Arts (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

In a culture, the bacteria count is 1,00,000. The number is increased by 10% in 2 hours. In how many hours will the count reach 2,00,000, if the rate of growth of bacteria is proportional to the number present?

The general solution of the differential equation `dy/dx = e^(x+y)` is ______.

Find the equation of the curve passing through the point `(0,pi/4)`, whose differential equation is sin x cos y dx + cos x sin y dy = 0.

Integrate the rational function:

`x/((x + 1)(x+ 2))`

Integrate the rational function:

`1/(x^2 - 9)`

Integrate the rational function:

`(3x - 1)/((x - 1)(x - 2)(x - 3))`

Integrate the rational function:

`x/((x-1)(x- 2)(x - 3))`

Integrate the rational function:

`(2x)/(x^2 + 3x + 2)`

Integrate the rational function:

`(1 - x^2)/(x(1-2x))`

Integrate the rational function:

`x/((x^2+1)(x - 1))`

Integrate the rational function:

`x/((x -1)^2 (x+ 2))`

Integrate the rational function:

`(3x + 5)/(x^3 - x^2 - x + 1)`

Integrate the rational function:

`(2x - 3)/((x^2 -1)(2x + 3))`

Integrate the rational function:

`(5x)/((x + 1)(x^2 - 4))`

Integrate the rational function:

`(x^3 + x + 1)/(x^2 -1)`

Integrate the rational function:

`2/((1-x)(1+x^2))`

Integrate the rational function:

`(3x -1)/(x + 2)^2`

Integrate the rational function:

`1/(x^4 - 1)`

Integrate the rational function:

`1/(x(x^n + 1))` [Hint: multiply numerator and denominator by x^{n − 1} and put xⁿ = t]

Integrate the rational function:

`(cos x)/((1-sinx)(2 - sin x))` [Hint: Put sin x = t]