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

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 ____________.

The general solution of `("d"y)/("d"x) = 2x"e"^(x^2 - y)` is ______.

The function f(x) = tan^-1 x is ____________.

The interval in which the function f is given by f(x) = x² e^-x is strictly increasing, is: ____________.

Let `"f (x) = x – cos x, x" in "R"`, then f is ____________.

In `(0, pi/2),`  the function f (x) = `"x"/"sin x"` is ____________.

Let f (x) = tan x – 4x, then in the interval `[- pi/3, pi/3], "f"("x")` is ____________.

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

The solution of the equation (2y – 1)dx – (2x + 3)dy = 0 is ______.

The differential equation for which y = acosx + bsinx is a solution, is ______.

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