Q. Tick the correct answer in the following:
Area of a sector of angle $\theta$ (in degrees) of a circle with radius R is

1. $\frac{\theta }{180}\times 2\pi R$
2. $\frac{\theta }{180}\times \pi R^2$
3. $\frac{\theta }{720}\times 2\pi R^2$
4. $\frac{\theta }{3600}\times 2\pi R$

Q.

Draw a circle of radius $6cm$. From a point $10cm$ away from its centre, construct the pair of tangents to the circle and measure their lengths.

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

Q. Find the discriminant of the quadratic equation $2x^2-6x+3=0$, and hence find the nature of its roots.

Q. Consider $\Delta$ACB, right-angled at C, in which $AB=29units,BC=21units$ and $\angle ABC=\theta$. Determine the value of $si{n}^2\theta +co{s}^2\theta$

Q. Which of the following cannot be the probability of an event?

1. $-1.5$
2. $\frac{2}{3}$
3. $15$%
4. $0.7$

Q. Write the formula for finding volume of a frustum of a cone.

Q. If tangents $PA$ and $PB$ from a point $P$ to a circle with centre $O$ are inclined to each other at angle of ${80}^o$, then $\angle POA$ is equal to.

1. ${50}^o$
2. ${60}^o$
3. ${80}^o$
4. ${70}^o$

Q. Divide the polynomial $p\left(x\right)=x^3-3x^2+5x-3$ by the polynomial $g\left(x\right)=x^2-2$. Find the quotient and remainder.

Q. An A.P. consists of $50$ terms of which $3$rd term is $12$ and last term is $106$. Find the $29$th term.

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

Q.

A child has a die whose six faces show the letters as given below :

$ABCDEA$. The die is thrown once. What is the probability of getting

i) $A$?

ii) $D$?

Q. The angle of elevation of the top of a tower from a point on the ground, which is $30\text{m}$ away from the foot of the tower, is ${30}^{\circ }$. Find the height of the tower.

Q.

Use Euclid's division algorithm to find HCF of $420$ and $130$, hence find LCM.

Q. The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.

Runs scored	Number of batsmen
$3000-4000$	$4$
$4000-5000$	$18$
$5000-6000$	$9$
$6000-7000$	$7$
$7000-8000$	$6$
$8000-9000$	$3$
$9000-10000$	$1$
$10000-11000$	$1$

Find the mode of the data.

Q. Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.

Q. Fill in the blacks.
If the area of a triangle is 0 square units then the vertices of a triangle are _____

Q. State whether the following are true or false.
$\sin (A+B)=\sin A+\sin B$

1. True
2. False

Q. Find the first term $a$ and the common difference $d$ of A.P. : $-5,-1,3,7,.....$

Q. In a class test, the sum of shefali's marks in Mathematics and English is $30$. Had she got $2$ marks more in Mathematics and $3$ marks less in English, the product of their marks would have been $210$. Find her marks in the two subjects.

Q. Two poles of height $6m$ and $11m$ stand on a plane ground. If the distance between the feet of the poles is $12m$, find the distance between their tops

1. $14m$
2. $13m$
3. $15m$
4. $16m$

Q. Every composite number can be expressed (factorized) as a product of primes.

1. True
2. False

Q. Fill in the blacks.
A polynomial of degree $1$ is called a _____ polynomial

Q. If A and B are $(-2,-2)$ and $(2,-4)$, respectively, find the coordinates of P such that $AP=\frac{3}{7}AB$ and P lies on the line segment AB.

Q. In the given figure, OACB is a quadrant of a circle with centre O and radius $3.5cm.$ If $OD=2cm$, find the area of the quadrant OACB

Q. The wickets taken by a bowler in $10$ cricket matches are as follows :
$2645021323$
Find the mode of the data

Q. Prove that :
$\frac{1+\sec A}{\sec A}=\frac{{\sin }^{2}A}{1-\cos A}$ angle A is an acute angle.

Q. Solve the pair of linear equation $2x+3y=11$ and $2x-4y=-24$

Q. D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C.
Prove that : $A{E}^2+B{D}^2=A{B}^2+D{E}^2$