Science (English Medium) कक्षा १२ - CBSE Question Bank Solutions for Mathematics

For the differential equation find a particular solution satisfying the given condition:

`(x^3 + x^2 + x + 1) dy/dx = 2x^2 + x; y = 1` When x = 0

For the differential equation find a particular solution satisfying the given condition:

`x(x^2 - 1) dy/dx = 1` , y = 0  when x = 2

For the differential equation find a particular solution satisfying the given condition:

`cos (dx/dy) = a(a in R); y = 1` when x = 0

For the differential equation find a particular solution satisfying the given condition:

`dy/dx` = y tan x; y = 1 when x = 0

Find the equation of a curve passing through the point (0, 0) and whose differential equation is y′ = e ^x sin x.

For the differential equation `xy(dy)/(dx) = (x + 2)(y + 2)`  find the solution curve passing through the point (1, –1).

Find the equation of a curve passing through the point (0, -2) given that at any point (x, y) on the curve, the product of the slope of its tangent and y-coordinate of the point is equal to the x-coordinate of the point.

At any point (x, y) of a curve, the slope of the tangent is twice the slope of the line segment joining the point of contact to the point (- 4, -3). Find the equation of the curve given that it passes through (-2, 1).

The volume of spherical balloon being inflated changes at a constant rate. If initially its radius is 3 units and after 3 seconds it is 6 units. Find the radius of balloon after t seconds.

In a bank, principal increases continuously at the rate of r% per year. Find the value of r if Rs 100 doubles itself in 10 years (log­_e 2 = 0.6931).

In a bank, principal increases continuously at the rate of 5% per year. An amount of Rs 1000 is deposited with this bank, how much will it worth after 10 years (e^0.5 = 1.648).

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))`