Q. The cost of $1$ pencil and $3$ erasers is Rs.$10$ and the cost of $4$ pencils and $6$ erasers is $Rs.28$.Find the cost of $5$ pencils and $4$ erasers.

Q. Prove that :
$\sqrt{\frac{1+\sin A}{1-\sin A}}=\sec A+\tan A;A<90°$.

Q. Write the definition of Pythagoras theorem.

Q. The length of a tangent from a point $A$ at distance $5$ cm from the centre of the circle is $4$ cm. Find the radius of the circle.

Q. A toy is in the form of a cone of radius $3.5\text{cm}$ mounted on a hemisphere of the same radius. The total height of the toy is $15.5\text{cm}$. Find the total surface area of the toy.

Q. Find the sum of first $15$ terms. For AP:$7,11,15,19,....$.

Q. Find the L.C.M and H.C.F of $6$ and $20$ by prime factorisation method?

Q. For the following A.P's write the first term and common difference:$\frac{3}{2},\frac{1}{2},-\frac{1}{2},-\frac{3}{2},......$

Q. Draw a circle of radius $4cm$. From a point $7cm$ away from a centre, construct a pair of tangents to the circle and measure its length.

Q. The following distribution gives the daily income of $50$ workers of a factory.

Daily Income in Rs.	$100-120$	$120-140$	$140-160$	$160-180$	$180-200$
No of Workers	$12$	$14$	$8$	$6$	$10$

Convert the above distribution to a less than type cumulative frequency distribution and draw its ogive.

Q. Show that $a_1,a_2,a_3,.......a_n$ form an AP where $a_n=3+4n$

Q. Two poles of equal height are standing opposite each other on either side of the road which is $80m$ wide.From a point between then on the road the angles of elevation of top of the poles are ${60}^o$ and ${30}^o$. Find the height of the poles and distance of the point from the poles.

Q. In the figure given below find the area of the shaded region where a circular arc of radius $6cm$ has been drawn with vertex O of an equilateral triangle $OAB$ of side $12cm$ as centre.

Q. Prove that the ratio of the area of two similar triangle is equal to the square of the ratio of their corresponding sides.

Q. For which value of $p$ does the pair of equation given below has unique solution
$4x+py+8=0$
$2x+2y+2=0$

Q. A survey conducted on $20$ household in a locality by a group of statement resulted in the following frequency table for the number of family
Members in a house hold.

$\text{Family}\text{size}$	$1-3$	$3-5$	$5-7$	$7-9$	$9-11$
$\text{Number}of\text{families}$	$7$	$8$	$2$	$2$	$1$

Find the mode of the data.

Q. Two concentric circles are of radii $5$ cm and $3$cm. Find the length of chord of the larger circle which touches the smaller circle.

Q. If $\tan (A+B)=\sqrt{3}$ and $\tan (A-B)=\frac{1}{\sqrt{3}};0^o<A+B\le {90}^o;A>B$ then the value of A and B

Q. Fill in the blank:
___________$-{\cot }^2\theta =1$

Q. A cylindrical bucket 32 cm high and with radius of base 18 cm is filled with sand. This bucket is emptied on the ground and conical heap of sand is formed, if the height of the conical heap is 24 cm, find the radius and slant height of the heap.

Q. Find the volume of sphere whose radius is $3$ cm.

Q. A bag contains $3$ red and $5$ black. A ball is drawn at random from the bag. What is the probability that the ball drawn is
(i) red
(ii)not red

Q. Prove that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other sides.

Q. Draw a line segment of length $6.5$cm and divide it in the ratio $3:4$

Q. Find the co-ordinates of the points of trisection (i.e point dividing the three equal parts) of the segment joining the points $A(2,-2)$ and $B(-7,4)$.

Q. In the figure given below a quadrilateral ABCD is draw to circumscribe a circle prove that :$AB+CD=AD+BC$

Q. Find such value of $k$ for quotation equation $k{x}^2-2kx+6=0$ so that they have two equal roots.

Q. In a circle of radius $21cm$ , an arc subtends an angle of ${60}^o$ at the centre.Find
(i) The length of the arc
(ii) Area of sector.