Science (English Medium) इयत्ता १२ - CBSE Question Bank Solutions for Mathematics

The smallest value of the polynomial x³ – 18x² + 96x in [0, 9] is ______.

The function f(x) = 2x³ – 3x² – 12x + 4, has ______.

The maximum value of sin x . cos x is ______.

Maximum slope of the curve y = –x³ + 3x² + 9x – 27 is ______.

The maximum value of `(1/x)^x` is ______.

The curves y = 4x² + 2x – 8 and y = x³ – x + 13 touch each other at the point ______.

Evaluate the following:

`int x/(sqrt(x) + 1) "d"x`  (Hint: Put  `sqrt(x)` = z)

Evaluate the following:

`int sqrt(("a" + x)/("a" - x)) "d"x`

Evaluate the following:

`int x^(1/2)/(1 + x^(3/4)) "d"x`   (Hint: Put `sqrt(x)` = z⁴)

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.