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

Ananth had Rs 50 shares of 'Esco' paying 6% dividend. He sold them at a market price of Rs 80 and invested the proceeds in buying Rs 100 shares of 'Y2K Software' at Rs 150 and paying 11% dividend. He thus increased his annual income by Rs 2,150. How many shares of 'Esco' did he sell?

Krithika wants to invest Rs 10,000 in shares of different companies such that the percentage return on her investment is 8%. She invested Rs 4,500 in 6% Rs 100 shares at Rs 75, Rs 2,500 in 8% Rs 100 shares at par and the rest in 16% Rs 100 shares. Find the rate at which she bought the 16% shares.

Pramod wants to invest Rs 35,000 in shares such that the percentage return on his investment is `8 1/7 %`. He invested Rs 6,000 in 6 % Rs 50 shares of  'Lakme' at Rs 40, Rs 15,000 in 8 % Rs 100 shares of 'Volta' at Rs 125 and the remaining in 12 %  shares of 'BPL'. At what rate did he buy the 'BPL' shares? 

Find without division, the remainder in the following: 

5x² - 9x + 4 is divided by (x - 2) 

Find without division, the remainder in the following: 

5x³ - 7x² +3 is divided by (x-1)  

Find without division, the remainder in the following: 

8x² - 2x + 1 is divided by (2x+ 1) 

Find without division, the remainder in the following :

x³ + 8x² + 7x- 11 is divisible by (x+4)

Find without division, the remainder in the following: 

2x³ - 3x² + 6x - 4 is divisible by (2x-3) 

Using remainder theorem, find the value of m if the polynomial f(x)= x³ + 5x² -mx +6 leaves a remainder 2m when divided by (x-1),  

Find the values of p and q in the polynomial f(x)= x³ - px² + 14x -q, if it is exactly divisible by (x-1) and (x-2). 

Find the values of a and b when the polynomial f(x)= ax³ + 3x² +bx -3 is exactly divisible by (2x+3) and leaves a remainder -3 when divided by (x+2). 

Find the values of m and n when the polynomial f(x)= x³ - 2x² + m x +n has a factor (x+2) and leaves a remainder 9 when divided by (x+1).

Find the values of a and b when the polynomials f(x)= 2x² -5x +a and g(x)= 2x² + 5x +b both have a factor (2x+1).

Find the values of a and b when the factors of the polynomial f(x)= ax³ + bx² + x a are (x+3) and (2x-1). Factorize the polynomial completely.

What number should be subtracted from x² + x + 1 so that the resulting polynomial is exactly divisible by (x-2) ? 

What number should be added to 2x³ - 3x² + 7x -8 so that the resulting polynomial is exactly divisible by (x-1) ?

What number should be subtracted from the polynomial f(x)= 2x³ - 5x² +8x -17 so that the resulting polynomial is exactly divisible by (2x - 5)?

What number should be added to polynomial f(x)= 12x³ + 16x² - 5x - 8 so that the resulting polynomial is exactly divisible by (2x - 1) ?

use the rernainder theorem to find the factors of ( a-b )³ + (b-c )³ + ( c-a)³ 

A polynomial f(x) when divided by (x - 1) leaves a remainder 3 and when divided by (x - 2) leaves a remainder of 1. Show that when its divided by  (x - i)(x - 2), the remainder is (-2x + 5).