Q. If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points then prove that the two sides are divided in the same ratio.

Q. Find the eleventh term of the A.P. $2,7,12,....$

Q. Find the value of $\sin {35}^{\circ }\cos {55}^{\circ }+\cos {35}^{\circ }\sin {55}^{\circ }$

Q. A life Insurance agent found the following data for distribution of ages of $100$ policy holders. Calculate the median age, if policies are given only to persons having age $18$ years onwards but less than $60$ years.

Age (in years)	Number of policy holders
Below $20$	$2$
Below $25$	$6$
Below $30$	$24$
Below $35$	$45$
Below $40$	$78$
Below $45$	$89$
Below $50$	$92$
Below $55$	$98$
Below $60$	$100$

Q. A metallic sphere of radius $4.2cm$ is melted and recast into the shape of a cylinder of radius $7cm$. Find the height of the cylinder (in cm).

Q. Write down the distance of the point $(7,-3)$ from y-axis

Q. Find the coordinates of the point which divides the join of points $(-1,7)$ and $(4,-3)$ in the ratio $2:3$

Q. Find the highest positive integer by which dividing the numbers $396,436$ and $542$ remainders are $5,11$ and $15$ respectively

Q. Divide $x^3-3x^2+3x-5$ by $x-1-x^2$, and verify the division algorithm

Q. Divide the line segment of $7.5cm$ in the ratio of $2:3$. Draw the figure.

Q. If the radius of a circle is $14cm$, then find the area of the circle.

Q. Prove that in a triangle, if square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.

Q. The shadow of a tower standing on a plane ground is found to be $40m$ longer when the sun's altitude reduces to ${30}^{\circ }$ from ${60}^{\circ }$. Find the height of the tower.

Q. If $\tan 2A=\cot (A-18)$, where $2A$ is an acute angle, then find the value of $A$

Q. The coach of a cricket team buys one bat and $2$ balls for $Rs.300$. Later he buys another $2$ bats and $3$ balls of the same kind for $Rs.525$. Represent this situation algebraically and solve it by graphical method. Also, find out that how much money the coach will pay for the purchase of one bat and one ball.

Q. In tangents $PA$ and $PB$ from a point $P$ to a circle with center $O$ are inclined to each other at an angle of ${80}^{\circ }$, then find $\angle POA$ (in degrees).

Q. Radius of the circle is $r$ and $\theta$ is the angle of the sector in degree. Write down the formula of length of corresponding arc

Q. If $DE\parallel BC$ in $△ABC,AD=1.5cm,BD=3cm$ and $AE=1cm$, then find $EC$ ( in cm ).

Q. Construct a triangle with sides $5cm,6cm$ and $7cm$ and then another triangle whose sides are $\frac{7}{5}$ times of the corresponding sides of the first triangle. Write down the steps of construction.

Q. Suresh started work in $1985$ at an annual salary of $Rs.5000$ and received an increment of $Rs.200$ each year. After how many years did his income reach $Rs.7000$?

Q. Find the H.C.F. of numbers $44$ and $99$.

Q. If $\sin A=\frac{3}{5}$, then find $\cos A$ and $cosecA$

Q. Prove that the lengths of tangents drawn from an external point to the circle are equal.

Q. $12$ defective pens are accidentally mixed with $132$ good ones. It is not possible to just look at a pen and tell whether it is defective or not. One pen is taken out at random from this lot. Determine the probability that the pen taken out is a good one.

Q. The marks distribution of $30$ students in a mathematics examination are as follows:

Q. Write down the sum of the probabilities of all the elementary events of an experiment.

Q. Find the value of $\frac{\tan {65}^{\circ }}{\cot {25}^{\circ }}$

Q. Find the area of the triangle formed by joining the mid-points of the sides of the triangle $ABC$ whose vertices are $A(0,-1),B(2,1)$ and $C(0,3)$. Find the ratio of this area of the triangle $ABC$.

Q. Find the area of the sector of a circle with radius $4cm$ and of angle ${60}^{\circ }$. Also find the area of the corresponding major sector.
(Use $\pi =3.14$)

Q. Total price of $7$ pencils and $5$ pens is $Rs.29$. Write it down in the algebraic form