(English Medium) ICSE Class 10 - CISCE Question Bank Solutions for Mathematics

Spherical marbles of diameter 1.4 cm are dropped into beaker containing some water and are fully submerged. The diameter of the beaker is 7 cm. Find how many marbles have been dropped in it if the water rises by 5.6 cm.

What is the least number of solid metallic spheres, each of 6 cm diameter, that should be melted and recast to form a solid metal cone whose height is 45 cm and diameter 12 cm?

A largest sphere is to be carved out of a right circular cylinder of radius 7 cm and height 14 cm. Find the volume of the sphere. 

A solid is in the form of a cone standing on a hemi-sphere with both their radii being equal to 8 cm and the height of cone is equal to its radius. Find, in terms of π, the volume of the solid. 

The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 0.2 cm. Find the length of the wire. 

Determine the ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube.

The cross-section of a tunnel is a square of side 7 m surmounted by a semi-circle as shown in the adjoining figure. The tunnel is 80 m long.

Calculate:

1. its volume,
2. the surface area of the tunnel (excluding the floor) and
3. its floor area.   

Find the value of k, if 2x + 1 is a factor of (3k + 2)x³ + (k − 1).

Using the factor Theorem, show that:

2x + 7 is a factor 2x³ + 5x² − 11x – 14. Hence, factorise the given expression completely.

For what value of n, the n^th terms of the arithmetic progressions 63, 65, 67, ... and 3, 10, 17, ... equal?

Two cars start together in the same direction from the same place. The first car goes at uniform speed of 10 km h^–1. The second car goes at a speed of 8 km h^–1 in the first hour and thereafter increasing the speed by 0.5 km h^–1 each succeeding hour. After how many hours will the two cars meet?

A sum of Rs. 700 is to be paid to give seven cash prizes to the students of a school for their overall academic performance. If the cost of each prize is Rs. 20 less than its preceding prize; find the value of each of the prizes.

An article can be bought by paying Rs. 28,000 at once or by making 12 monthly installments. If the first installment paid is Rs. 3,000 and every other installment is Rs. 100 less than the previous one, find:

1. amount of installments paid in the 9^th month.
2. total amount paid in the installment scheme.

A manufacturer of TV sets produces 600 units in the third year and 700 units in the 7^th year. Assuming that the production increases uniformly by a fixed number every year, find:

1. the production in the first year.
2. the production in the 10^th year.
3. the total production in 7 years.

Mrs. Gupta repays her total loan of Rs. 1,18,000 by paying installments every month. If the installments for the first month is Rs. 1,000 and it increases by Rs. 100 every month, What amount will she pays as the 30^th installments of loan? What amount of loan she still has to pay after the 30^th installment?

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