Find the zeroes of the quadratic polynomial x^{2} + 7x + 10, and verify the relationship between the zeroes and the coefficients.

Find the HCF and LCM of 6, 72 and 120, using the prime factorisation method.

Find the HCF of 96 and 404 by the prime factorisation method. Hence, find their LCM.

A sweet seller has 420 *kaju barfis* and 130 *badam barfis*. She wants to stack them in such a way that each stack has the same number, and they take up the least area of the tray. What is the number of that can be placed in each stack for this purpose?

Two dairy owners A and B sell flavoured milk filled to capacity in mugs of negligible thickness, which are cylindrical in shape with a raised hemispherical bottom. The mugs are 14 cm high and have diameter of 7 cm as shown in given figure. Both A and B sell flavoured milk at the rate of Rs. 80 per litre. The dairy owner A uses the formula πr^{2}h to find the volume of milk in the mug and charges Rs. 43.12 for it. The dairy owner B is of the view that the price of actual quantity of milk should be charged. What according to him should be the price of one mug of milk? Which value is exhibited by the dairy owner B? (Use π = 22/7)

Find the mode of the following distribution of marks obtained by the students in an examination:

Given the mean of the above distribution is 53, using empirical relationship estimate the value of its median.

Water in a canal, 6 m wide and 1.5 m deep, is flowing with a speed of 10 km/h. How much area will it irrigate in 30 minutes, if 8 cm of standing water is needed?

In given figure ABPC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region.

**Show that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.**

In given figure XY and X'Y' are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and X'Y' at B. Prove that ∠ AOB = 90°.

**In given figure ∠1 = ∠2 and ΔNSQ ≅ ΔMTR , then prove that ΔPTS ~ ΔPRQ.**

**The points A(4, –2), B(7, 2), C(0, 9) and D(–3, 5) form a parallelogram. Find the length of the altitude of the parallelogram on the base AB.**

**In what ratio does the x-axis divide the line segment joining the points (–4, –6) and (–1, 7)? Find the co-ordinates of the point of division.**

**If (1, p/3) is the mid-point of the line segment joining the points (2, 0) and (0, 2/9), then show that the line 5x + 3y + 2 = 0 passes through the point (–1, 3p).**