{2}+10x+1}$ is:

Option 1: $\frac{1}{2}$

Option 2: $\frac{1}{3}$

Option 3: $\frac{2}{3}$

Option 4: $3$