Q. In the given figure below, $AD$ is a diameter. $O$ is the centre of the circle. $AD$ is parallel to $BC$ and $\angle CBD={32}^{\circ }$. Find $\angle BED$ (in ${}^{\circ }$)

Q. Use graph paper for this question.
(Take $2cm=1$ unit along both $x$ and $y$ axis).
Plot the point $O(0,0),A(-4,4),B(-3,0)$ and $C(0,-3)$.
State the line of symmetry of this figure

1. Origin
2. X-axis
3. Y-axis
4. Both x-axis and y-axis

Q. Use graph paper for this question.
(Take $2cm=1$ unit along both $x$ and $y$ axis).
Plot the point $O(0,0),A(-4,4),B(-3,0)$ and $C(0,-3)$.

Q. Use graph paper for this question.
(Take $2cm=1$ unit along both $x$ and $y$ axis).
Plot the point $O(0,0),A(-4,4),B(-3,0)$ and $C(0,-3)$.
Reflect points $A$ and $B$ on the $y$-axis and name them $A^{\prime }$ and $B^{\prime }$ respectively. Write down their coordinates

Q. Construct a regular hexagon of side $5cm$. Hence determine the number of lines of symmetry of the hexagon.

Q. In the given figure $PQRS$ is a cyclic quadrilateral $PQ$ and $SR$ produced meet at $T$. Find $SP$ if $TP=18cm,RQ=4cm$ and $TR=6cm$.

Q. Solve the following inequation, write the solution set and represent it on the number line.
$-3(x-7)\ge 15-7x>\frac{x+1}{3},x\in R$

Q. The table shows the distribution of the scores obtained by $160$ shooters in a shooting competition. Use a graph sheet and draw an ogive for the distribution.

Scores	No. of shooters
$0-10$	$9$
$10-20$	$13$
$20-30$	$20$
$30-40$	$26$
$40-50$	$30$
$50-60$	$22$
$60-70$	$15$
$70-80$	$10$
$80-90$	$8$
$90-100$	$7$

Use your graph to estimate the median.

Q. In the given figure, $AD$ is a diameter. $O$ is the centre of the circle. $AD$ is parallel to $BC$ and $\angle CBD={32}^{\circ }$. Find $\angle OBD$ (in ${}^{\circ }$).

Q. A game of number has cards marked with $11,12,13,....40$. A card is drawn at random. Find the Probability that the number on the card drawn is a perfect square

Q. Given matrix $A=\left[\begin{array}{cc}4\sin {30}^{\circ }& \cos 0^{\circ }\\ \cos 0^{\circ }& 4\sin {30}^{\circ }\end{array}\right]$ and $B=\left[\begin{array}{c}4\\ 5\end{array}\right]$. If $AX=B$.
Find the matrix $X$.

Q. Given matrix $A=\left[\begin{array}{cc}4\sin {30}^{\circ }& \cos 0^{\circ }\\ \cos 0^{\circ }& 4\sin {30}^{\circ }\end{array}\right]$ and $B=\left[\begin{array}{c}4\\ 5\end{array}\right]$ If $AX=B$
Write the order the matrix $X$

Q. Without using trigonometric tables, evaluate:
$\text{cosec}{}^2{57}^{\circ }-{\tan }^2{33}^{\circ }+\cos {44}^{\circ }\text{cosec}{46}^{\circ }$

Q. In how many years will Rs. $1500$ yield Rs. $1996.50$ as amount at $10\%$ per annum compounded annually?

Q. A game of numbers has cards marked from $11,12,13,\dots ,40.$ One card is drawn at random. Find the probability that the number drawn is divisible by $7.$

Q. In the given figure below, $AD$ is a diameter. $O$ is the centre of the circle. $AD$ is parallel to $BC$ and $\angle CBD={32}^{\circ }$. Find $\angle AOB$ (in ${}^{\circ }$)

Q. The table shows the distribution of the scores obtained by $160$ shooters in a shooting competition. Use a graph sheet and draw an ogive for the distribution.

Scores	No. of shooters
$0-10$	$9$
$10-20$	$13$
$20-30$	$20$
$30-40$	$26$
$40-50$	$30$
$50-60$	$22$
$60-70$	$15$
$70-80$	$10$
$80-90$	$8$
$90-100$	$7$

Q. Using remainder theorem, find the value of $k$ if on dividing $2x^3+3x^2-kx+5$ by $x-2$, leaves a remainder $7$

Q. Mr. Lalit invested Rs. $5,000$ at a certain rate of interest, compounded annually for two years. At the end of first year it amounts to Rs. $5,325$. The rate of interest is $R$. Then $2R=$ (in $\%$)?

Q. Mr. Lalit invested Rs. $5,000$ at a certain rate of interest, compounded annually for two years. At the end of first year it amounts to Rs. $5,325$. Calculate the amount at the end of second year, to the nearest rupee.

Q. The slope of a line joining $P(6,k)$ and $Q(1-3k,3)$ is $\frac{1}{2}$. Find: $|k|$

Q. The slope of a line joining $P(6,k)$ and $Q(1-3k,3)$ is $\frac{1}{2}$. Find midpoint of $PQ$

Q. Given $A=\left[\begin{array}{cc}2& 0\\ -1& 7\end{array}\right]$ and $I=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$ and $A^2=9A+mI$. Find $m.$

Q. Solve the quadratic equation $x^2-3(x+3)=0$; Given your answer correct to two significant figures.

Q. The mean of following numbers is $68$. Find the value of $x$.
$45,52,60,x,69,70,26,81$ and $94$.
Hence estimate the median.

Q. A page from the saving bank account of Mrs. Ravi in the year $2006$ is given below:

Date	Particulars	Withdrawal (Rs)	Deposit (Rs)	Balance (Rs)
April $3^{rd}$	B/F	-	-	$6,000$
April $7^{th}$	By Cash	-	$2,300$	$8,300$
April ${15}^{th}$	By cheque	-	$3,500$	$11,800$
May ${20}^{th}$	To Self	$4,200$	-	$7,600$
June ${10}^{th}$	By cash	-	$5,800$	$13,400$
June ${15}^{th}$	To self	$3,100$	-	$10,300$
August ${13}^{th}$	By cheque	-	$1,000$	$11,300$
August ${25}^{th}$	To self	$7,400$	-	$3,900$
September $6^{th}$	By cash	-	$2,000$	$5,900$

She closed the account on ${30}^{th}$ September, $2006$. Calculate the interest Mrs. Ravi earned at the end of ${30}^{th}$ September, $2006$ at $4.5\%$ per annum interest. Hence find the amount she receives on closing the account.

Q. In the given figure $PQRS$ is a cyclic quadrilateral $PQ$ and $SR$ produced meet at $T$. Find area of quadrilateral $PQRS$ if area of $△PTS=27c{m}^2$ (given Triangle TPS is similar to TRQ)

Q. An aeroplane at an altitude of $1500$ metres finds that two ships are sailing towards it in the same direction. The angles of depression as observed from the aeroplane are ${45}^{\circ }$ and ${30}^{\circ }$ respectively. Find thee distance (in $m$) between the two ships

Q. A certain number of metallic cones, each of radius $2cm$ and height $3cm$ are melted and recast into a solid sphere of radius $6cm$. Find the number of cones

Q. If $(3a+2b):(5a+3b)=18:29$. Find $a:b$