Q.

Find the radius of that circle whose area is $616c{m}^2$.

Q. If the angle of major sector of a circle is 250${}^o$. Then find the angle of minor sector (in degrees).

Q. A coin is tossed once. Find the probability that it is not a tail.

Q. The total surface area of a solid hemisphere is 462 cm${}^2$. Find its radius.

Q. Find the zeroes of the quadratic polynomial $x^2+x-2$, and verify the relationship between the zeroes and coefficients.

Q. Find the area of the triangle whose vertices are $(-5,7),(4,5)$ and $(-4,-5).$

Q. The following table shows the marks obtained by 50 students in mathematics of class X in a school.

Obtained Marks	20-30	30-40	40-50	50-60	60-70	70-80
Number of students	5	9	8	12	13	3

Find the median marks.

Q. A Pole has to be erected at a point on the boundary of a circular park of diameter 17 meters in such a way that the differences of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 meters. Is it possible to do so? If yes, at what distances from the two gates should the pole be erected?

Q. Find the sum of first 15 terms of an A.P. whose 5th and 9th terms are 26 and 42 respectively

Q. In an arc of a circle subtends an angle of 45${}^o$ at the centre and if the area of minor sector is 77 cm${}^2$, then find the radius of the circle (in cm).

Q. For traffic control, a CCTV camera is fixed on a 8m straight pole. The camera can see 17m distance sight line from the top. Find the area visible by the camera around the pole?

Q. The angle of elevation of the top of a building from the foot of the tower is 30${}^o$ and the angle of elevation of the top of the tower from the foot of the building is 60${}^o$. If the tower is 48 meters high, find the height of the building (in m.)

Q. Construct a triangle with sides 4 cm, 5 cm and 7 cm and then another triangle whose sides are $\frac{3}{4}$ of the corresponding sides of the first triangle.

Q. (i) If $\cos 3A=\sin (A-{34}^0)$, where A is an acute angle, find the value of A.
(ii) Prove the following identity, where the angles involved are acute angles for which the expression is define.
$\frac{1+{\cot }^{2}A}{1+{\tan }^{2}A}={\left(\frac{1-\cot A}{1-\tan A}\right)}^2$

Q. The diagonal of a rectangular field is 40 meters more than the shorter side. If longer side is 20 meters more than the shorter side, find the sides of the field.

Q. In the given figure ABC is a triangle. If $\frac{AD}{AB}=\frac{AE}{AC}$, then prove that DE || BC.

Q. A piggy bank contains hundred coins of Rs. 1, twenty five coins of Rs. 2, fifteen coins of Rs. 5 and ten coins of Rs. 10. If it is equally likely that one coin will fall, when the bank is turned upside down, what is the probability that the coin
(i) Will be a Rs. 2 coin?
(ii) Will not be a Rs. 5 coin?

Q. Prove that $\sqrt{6}$ is an irrational number

Q. Find the HCF of integers 375 and 675

Q. In the given figure, O is the center of a circle and two tangents QP and QR are drawn on the circle from a point Q lying outside the circle. Find the value of angle POR ( in degrees).

Q. Seven spheres of equal radii are made by melting a silver-cuboid of dimensions 8 cm ×× 11 cm x 9cm. Find the radius of a silver sphere (in cm).

Q. Express the trigonometric ratio tan A in terms of sec A.

Q. How many tangents can be drawn on the circle of radius $5\text{cm}$ from a point lying outside the circle at distance $9\text{cm}$ from the center.

Q. Find 11th term of the A.P. -17, -12, -7, ...............

Q. The cost of 2 exercise books and 3 pencils is Rs. 17 and the cost of 3 exercise books and 4 pencils is Rs. 24. Formulate the problem algebrically and solve it graphically.

Q. In the given figure, O is the center of a circle and two tangents CA, CB are drawn on the circle from a point C lying outside the circle. Prove that $\angle AOB$ and $\angle ACB$ are supplementary.

Q. Per day expenses of 25 families of the frequency distribution of a Dhani of a village is given as follows.

Per day expense (In Rs.)	25-35	35-45	45-55	55-65	65-75
Number of families	3	7	6	6	3

Find the mean expense of families by Direct Method.

Q. A motor car travels 175 distance from a place A to place B, at a uniform speed 70km/hr passes though all ten green traffic signals. Due to heavy traffic it stops for one minute at first signal, 3 minutes at second signal, 5 minutes at third signal and so on stops for 19 minutes at tenth signal. How much total time it takes to reach at the place B. Solve by suitable mathematical method.

Q. If the middle point of two points A(-2, 5) and B(-5, y) is $(\frac{-7}{2},3)$, then find the distance between points A and B.

Q. If $\cos A=\frac{12}{13}$, then calculate cot A.