Q. Write the distance of the point $(3,-2)$ from y-axis

Q. In the figure, $CD$ and $RS$ are respectively the medians of $△ABC$ and $△PQR$. If $△ABC\sim △PQR$, prove that
(i) $△ADC\sim △PSR$
(ii) $\frac{CD}{RS}=\frac{AB}{PQ}$

Q. If the sum of zeroes of the quadratic polynomial $k{x}^2+5x+3k$ is equal to their product, find the value of $k$

Q. Two cubes each of volume $27c{m}^3$ are joined end to end to form a solid. Find the surface area (cm${}^2$) of the resulting cuboid.

Q. An express train takes $2$ hour less time than a passenger train to travel $400km$ between two stations (without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is $10km/h$ more than of the passenger train, find the average speed of the two trains

Q. $BE$ and $CF$ are medians of a triangle $ABC$ right angles at $A$. Prove that $4(B{E}^2+C{F}^2)=5B{C}^2$.

Q. In the figure, a quadrilateral $PQRS$ is drawn to circumscribe a circle. Prove that $PQ+RS=PS+QR$

Q. Find the $L.C.M.$ of the numbers $180,72$ and $252$.

Q. From the top of a $10m$ high building, the angle of elevation of a tower is ${60}^{\circ }$ and the angle of depression of its foot at ${45}^{\circ }$. Determine the height of the tower.

Q. Find the co-ordinates of the points of trisection of the line segment joining the points $P(-3,4)$ and $Q(4,5)$

Q. Show that $\tan {36}^{\circ }\tan {17}^{\circ }\tan {54}^{\circ }\tan {73}^{\circ }=1$

Q. If the median of the distribution given below is $28.5$, find the values of $x$ and $y$.

Class-interval	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	Total
Frequency	$5$	$x$	$20$	$15$	$y$	$5$	$60$

Q. Write the area of a sector of a circle with radius $r$ and angle with degree measure $\theta$.

Q. Find the value of ${\cos }^2{12}^{\circ }+{\cos }^2{78}^{\circ }$

Q. Find the area of the shaded region in the figure, if $AB=5cm,AC=12cm$ and $O$ is the centre of the circle

Q. A box contains $30$ discs which are numbered $1$ to $30$. If one disc is drawn at random from the box, find the probability that it bears
(i) a two digit number
(ii) a perfect square number

Q. Write the next two terms of $A.P.4,1,-2,-5,.....$

Q. A hemispherical tank full of water is emptied by a pipe at the rate of $5$ litres per second. How much time will it take to empty half of the tank, if it is $3.5m$ in diameter?

Q. If the probability of solving a problem by a student is $\frac{2}{3}$, then find the probability of not solving the problem by the student.

Q. If tangents $TA$ and $TB$ from a point $T$ to a circle with centre $O$ are inclined to each other at an angle of ${70}^{\circ }$, then find $\angle AOB$ (in degrees).

Q. If the sum of the first $12$ terms of an A.P. is $468$ and its common difference is $6$, find the ${10}^{th}$ term

Q. Find the area of a circle whose circumference is 44 cm44 cm in sq cm.

Q. The mean of the following frequency table is $50$. Find the values of $x$ and $y$.

Class-interval	$0-20$	$20-40$	$40-60$	$60-80$	$80-100$	Total
Frequency	$17$	$x$	$32$	$y$	$19$	$120$

Q. Write the solution of the pair of linear equations $3x+4y=0$ and $2x-y=0$

Q. A boy $2m$ long casts a shadow $1m$ long on the plane ground. At the same time, a tower casts a shadow $5m$ long on the ground. Find the height of the tower (in m).

Q. Number $\frac{3}{625}$ is a terminating decimal or a non-terminating repeating decimal? Write it in decimal form.

Q. If $M(4,5)$ is the mid-point of the line segment $AB$ and co-ordinates of $A$ are $(3,4)$, then find the co-ordinates of point $B$.

Q. Prove that $\sqrt{\frac{1+\cos A}{1-\cos A}}=cosecA+\cot A$

Q. If $\sin \theta =\frac{1}{2}$, then find the value of $\frac{1-2{\sin }^2\theta }{\sin \theta }$

Q. Construct a tangent to any point on the circle of radius $3cm$.