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

Integrating factor of the differential equation `cosx ("d"y)/("d"x) + ysinx` = 1 is ______.

Solution of the differential equation tany sec²xdx + tanx sec²ydy = 0 is ______.

Integrating factor of `(x"d"y)/("d"x) - y = x^4 - 3x` is ______.

Solution of `("d"y)/("d"x) - y` = 1, y(0) = 1 is given by ______.

The number of solutions of `("d"y)/("d"x) = (y + 1)/(x - 1)` when y (1) = 2 is ______. 

tan^–1x + tan^–1y = c is the general solution of the differential equation ______.

The general solution of e^x cosy dx – e^x siny dy = 0 is ______.

The solution of `("d"y)/("d"x) + y = "e"^-x`, y(0) = 0 is ______.

Integrating factor of the differential equation `("d"y)/("d"x) + y tanx - secx` = 0 is ______.

The solution of the differential equation `("d"y)/("d"x) + (1 + y^2)/(1 + x^2)` is ______.

The integrating factor of the differential equation `("d"y)/("d"x) + y = (1 + y)/x` is ______.

y = ae^mx+ be^–mx satisfies which of the following differential equation?

The solution of the differential equation cosx siny dx + sinx cosy dy = 0 is ______.

Let f be a real valued function defined on (0, 1) ∪ (2, 4) such that f '(x) = 0 for every x, then ____________.

The solution of `x ("d"y)/("d"x) + y` = e^x is ______.

In case of decreasing functions, slope of tangent and hence derivative is ____________.

The function f (x) = 2 – 3 x is ____________.

The function f(x) = x² – 2x is increasing in the interval ____________.

The function f (x) = x², for all real x, is ____________.

The function f(x) = mx + c where m, c are constants, is a strict decreasing function for all `"x" in "R"` , if ____________.