SAMPLE QUESTION PAPER

Factorise $9z^3-27z^2-100z+300$, if it is given that $\left(3z+10\right)$ is a factor of it.

A family has $3$ children. Find the probability that the family has exactly one girl child.

$P\text{'} \mathrm{and} Q\text{'}$be the images of $P\left(-3, 5\right) \mathrm{and} Q\left(-5, 3\right)$ respectively on reflection in $Y- \mathrm{axis}$. Find the coordinates of $P\text{'} \mathrm{and} Q\text{'}$.

$P^{\text{'}}$ and $Q^{\text{'}}$ be the images of $P\left(-3, 5\right)$ and $Q\left(-5, 3\right)$ respectively, on reflection in $Y-$axis. Are $P{Q}^{\text{'}}$ and $Q{P}^{\text{'}}$ equal in length?

A right circular cylinder just encloses a sphere of radius $r$.

Find the surface area of the sphere.

A right circular cylinder just encloses a sphere of radius $r$.

Find the curved surface area of the cylinder.

Find the mode of the following frequency distribution by drawing a histogram.

A company gives $x\%$ dividends on its$₹ 60$ shares, whereas the return on the investment in these shares is $\left(x+3\right)\%$. If the market value of each share is $₹ 50$, then find the value of $x$.