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

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

The solution of the differential equation ydx + (x + xy)dy = 0 is ______.

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

The solution of differential equation coty dx = xdy is ______.

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

Let f : R → R be defind by f(x) = `1/"x"  AA  "x" in "R".` Then f is ____________.

Which of the following functions from Z into Z is bijective?

Number of arbitrary constants in the particular solution of a differential equation of order two is two.

The solution of `("d"y)/("d"x) = (y/x)^(1/3)` is `y^(2/3) - x^(2/3)` = c.

The solution of the differential equation `("d"y)/("d"x) = (x + 2y)/x` is x + y = kx².

Let X = {-1, 0, 1}, Y = {0, 2} and a function f : X → Y defiend by y = 2x⁴, is ____________.

Let f : R → R be a function defined by f(x) `= ("e"^abs"x" - "e"^-"x")/("e"^"x" + "e"^-"x")` then f(x) is

Let g(x) = x² – 4x – 5, then ____________.

Let A = R – {3}, B = R – {1}. Let f : A → B be defined by `"f"("x") = ("x" - 2)/("x" - 3)` Then, ____________.

The mapping f : N → N is given by f(n) = 1 + n², n ∈ N when N is the set of natural numbers is ____________.

The function f : R → R given by f(x) = x³ – 1 is ____________.

Let f : [0, ∞) → [0, 2] be defined by `"f" ("x") = (2"x")/(1 + "x"),` then f is ____________.

If N be the set of all-natural numbers, consider f: N → N such that f(x) = 2x, ∀ x ∈ N, then f is ____________.

Let f : R `->` R be a function defined by f(x) = x³ + 4, then f is ______.

Let f : R → R, g : R → R be two functions such that f(x) = 2x – 3, g(x) = x³ + 5. The function (fog)^-1 (x) is equal to ____________.