If the quadratic equation x² - 4x + k = 0 has equal roots, what is the value of k?

What is the sum of the first 20 terms of the arithmetic progression 2, 5, 8, ...?

A tower stands vertically on the ground. From a point on the ground, which is 30 m away from the foot of the tower, the angle of elevation of the top of the tower is 60°. What is the height of the tower?

Two tangents making an angle of 60° are drawn to a circle of radius √3 cm. Find the length of each tangent.

A solid metallic sphere of radius 10.5 cm is melted and recast into several smaller cones, each of radius 3.5 cm and height 3 cm. Find the number of cones so formed.

Find the probability of getting a sum of 9, when two dice are thrown simultaneously.

The coordinates of the mid-point of the line segment joining the points A(2,3) and B(4,k) is (3,5). What is the value of k?

The angle of depression of a car parked on the road from the top of a 150 m high tower is 30°. What is the distance of the car from the base of the tower?

If the HCF of 65 and 117 is expressible in the form 65m - 117, then the value of m is:

If tan A = cot B, then the value of (A + B) is: