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

If `"sec" theta = "x" + 1/(4 "x"), "x" in "R, x" ne 0,`then the value of  `"sec" theta + "tan" theta` is ____________.

If A = `[(0,0,0),(0,0,0),(0,1,0)]` then A is ____________.

A square matrix A = [a_ij]_nxn is called a diagonal matrix if a_ij = 0 for ____________.

Find the differential equation of all non-horizontal lines in a plane.

If `[("a","b"),("c", "-a")]`is a square root of the 2 x 2 identity matrix, then a, b, c satisfy the relation ____________.

Solution of the differential equation `"dx"/x + "dy"/y` = 0 is ______.

The solution of the differential equation `x "dt"/"dx" + 2y` = x² is ______.

The number of arbitrary constants in a particular solution of the differential equation tan x dx + tan y dy = 0 is ______.

The general solution of the differential equation `"dy"/"dx" = "e"^(x - y)` is ______.

The general solution of the differential equation `"dy"/"dx" + y/x` = 1 is ______.

The general solution of the differential equation x(1 + y²)dx + y(1 + x²)dy = 0 is (1 + x²)(1 + y²) = k.

The general solution of the differential equation `"dy"/"dx" + y sec x` = tan x is y(secx – tanx) = secx – tanx + x + k.

x + y = tan^–1y is a solution of the differential equation `y^2 "dy"/"dx" + y^2 + 1` = 0.

y = x is a particular solution of the differential equation `("d"^2y)/("d"x^2) - x^2 "dy"/"dx" + xy` = x.

Find the general solution of `"dy"/"dx" + "a"y` = e^mx 

Find the general solution of `(x + 2y^3)  "dy"/"dx"` = y

If y(x) is a solution of `((2 + sinx)/(1 + y))"dy"/"dx"` = – cosx and y (0) = 1, then find the value of `y(pi/2)`.

If y(t) is a solution of `(1 + "t")"dy"/"dt" - "t"y` = 1 and y(0) = – 1, then show that y(1) = `-1/2`.

Form the differential equation having y = (sin^–1x)² + Acos^–1x + B, where A and B are arbitrary constants, as its general solution.

Find the general solution of the differential equation `(1 + y^2) + (x - "e"^(tan - 1y)) "dy"/"dx"` = 0.