A rectangular box of width(a), length(b), and height(c) has a solid cylinder of height 'c' and of diameter 'a' placed within it. If a= 6, b =8 and c =10, how much volume is left in the rectangular box ?

It costs Rs. 6,000 and Rs. 6,100 respectively to paint the 4 walls of 2 square halls of the same height. If the length of one hall exceeds the length of the other by 1 m and the cost of painting is Rs. 5 per sq. m, what is the height of the two halls?

If f(x) = x³ − 4x + p and f(0) and f(1) are of opposite signs, which one of the following is necessarily true?

The length, breadth and height of a rectangular cuboid are in the ratio 1: 2 : 3. If the length, breadth and height are increased by 100% each then what would be the increase in the volume of the cuboid ?

The speed of a boat in still water is 5 km/hr. If it takes thrice as much time in going 20 km upstream as in going the same distance downstream, find the speed of the stream.

In a simultaneous throw of a pair of dice, find the probability of getting a total of 9 or more.

Three solid cubes of sides 1 cm, 6 cm and 8 cm are melted to form a new cube. Find the surface area of the cube so formed.

The sum of three consecutive odd numbers is 20 more than the first number. What is the middle number ?

The speeds of 3 cars are in the ratio 5 : 4 : 6. The ratio between the time taken by them to travel the same distance is