If a + b = 1 and a³ + b³ + 3ab = k, then the value of k is

The slant height and the radius of a right circular cone are 11 cm and 6 cm, respectively. What is the curved surface area of the cone?

After seeing a policeman from a distance of 500 m, a thief starts running at a speed of 10 km/h. After noticing, the policeman chases immediately with a speed of 12 km h, and the thief is caught. The distance run by the policeman is:

An equilateral triangle ABC is inscribed in a circle with centre O. D is a point on the minor are BC and ∠CBD=40⁰. Find the measure of ∠BCD.

Annual salary of Varun is 7.68 lac. In a month if he spends 12000 on his children, 1/13th of rest on food and 8000 in  mutual funds from his monthly salary, then find the monthly saving he is left with.

When positive numbers x, y and z are divided by 31, the remainders are 17, 24 and 27, respectively. When (4x-2y+32) is divided by 31, the remainder will be:

If cos(2θ+54°) = sinθ, 0°<(2θ-54°)<90°, then what is the value of $$1\over tan5θ+cosec{5θ\over 2}$$   

The difference of two numbers is equal to 20% of the larger of the numbers. If the smaller number is 40, then find the larger number