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

Which of the following is a homogeneous differential equation?

Differentiate : \[\tan^{- 1} \left( \frac{1 + \cos x}{\sin x} \right)\] with respect to x .

Solve the following differential equation : \[\left[ y - x  \cos\left( \frac{y}{x} \right) \right]dy + \left[ y  \cos\left( \frac{y}{x} \right) - 2x  \sin\left( \frac{y}{x} \right) \right]dx = 0\] .

Evaluate : \[\int\limits_0^\pi \frac{x \tan x}{\sec x \cdot cosec x}dx\] .

Solve the differential equation:  ` (dy)/(dx) = (x + y )/ (x - y )`

Find `int_  (sin "x" - cos "x" )/sqrt(1 + sin 2"x") d"x", 0 < "x" < π / 2 `

Find `int_  sin ("x" - a)/(sin ("x" + a )) d"x"`

Find `int_  (log "x")^2 d"x"`

Find `int_  (sin2"x")/((sin^2 "x"+1)(sin^2"x"+3))d"x"`

Find the area of the triangle whose vertices are (-1, 1), (0, 5) and (3, 2), using integration. 

Find: `int_  (cos"x")/((1 + sin "x") (2+ sin"x")) "dx"`

Find: `int sec^2 x /sqrt(tan^2 x+4) dx.`

Find: `intsqrt(1 - sin 2x) dx, pi/4 < x < pi/2`

Find: `int sin^-1 (2x) dx.`

Solve the differential equation: x dy - y dx = `sqrt(x^2 + y^2)dx,` given that y = 0 when x = 1.

The product of any matrix by the scalar ______ is the null matrix.

Evaluate `int tan^8 x sec^4 x"d"x`

Find `int "dx"/(2sin^2x + 5cos^2x)`

Find `int x^2tan^-1x"d"x`

`int "e"^x (cosx - sinx)"d"x` is equal to ______.