Q. Find the value of $k$ for which $x=3$ is a solution of the quadratic equation, $(k+2)x^2-kx+6=0$.
Thus find the other root of the equation.

Q. A bag contains $5$ white balls, $6$ red balls and $9$ green balls. A ball is drawn at random from the bag. Find the probability that the ball drawn is :
(i) a green ball.
(ii) a white or a red ball.
(iii) is neither a green ball nor a white ball.

Q. Use a graph paper for this question taking $1cm=1$ unit along both the $x$ and $y$ axis :
(i) Plot the points $A(0,5),B(2,5),C(5,2),D(5,-2),E(2,-5)$ and $F(0,-5)$
(ii) Reflect the points $B,C,D$ and $E$ on the $y$-axis and name them respectively as $B^{\prime },C^{\prime },D^{\prime }$ and $E^{\prime }$.
(iii) Write the coordinates of $B^{\prime },C^{\prime },D^{\prime }$ and $E^{\prime }$.
(iv) Name the figure formed by $BCDE{E}^{\prime }{D}^{\prime }{C}^{\prime }{B}^{\prime }$.
(v) Name a line of symmetry for the figure formed.

Q. Virat opened a Saving Bank account in a bank on ${16}^{th}$ April, $2010$. His pass book shows the following entries:

Date	Particulars	Withdrawal (Rs.)	Deposit (Rs.)	Balance (Rs.)
April ${16}^{th}$	By cash	___	$2500$	$2500$
April ${28}^{th}$	By cheque	___	$3000$	$5500$
May $9^{th}$	To cheque	$850$	___	$4650$
May ${15}^{th}$	By cash	___	$1600$	$6250$
May ${24}^{th}$	To cash	$1000$	___	$5250$
June $4^{th}$	To cash	$500$	___	$4750$
June ${30}^{th}$	By cheque	___	$2400$	$7150$
July $3^{rd}$	By cash	___	$1800$	$8950$

Calculate the interest Virat earned at the end of ${31}^{st}$ July, $2010$ at $4\%$ per annum interest. What sum of money will he receive if he closes the account on $1^{st}$ August, $2010$?

Q. Sum of two natural numbers is $8$ and the difference of their reciprocal is $\frac{2}{15}$. Find the numbers.

Q. Prove that $\frac{\sin \theta }{1-\cot \theta }+\frac{\cos \theta }{1-\tan \theta }=\cos \theta +\sin \theta$.

Q. If $A=\left[\begin{array}{cc}3& 7\\ 2& 4\end{array}\right]$, $B=\left[\begin{array}{cc}0& 2\\ 5& 3\end{array}\right]$ and $C=\left[\begin{array}{cc}1& -5\\ -4& 6\end{array}\right]$. Find $AB-5C$.

Q.

Q. Solve the following inequation and write the solution set :
$13x-5<15x+4<7x+12,x\in R$
Represent the solution on a real number line.

Q. A wholesaler buys a TV from the manufacturer for Rs. $25,000$. He marks the price of the TV $20\%$ above his cost price and sell it to a retailer at $10$% discount on the marked price. If the rate of VAT is $8\%$, find the:
(i) marked price.
(ii) retailer's cost price inclusive of tax.
(iii) VAT paid by the wholesaler.

Q. In the given figure, $ABCD$ is a square of side $21cm$. $AC$ and $BD$ are two diagonals of the square. Two semi circles are drawn with $AD$ and $BC$ as diameters. Find the area of the shaded region (in $c{m}^2$). (Take $\pi =\frac{22}{7}$)

Q. Find $a$ if the two polynomials $a{x}^3+3x^2-9$ and $2x^3+4x+a$, leaves the same remainder when divided by $x+3$.

Q. The horizontal distance between two towers is $120m$. The angle of elevation of the top and angle of depression of the bottom of the first tower as observed from the second tower is ${30}^o$ and ${24}^o$ respectively.
Find the height of the two towers. Give your answer correct to $4$ significant figures.

