List of top Questions asked in CBSE CLASS XII

$y=\begin{vmatrix}  f(x)&g(x)  &h(x) \\   l&m  &n \\   a&b  &c  \end{vmatrix}$,prove that $\frac{dy}{dx}=\begin{vmatrix}  f'(x)&g'(x)  &h'(x) \\   l&m  &n \\   a&b  &c  \end{vmatrix}$

Using mathematical induction prove that $\frac{d}{dx}$(xⁿ)=nx^n-1 for all positive integers n

If f(x)=|x|³, show that f"(x)exists for all real x, and find it.

If x=a(cost+tsint) and y=a(sint-tcost),find $\frac{d^2y}{dx^2}$

If cosy=xcos(a+y) with cosa≠±1,prove that $\frac{dy}{dx}$=$\frac{cos^2(a+y)}{sin\,a}$

If (x-a)²+(y-b)²=c², for some c>0 prove that
[1+($\frac{dy}{dx}$)²]$^{\frac{3}{2}}$/$\frac{d^2y}{dx^2}$ is a constant independent of a and b

$x\sqrt{1+y}+y\sqrt{1+x}=0$, for -1<x<1,prove that $\frac{dy}{dx}$=$-$$\frac{1}{(1+x)^2}$

Find $\frac{dy}{dx}$, if y=sin^-1x+sin^-1$\sqrt{1-x^2}$, -1≤x≤1

The general solution of the differential equation $e^{x}dy+(ye^{x}+2x)dx=0$ is

The general solution of a differential equation of the type $\frac{dx}{dy}+p_{1}x=Q1$ is

Choose the correct answer.
If x,y,z are nonzero real numbers,then the inverse of matrix
A=$\begin{bmatrix}x& 0& 0\\ 0& y& 0\\0&0& z\end{bmatrix}$is