Q. Using properties of proportion, solve for $x$. Given that $x$ is positive :
$\frac{2x+\sqrt{4x^2-1}}{2x-\sqrt{4x^2-1}}=4$

Q. If $(k-3),(2k+1)$ and $(4k+3)$ are three consecutive terms of an A.P., find the value of k.

Q. Sonia has a recurring deposit account in a bank and deposited Rs. $600$ per month for $2\frac{1}{2}$ years. If the rate of interest was $10\%$ p.a., find the maturity value of this account.

Q. Rs. $7500$ were divided equally among a certain number of children. Had there been $20$ less children, each would have received Rs. $100$ more. Find the original number of children.

Q. If $(x+2)$ and $(x+3)$ are factors of $x^3+ax+b$, find the value of 'a' and 'b'.

Q. Solve the following inequation, write down the solution set and represent it on the real number line:
$-2+10x\le 13x+10<24+10x$, x$ϵ$Z.

Q. Find the value of $x+y$ if:

Q. If $A=\left[\begin{array}{cc}2& 3\\ 5& 7\end{array}\right],B=\left[\begin{array}{cc}0& 4\\ -1& 7\end{array}\right]$ and $C=\left[\begin{array}{cc}1& 0\\ -1& 4\end{array}\right]$, find $AC+B^2-10C$.

Q. Use graph paper for the question (Take $2$cm $=$ $1$ unit along both x and y axis). ABCD is a quadrilateral whose vertices are $A(2,2),B(2,-2),C(0,-1)$ and $D(0,1)$. Reflect quadrilateral ABCD on the y-axis and name it as A'B'CD.

Q. If the straight lines $3x-5y=7$ and $4x+ay+9=0$ are perpendicular to one another, find the value of a.

Q. A man invests Rs. $22,500$ in Rs. $50$ shares available at $10\%$ discount. If the dividend paid by the company is $12\%$, calculate the rate of return he gets on his investment. Give your answer correct to the nearest whole number.

Q. PQRS is a cyclic quadrilateral. Given $\angle$QPS $={73}^o$, $\angle$PQS$={55}^o$ and $\angle$PSR$={82}^o$, calculate $\angle$QRS.

Q. Use graph paper for this question (Take $2$cm $=$ $1$unit along both x and y axis). ABCD is a quadrilateral whose vertices are $A(2,2),B(2,-2),C(0,-1)$ and $D(0,1)$. Name two points which are invariant under the above reflections.

Q. Find the value of k for which the following equation has equal roots. $x^2+4kx+(k^2-k+2)=0$.

Q. The $4^{th}$ term of a G.P. is $16$ and $7^{th}$ term is $128$. Find the first term and common ratio of the series.

Q. Solve $x^2+7x=7$ and give your answer correct to two decimal places.

Q. Use graph paper for this question (Take $2$cm $=$ $1$ unit along both x and y axis). ABCD is a quadrilateral whose vertices are $A(2,2),B(2,-2),C(0,-1)$ and $D(0,1)$. Name the property of A'B'CD.

Q. $PQRS$ is a cyclic quadrilateral. Given $\angle$QPS $={73}^{\circ }$, $\angle PQS={55}^{\circ }$ and $\angle PSR={82}^{\circ }$, calculate $\angle RQS.$

Q. A man invests Rs. $22,500$ in Rs. $50$ shares available at $10\%$ discount. If the dividend paid by the company is $12\%$, calculate the number of shares purchased.

Q. The circumference of the base of a cylindrical vessel is $132$ cm and its height is $25$cm. Find the radius of the cylinder.

Q. Using ruler and compass only, construct a $\Delta$ABC such that $BC=5$cm and $AB=6.5$cm and $\angle$ABC $={120}^o$. Construct a circum-circle of $\Delta$ABC.

Q. Prove that $\sqrt{{\sec }^2\theta +cose{c}^2\theta }=\tan \theta +\cot \theta$.

Q. $A(2,5),B(-1,2)$ and $C(5,8)$ are the vertices of a triangle ABC, 'M' is a point on AB such that AM $:$ MB $=1:2$. Find the co-ordinates of 'M'. Hence find the equation of the line passing through the points C and M.

Q. Use graph paper for this question (Take $2$cm $=$ $1$ unit along both x and y axis). ABCD is a quadrilateral whose vertices are $A(2,2),B(2,-2),C(0,-1)$ and $D(0,1)$. Write down the coordinates of A' and B'.

Q. On a map drawn to a scale of $1:50,000$, a rectangular plot of land ABCD has the following dimensions. AB$=6$cm; BC$=8$cm and all angles are right angles. Find the actual length of the diagonal distance AC of the plot in km.

Q. A man invests Rs. $22,500$ in Rs. $50$ shares available at $10\%$ discount. If the dividend paid by the company is $12\%$, calculate the annual dividend received.

Q. Cards bearing numbers $2,4,6,8,10,12,14,16,18$ and $20$ are kept in a bag. A card is drawn at random from the bag. Find the probability of getting a card which is?

Q. The circumference of the base of a cylindrical vessel is $132$ cm and its height is $25$ cm. Find the volume of cylinder. (use $\pi =\frac{22}{7}$).

Q. On a map drawn to a scale of $1:50,000$, a rectangular plot of land ABCD has the following dimensions. AB$=6$cm; BC$=8$cm and all angles are right angles. Find the actual area of the plot in sq km.

Q. If the mean of the following distribution is $24$, find the value of 'a'.

Marks	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$
Number of students	$7$	a	$8$	$10$	$5$