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

Find the integrals of the function:

`(cos 2x)/(cos x + sin x)^2`

Find the integrals of the function:

sin⁻¹ (cos x)

Find the integrals of the function:

`1/(cos(x - a) cos(x - b))`

`int (sin^2x - cos^2 x)/(sin^2 x cos^2 x) dx` is equal to ______.

`int (e^x(1 +x))/cos^2(e^x x) dx` equals ______.

if `x^y + y^x = a^b`then Find `dy/dx`

Find the particular solution of the differential equation `(x - y) dy/dx = (x + 2y)` given that y = 0 when x = 1.

Find `int (sin^2 x - cos^2x)/(sin x cos x) dx`

A small firm manufactures necklaces and bracelets. The total number of necklaces and bracelets that it can handle per day is at most 24. It takes one hour to make a bracelet and half an hour to make a necklace. The maximum number of hours available per day is 16. If the profit on a necklace is Rs 100 and that on a bracelet is Rs 300. Formulate on L.P.P. for finding how many of each should be produced daily to maximize the profit?

It is being given that at least one of each must be produced.

Find  `int dx/(x^2 + 4x + 8)`

Evaluate: `int_0^π (x sin x)/(1 + cos^2x) dx`.

Evaluate `int_0^(3/2) |x sin pix|dx`

Prove that x² – y² = c(x² + y²)² is the general solution of the differential equation (x³ – 3xy²)dx = (y³ – 3x²y)dy, where C is parameter

Find `int (2x)/((x^2 + 1)(x^4 + 4))`dx

Find `int((3 sin x - 2) cos x)/(13 - cos^2 x- 7 sin x) dx`

Find the value of `tan^(-1) sqrt3 - cot^(-1) (-sqrt3)`

if `(x^2 + y^2)^2 = xy` find `(dy)/(dx)`

Find the principal value of the following:

`sin^-1(-sqrt3/2)`

Find the principal value of the following:

`sin^-1(cos  (2pi)/3)`

Find the principal value of the following:

`sin^-1((sqrt3-1)/(2sqrt2))`