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

The present population of a town is 1, 
0/o per annum 1, 15,200. If it increases at the rate of `6 2/3` % per annum find  
Its population 2 years ago.

A machine was purchased 2 years ago. Its value decreases by 10% every year. Its present value is Rs 19,083.60. For how much money was the machine purchased?

The population of a city is 24,000. In the next 3 years it will be 27,783. Find the rate of growth of the population.

Under the electrification programme of villages, the number of villages with electricity rose to 27,040 from 25,000 in 2 years. Find the rate of growth in the number of villages with electricity.

A new car is purchased for Rs 4, 00,000 .Its value depreciates at the rate of 10% per annum. What will be its value after 4 years?

The value of a property decreases every year at the rate of 5%. If its value at the end of 3 years be Rs 44,540, what was the original value at the beginning of these 3 years?

The value of the refrigerator which was purchased 2 years ago, depreciates at 12% per annum. If its present value is Rs 9,680. For how much was it purchased?

A building worth Rs 1, 33,100 is constructed on a plot of land worth Rs 72,900. After how many years will the values of both be same, if the land appreciates at 10% p.a. and the building depreciates at 10% p.a.?

The cost of a T.V. was quoted Rs 17,000 at the beginning of the year 1999. In the beginning of 2000 the price was hiked by 5%. Because of decrease in demand the cost was reduced by 4% in the beginning of 2001. What is the cost of the T.V. in 2001?

A mango tree was planted 3 years ago. The rate of growth is 20% per annum. If at present, the height of the tree is 1 m 8 cm, how high was it when planted?

Prove by factor theorem that 

(x-2) is a factor of 2x³- 7x -2 

Prove by factor theorem that 

(2x+1) is a factor of 4x³ + 12x² + 7x +1 

Prove by factor theorem that 

(3x-2) is a factor of 18x³ - 3x² + 6x -12  

Prove by factor theorem that 

(2x - 1) is a factor of 6x³ - x² - 5x +2 

Prove by factor theorem that 

(x - 3) is a factor of 5x² - 21 x +18 

Find the value of m ·when x³ + 3x² -m x +4 is exactly divisible by (x-2) 

Prove that ( p-q) is a factor of (q - r)³ + (r - p) ³ 

Prove that (x - y) is a factor of yz( y² - z²) + zx( z² - x²) + xy ( x² - y²) 

Prove that (x-3) is a factor of x³ - x² - 9x +9 and hence factorize it completely. 

Prove that  (x+ 1) is a factor of x³ - 6x² + 5x + 12 and hence factorize it completely.