(English Medium) ICSE Class 10 - CISCE Important Questions for Mathematics

If b is the mean proportion between a and c, show that: `(a^4 + a^2b^2 + b^4)/(b^4 + b^2c^2 + c^4) = a^2/c^2`.

If (3a + 2b) : (5a + 3b) = 18 : 29. Find a : b

The 4th term of a G.P. is 16 and the 7th term is 128. Find the first term and common ratio of the series

Using properties of proportion, solve for x. Given that x is positive:

`(2x + sqrt(4x^2 -1))/(2x - sqrt(4x^2 - 1)) = 4`

Calculate the ratio in which the line joining A(−4, 2) and B(3, 6) is divided by point P(x, 3). Also, find

1. x
2. length of AP.

If (x - 9) : (3x + 6) is the duplicate ratio of 4: 9, find the value of x.

What least number must be added to each of the numbers 6, 15, 20 and 43 to make them proportional?

Using the properties of proportion, solve for x, given `(x^4 + 1)/(2x^2) = 17/8`.

The monthly pocket money of Ravi and Sanjeev are in the ratio 5 : 7. Their expenditures are in the ratio 3 : 5. If each saves Rs. 80 every month, find their monthly pocket money.

6 is the mean proportion between two numbers x and y and 48 is the third proportional of x and y. Find the numbers.

If x, y, z are in continued proportion, prove that `(x + y)^2/(y + z)^2 = x/z`

The following numbers, K + 3, K + 2, 3K – 7 and 2K – 3 are in proportion. Find k. 

Using properties of proportion solve for x, given

`(sqrt(5x)+sqrt(2x -6))/(sqrt(5x)- sqrt(2x -6)) = 4`

The mean proportional between 4 and 9 is ______.

What number must be added to each of the numbers 4, 6, 8, 11 in order to get the four numbers in proportion?

If `(a + b)^3/(a - b)^3 = 64/27`

1. Find `(a + b)/(a - b)`
2. Hence using properties of proportion, find a : b.

What must be subtracted from 16x³ – 8x² + 4x + 7 so that the resulting expression has 2x + 1 as a factor?

Using remainder theorem, find the value of k if on dividing 2x³ + 3x² – kx + 5 by x – 2, leaves a remainder 7.

If (x + 2) and (x + 3) are factors of x³ + ax + b, find the values of ‘a’ and ‘b’.

Use Remainder theorem to factorize the following polynomial:

`2x^3 + 3x^2 - 9x - 10`