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

Evaluate the following:

`int (sin^6x + cos^6x)/(sin^2x cos^2x) "d"x`

Evaluate the following:

`int (cosx - cos2x)/(1 - cosx) "d"x`

Evaluate the following:

`int "e"^(tan^-1x) ((1 + x + x^2)/(1 + x^2)) "d"x`

Evaluate the following:

`int sin^-1 sqrt(x/("a" + x)) "d"x`  (Hint: Put x = a tan²θ)

`int (x + sinx)/(1 + cosx) "d"x` is equal to ______.

`int sinx/(3 + 4cos^2x) "d"x` = ______.

Find the equation of a curve passing through `(1, pi/4)` if the slope of the tangent to the curve at any point P(x, y) is `y/x - cos^2  y/x`.

State the type of the differential equation for the equation. xdy – ydx = `sqrt(x^2 + y^2)  "d"x` and solve it

Which of the following is not a homogeneous function of x and y.

F(x, y) = `(sqrt(x^2 + y^2) + y)/x` is a homogeneous function of degree ______.

F(x, y) = `(ycos(y/x) + x)/(xcos(y/x))` is not a homogeneous function.

F(x, y) = `(x^2 + y^2)/(x - y)` is a homogeneous function of degree 1.

Solve : `x^2 "dy"/"dx"` = x² + xy + y².

Solcve: `x ("d"y)/("d"x) = y(log y – log x + 1)`

If A `= [(1,2),(2,1)]` and f(x) = (1 + x) (1 - x), then f(a) is ____________.

If A `= [(2"x", 0),("x","x")] "and A"^-1 = [(1,0),(-1,2)],` then x equals ____________.

If | A | = | kA |, where A is a square matrix of order 2, then sum of all possible values of k is ______.

Find the general solution of the differential equation:

(xy – x²) dy = y² dx

Read the following passage:

Based on the above, answer the following questions:

1. Show that (x² – y²) dx + 2xy dy = 0 is a differential equation of the type `dy/dx = g(y/x)`. (2)
2. Solve the above equation to find its general solution. (2)

If `|[2x,5],[8,x]|=|[6,-2],[7,3]|`, write the value of x.