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

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 ______.

General solution of the differential equation of the type `("d"x)/("d"x) + "P"_1x = "Q"_1` is given by ______.

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 ____________.