Q. If $a,b,c$ are in continued proportion, prove that
$(a+b+c)(a-b+c)=a^2+b^2+c^2$

Q. Rohit invested Rs. $9,600$ on Rs. $100$ shares at Rs. $20$ premium paying $8$% dividend. Rohit sold the shares when the price rose to Rs. $160$. He invested the proceeds (excluding dividend) in $10$% Rs. $50$ shares at Rs. $40$. Find the :
(i) original number of shares.
(ii) sale proceeds.
(iii) new number of shares.
(iv) change in the two dividends.

Q. The weight of $50$ workers is given below:

Weight in Kg.	$50-60$	$60-70$	$70-80$	$80-90$	$90-100$	$100-110$	$110-120$
No. workers	$4$	$7$	$11$	$14$	$6$	$5$	$3$

Draw an ogive of the given distribution using a graph sheet. Take $2cm=10kg$ on one axis and $2cm=5$ workers along the other axis. Use a graph to estimate the following:
(i) the upper and lower quartiles.
(ii) if weighing $95kg$ and above is considered overweight find the number of workers who are overweight.

Q. Katrina opened a recurring deposit account with a Nationalised Bank for a period of $2$ years. If the bank pays interest at the rate of $6\%$ per annum and the monthly installment is Rs. $1,000$, find the:
(i) interest earned in $2$ years
(ii) matured value.

Q. $ABC$ is a right angled triangle with $\angle ABC={90}^o$. $D$ is any point on $AB$ and $DE$ is perpendicular to $AC$. Prove that :
(i) $△ADE\sim △ACB$.
(ii) If $AC=13cm$, $BC=5cm$ and $AE=4cm$. Find $DE$ and $AD$.
(iii) Find, area of $△ADE:$ area of quadrilateral $BCED$.

Q. Given $\frac{x^3+12x}{6x^2+8}=\frac{y^3+27y}{9y^2+27}$. Using componendo and dividendo find $x:y$.

Q. Two solid spheres of radii $2\text{cm}$ and $4\text{cm}$ are melted and recast into a cone of height $8\text{cm}$. Find the radius of the cone (in $\text{cm}$) so formed.

Q. In the figure given below, $O$ is the centre of the circle and $SP$ is a tangent. If $\angle SRT={65}^o$, find the value of $x$, $y$ and $z$.

Q. The present population of a town is $2,00,000$. Its population increases by $10$% in the first year and $15$% in the second year. Find the population of the town at the end of the two years.

Q. Calculate the mean of the following distribution:

Class Interval	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$
Frequency	$8$	$5$	$12$	$35$	$24$	$16$

Q. If $A=\left[\begin{array}{cc}3& x\\ 0& 1\end{array}\right]$ and $B=\left[\begin{array}{cc}9& 16\\ 0& -y\end{array}\right]$, find $x$ and $y$ when $A^2=B$.

Q. In the given figure $ABC$ is a triangle and $BC$ is parallel to the $y$-axis. $AB$ and $AC$ intersects the $y$-axis at $P$ and $Q$ respectively.
(i) Write the coordinates of $A$.
(ii) Find the length of $AB$ and $AC$.
(iii) Find the ratio in which $Q$ divides $AC$.
(iv) Find the equation of the line $AC$.

Q. A shopkeeper bought an article for Rs. $3,450$. He marks the price of the article $16\%$ above the cost price. The rate of sales tax charged on the article is $10\%$. Find the :
(i) marked price of the article
(ii) price paid by a customer who buys the article.

Q. Three vertices of a parallelogram $\text{ABCD}$ taken in order are $\text{A}(3,6)$, $\text{B}(5,10)$ and $\text{C}(3,2)$ find :
(i) the coordinates of the fourth vertex $\text{D}$.
(ii) length of diagonal $\text{BD}$.

Q. The marks obtained by $30$ students in a class assessment of $5$ marks is given below :

Marks	0	1	2	3	4	5
Number of Students	1	3	6	10	5	5

Calculate the mean, median and mode of the above distribution.

Q. $AB$ and $CD$ are two chords of a circle intersecting at $P$. Prove that $AP\times PB=CP\times PD$.