PART A

Find the coefficient of $x^2$ in $\left(3x+x^3\right)\left(x+\frac{1}{x}\right)$.

If $△ABC\cong △FDE$ and $AB=5 \mathrm{cm}, \angle B=40°$, $\angle A=80°$, then find $\angle E$.

In square $ABCD$, $P$ and $Q$ are mid-points of $AB$ and $CD$, respectively. If $AB=8 \mathrm{cm}$ and $PQ$ and $BD$ intersect at $O$, then find the area of $△OPB$ in ${\mathrm{cm}}^2$.

Find the class mark of the class $35-55$.

The radius of a circle is $10 \mathrm{cm}$ and the length of one of its chords is $12 \mathrm{cm}$. Find the distance of the chord from the centre in $\mathrm{cm}$.

To improve the practical knowledge and awareness about the social life Directorate of Education announces a visit in a Delhi Public School. Girls are asked to prepare a rangoli in triangular shape as shown in figure.

Dimensions of rangoli $(△ABC)$ are $25 \mathrm{cm}, 28 \mathrm{cm}, 26 \mathrm{cm}$. Garland is to be placed along the side of $△PQR$, which is formed by joining the mid-points of sides of $△ABC$, then find the length of garland in $\mathrm{cm}$.

Express the following decimal as a fraction in simplest form

$0.\overline{7}$

Express the following decimal as a fraction in simplest form

$0.\overline{5}$