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

Divide 16 into two parts such that the twice the square of the larger part exceeds the square of the smaller part by 164.

Two natural numbers are in the ratio 3 : 4. Find the numbers if the difference between their squares is 175.

Two squares have sides A cm and (x + 4) cm. The sum of their areas is 656 sq. cm.Express this as an algebraic equation and solve it to find the sides of the squares.

The length of a rectangular garden is 12 m more than its breadth. The numerical value of its area is equal to 4 times the numerical value of its perimeter. Find the dimensions of the garden.

A farmer wishes to grow a 100 m² rectangular vegetable garden. Since he has with him only 30 m barbed wire, he fences three sides of the rectangular garden letting compound wall of his house act as the fourth side fence. Find the dimensions of his garden.

The hypotenuse of a right-angled triangle is 1 m less than twice the shortest side. If the third side is 1 m more than the shortest side, find the sides of the triangle.

A wire ; 112 cm long is bent to form a right angled triangle. If the hypotenuse is 50 cm long, find the area of the triangle.

Car A travels ‘x’ km for every litre of petrol, while car B travels (x + 5) km for every litre of petrol.

1. Write down the number of litres of petrol used by car A and car B in covering a distance of 400 km.
2. If car A uses 4 litres of petrol more than car B in covering 400 km. write down an equation, in A and solve it to determine the number of litres of petrol used by car B for the journey.

The speed of a boat in still water is 11 km/ hr. It can go 12 km up-stream and return downstream to the original point in 2 hours 45 minutes. Find the speed of the stream

By selling an article for Rs. 21, a trader loses as much per cent as the cost price of the article. Find the cost price.

A man spent Rs. 2800 on buying a number of plants priced at Rs x each. Because of the number involved, the supplier reduced the price of each plant by Rupee 1.The man finally paid Rs. 2730 and received 10 more plants. Find x.

Forty years hence, Mr. Pratap’s age will be the square of what it was 32 years ago. Find his present age.

The point (3, 0) is invariant under reflection in:

Naveen deposits ₹ 800 every month in a recurring deposit account for 6 months. If he receives ₹ 4884 at the time of maturity, then the interest he earns is ______.

Salman deposits ₹ 1000 every month in a recurring deposit account for 2 years. If he receives ₹ 26000 on maturity, find:

1. the total interest Salman earns.
2. the rate of interest.

Use graph sheet to Solution this question. Take 2 cm = 1 unit alogn both the axes.

1. Plot A, B, C where A(0, 4), B(1, 1) and C(4, 0)
2. Reflect A and B on the x-axis and name them as E and D respectively.
3. Reflect B through the origion and name it F. Write down the coordinates of F.
4. Reflect B and C on the y-axis and name them as H and G respectively.
5. Join points A, B, C, D, E, F, G, H and A in order and name the closed figure formed.

Use graph sheet for this question. Take 2 cm = 1 unit along the axes.

1. Plot A(0, 3), B(2, 1) and C(4, –1).
2. Reflect point B and C in y-axis and name their images as B' and C' respectively. Plot and write coordinates of the points B' and C'.
3. Reflect point A in the line BB' and name its images as A'.
4. Plot and write coordinates of point A'.
5. Join the points ABA'B' and give the geometrical name of the closed figure so formed.

Suresh has a recurring deposit account in a bank. He deposits ₹ 2000 per month and the bank pays interest at the rate of 8% per annum. If he gets ₹ 1040 as interest at the time of maturity, find in years total time for which the account was held.

Radha deposited ₹ 400 per month in a recurring deposit account for 18 months. The qualifying sum of money for the calculation of interest is ______.

Study the graph and answer each of the following:

1. Write the coordinates of points A, B, C and D.
2. Given that, point C is the image of point A. Name and write the equation of the line of reflection.
3. Write the coordinates of the image of the point D under reflection in y-axis.
4. Whats the name given to a point whose image is the point itself?
5. On joining the points A, B, C, D and A in order, a figure is formed. Name the closed figure.