If a : b = 5 : 3; find : 

A diagonal matrix in which each element of its leading diagonal is unity or identity, is called a

Find the value of a, if x - 2 is a factor of 2x⁵ - 6x⁴ - 2ax³ + 6ax² + 4ax + 8.

Find the remainder when :
x⁴ + 1 is divided by x + 1

The equation 3x² - 12x + (n - 5) = 0 has equal roots. Find the value of n.

The point (-3, 2) lies on the line ax + 3y + 6 = 0, calculate the value of 'a'.

Solve the following equation by factorisation.
x (x - 5) = 24

If x - 1 is a factor of x² + x + k , then the value of k is

In a two digit number, the ten's digit is bigger. The product of the digits is 27 and the difference between two digits is 6. Find the number.

Solve the following equation using the formula:
x² - 6x = 27