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

\[\frac{dy}{dx} = \sin^3 x \cos^2 x + x e^x\]

tan y dx + tan x dy = 0

(1 + x) y dx + (1 + y) x dy = 0

x cos² y dx = y cos² x dy

cos y log (sec x + tan x) dx = cos x log (sec y + tan y) dy

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")`

A is a square matrix with ∣A∣ = 4. then find the value of ∣A. (adj A)∣.

If y = (log x)^x + x^log x, find `"dy"/"dx".`

If e^y = y^x, then show that `"dy"/"dx" = (logy)^2/(log y - 1)`.

Evaluate: `int e^x/sqrt(e^(2x) + 4e^x + 13)` dx

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.