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

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 ______.

Which of the following is the general solution of `("d"^2y)/("d"x^2) - 2 ("d"y)/("d"x) + y` = 0?

If k be an integer, then `lim_("x" -> "k") ("x" - ["x"])` ____________.

General solution of `("d"y)/("d"x) + ytanx = secx` is ______.

The function f : A → B defined by f(x) = 4x + 7, x ∈ R is ____________.

The smallest integer function f(x) = [x] is ____________.

The function f : R → R defined by f(x) = 3 – 4x is ____________.

Solution of the differential equation `("d"y)/("d"x) + y/x` = sec x is ______.

The number of bijective functions from set A to itself when A contains 106 elements is ____________.

The general solution of the differential equation (e^x + 1) ydy = (y + 1) e^xdx is ______.

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

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

The number of arbitrary constants in the general solution of a differential equation of order three is ______.