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

For the differential equation, find the general solution:

`dy/dx = sqrt(4-y^2)      (-2 < y < 2)`

For the differential equation, find the general solution:

`dy/dx + y = 1(y != 1)`

For the differential equation, find the general solution:

sec² x tan y dx + sec² y tan x dy = 0

For the differential equation, find the general solution:

(e^x + e^–x) dy – (e^x – e–x) dx = 0

For the differential equation, find the general solution:

`dy/dx = (1+x^2)(1+y^2)`

For the differential equation, find the general solution:

y log y dx - x dy = 0

For the differential equation, find the general solution:

`x^5  dy/dx = - y^5`

For the differential equation, find the general solution:

`dy/dx = sin^(-1) x`

For the differential equation, find the general solution:

e^x tan y dx + (1 – e^x) sec² y dy = 0

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).