Question 1 :
Five tables and eight chairs cost Rs. $7350$; three tables and five chairs cost Rs. $4475$. The price of a table is

Question 2 :
If $2p + 3q = 18$ and $4p^{2} + 4pq - 3q^{2} - 36 = 0$ then what is $(2p + q)$ equal to?

Question 3 :
Solve : $\displaystyle \frac{2}{x}+\displaystyle \frac{2}{3y}= \displaystyle \frac{1}{6}$ and $\displaystyle \frac{3}{x}+\displaystyle \frac{2}{y}= 0$.&#160;<br/>Hence, find $'m'$ for which $y= mx-4$.

Question 4 :
Find the value of x and y using cross multiplication method:<br/>$ x + 2y = 8$ and $2x -3y = 2$

Question 5 :
Find the value of x and y using cross multiplication method: <br>$x - 6y = 2$ and $x + y = 4$

Question 7 :
Father's age is three times the sum of ages of his two children. After $5$ years his age will be twice the sum of ages of two children. Find the age of father.<br/>

Question 8 :
State whether the following statement is True or False.<br/>3.54672 is an irrational number.

Question 10 :
Divide the first expression by the second. Write the quotient and the remainder.<br/>$a^2-b^2 ; a-b$

Question 11 :
The sides of a triangle are given below. Check whether or not the sides form a right angled triangle.$50cm, 80cm, 100cm$

Question 12 :
The perimeters of two similar triangles ABC and LMN are 60 cm and 48 cm respectively If LM=8 cm, the length of AB is

Question 13 :
If the sides of a right-angled triangle are&#160;$\displaystyle \left \{ \cos 2\alpha +\cos 2\beta +2\cos \left ( \alpha +\beta &#160;\right ) \right \}$ and&#160;$\displaystyle \left \{ \sin 2\alpha +\sin 2b+2\sin (\alpha +\beta ) \right \},$ then the length of the hypotenuse is:&#160;

Question 14 :
In quadrilateral ABCD, the diagonals AC and BD intersect each at point O. If $AO=2CO$ and $BO=2DO$; Then,$\displaystyle \Delta AOB$ is similar to $\displaystyle \Delta COD$<br/>

Question 15 :
The perimeter of two similar triangle are $30\ cm$ and $20\ cm$. If one side of first triangle is $12\ cm$ determine the corresponding side of second triangle.

Question 16 :
Three sides of a triangle are 6 cm, 12 cm and 13 cm then<br>

Question 17 :
Match the column.<br/><table class="wysiwyg-table"><tbody><tr><td>1. In&#160;$\displaystyle \Delta ABC$ and&#160;$\displaystyle \Delta PQR$,<br/>$\displaystyle \frac{AB}{PQ}=\frac{AC}{PR},\angle A=\angle P$<br/></td><td>(a) AA similarity criterion&#160;</td></tr><tr><td>2.&#160;In&#160;$\displaystyle \Delta ABC$ and&#160;$\displaystyle \Delta PQR$,<br/>$\displaystyle \angle A=\angle P,\angle B=\angle Q$<br/><br/></td><td>(b) SAS similarity criterion&#160;</td></tr><tr><td>3.&#160;In&#160;$\displaystyle \Delta ABC$ and&#160;$\displaystyle \Delta PQR$,<br/>$\displaystyle \frac{AB}{PQ}=\frac{AC}{PR}=\frac{BC}{QR}$<br/>$\angle A=\angle P$<br/></td><td>(c) SSS similarity criterion&#160;</td></tr><tr><td>4. In&#160;$\displaystyle \Delta ACB,DE||BC$<br/>$\displaystyle \Rightarrow \frac{AD}{BD}=\frac{AE}{CE}$<br/></td><td>(d) BPT</td></tr></tbody></table>

Question 18 :
State whether the following statements are true or false . Justify your answer.<br>The points $ (0 , 5) , (0 , -9) $ and $ (3 , 6) $ are collinear .

Question 19 :
If the line $2x+y=k$ passes through the point which divides the line segment joining the point $(1,1)$ &amp; $(2,4)$ in the ratio $3:2$ then $k$ equal

Question 20 :
If the point P (2, 1) lies on the segment joining Points A (4, 2) and B (8, 4) then

Question 21 :
<i></i>If the coordinates of opposite vertices of a square are $(1,3)$ and $(6,0)$, the length if a side od a square is&#160;

Question 22 :
If $(-6, -4), (3, 5), (-2, 1)$ are the vertices of a parallelogram, then remaining vertex can be

Question 23 :
A fair coin is tossed five times. Calculate the probability that it lands head-up at least twice.

Question 24 :
Solve : $\dfrac { 2tan{ 30 }^{ \circ&#160; } }{ 1+{ tan }^{ 2 }{ 30 }^{ \circ&#160; } } $

Question 26 :
If $\cos 9 \alpha = \sin &#160;\alpha$ and $9 \alpha &lt; 90^o$, what is the value of $\tan &#160;5 \alpha$?

Question 27 :
The value of the expression $\displaystyle 1\, - \,\frac{{{{\sin }^2}y}}{{1\, + \cos \,y}}\, + \frac{{1\, + \cos \,y}}{{\sin \,y}}\, - \,\frac{{\sin \,y}}{{1\, - \cos \,y}}$ is equal to&#160;

Question 28 :
If $\displaystyle \sin x+ \sin^{2}x= 1,$ then the value of $\displaystyle \cos ^{12}x +3\cos ^{10}x+3\cos ^{8}x+\cos ^{6}x-2$ is equal to<br/>