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

cosec x (log y) dy + x²y dx = 0

(1 − x²) dy + xy dx = xy² dx

If `y = sin^-1 x + cos^-1 x , "find"  dy/dx`

Find : 

`∫(log x)^2 dx`

If e^y ( x +1)  = 1, then show that  `(d^2 y)/(dx^2) = ((dy)/(dx))^2 .`

Find `(dy)/(dx) , if y = sin ^(-1) [2^(x +1 )/(1+4^x)]`

If `(sin "x")^"y" = "x" + "y", "find" (d"y")/(d"x")`

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)`