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

If A is square matrix such that A² = A, show that (I + A)³ = 7A + I..

If A is a square matrix such that A² = I, then (A – I)³ + (A + I)³ –7A is equal to ______.

Matrix addition is associative as well as commutative.

Matrix multiplication is commutative.

If A and B are two square matrices of the same order, then A + B = B + A.

(AB)^–1 = A^–1. B^–1, where A and B are invertible matrices satisfying commutative property with respect to multiplication.

`2^(cos^(2_x)`

`8^x/x^8`

`log (x + sqrt(x^2 + "a"))`

`log [log(logx^5)]`

If x^m . yⁿ = (x + y)^m+n, prove that `"dy"/"dx" = y/x`

If y = `log ((1 - x^2)/(1 + x^2))`, then `"dy"/"dx"` is equal to ______.

Using differentials, find the approximate value of `sqrt(0.082)`

Find the approximate value of (1.999)⁵.

Find the approximate volume of metal in a hollow spherical shell whose internal and external radii are 3 cm and 3.0005 cm respectively

If y = x⁴ – 10 and if x changes from 2 to 1.99, what is the change in y ______.

Find `int_0^1 x(tan^-1x)  "d"x`

Evaluate the following:

`int (sin^-1 x)/((1 - x)^(3/2)) "d"x`

Evaluate the following:

`int ((cos 5x + cos 4x))/(1 - 2 cos 3x) "d"x`

Evaluate the following:

`int_0^1 x log(1 + 2x)  "d"x`