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

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.

Prove that (5x - 4) is a factor of the polynomial f(x) = 5x³ - 4x² - 5x +4. Hence factorize It completely.

In  Δ ABC, the perpendicular bisector of AB and AC meet at 0. Prove that O is equidistant from the three vertices. Also, prove that if M is the mid-point of BC then OM meets BC at right angles. 

In a quadrilateral PQRS, if the bisectors of ∠ SPQ and ∠ PQR meet at O, prove that O is equidistant from PS and QR.