List of top Mathematics Questions asked in AP ECET Ceramic Tech, AP ECET Agricultural Engg

If the matrix \[ A=\begin{bmatrix} 1 & 2 & 3\\ 4 & 5 & 6\\ 7 & 8 & 9 \end{bmatrix}, \] then which of the following is true?

If \[ \sin^{-1}\frac{5}{x}+\sin^{-1}\frac{12}{x}=\frac{\pi}{2}, \] then \(x=\)

If \[ \frac{x}{(x-1)^2(x+2)} = \frac{A}{(x-1)^2} + \frac{2}{9(x-1)} + \frac{B}{x+2}, \] then \(A+B=\)

If \[ \frac{x+4}{(x+2)^2(x+3)} = \frac{A}{(x+2)^2} + \frac{B}{x+2} + \frac{C}{x+3}, \] then \(A+B+C=\)

If \(2\sin^{-1}x=\sin^{-1}k\), then \(k=\)

If \(\tan A=\frac{1}{2}\) and \(\tan B=\frac{1}{3}\), then \(A+B=\)

If \[ \begin{bmatrix} x+y & 2 1 & x-y \end{bmatrix} = \begin{bmatrix} 4 & 2 1 & 2 \end{bmatrix}, \] then the values of \(x\) and \(y\) are:

The differential equation is \[ \frac{dy}{dx}+y\tan x=\sec x \] and \(y(0)=1\). Then the value of \(y\left(\frac{\pi}{4}\right)\) is

The differential equation is \[ \frac{dy}{dx}+\frac{y}{x}=0 \] and \(y(1)=2\). Then the value of \(y(3)\) is

Degree of the differential equation \[ y=x\frac{dy}{dx}+a\sqrt{1+\left(\frac{dy}{dx}\right)^2} \] is

If \(a\) and \(b\) are arbitrary constants, then the differential equation representing the family of curves \[ y=a\sin(x+b) \] is

The solution of the differential equation \[ x\frac{dy}{dx}+y=0 \] passing through the point \((1,1)\) is \(y=\)

The general solution of the differential equation \[ \frac{dy}{dx}=e^{x-y}+x^2e^{-y} \] is

The order of the differential equation of all circles passing through the origin and having their centres on the \(x\)-axis is

\[ \int_0^{\frac{\pi}{2}} \frac{\sin^{100}x}{\sin^{100}x+\cos^{100}x}\,dx = \]

If \[ \int \frac{\sin^3x+\cos^3x}{\sin^2x\cos^2x}\,dx = A\sec x+B\cosec x+c, \] then \((A,B)\) are

\[ \int_0^1 x\sqrt{x^2+4}\,dx= \]

The integral of \(f(x)=1+x^2+x^4\) with respect to \(x^2\) is

\[ \int \frac{dx}{\sqrt{16-25x^2}}= \]

\[ \int_{-\frac{\pi}{6}}^{\frac{\pi}{6}} \frac{\sin^5x\cos^3x}{x^4}\,dx= \]

\[ \int \frac{dx}{\sqrt{x+1}+\sqrt{x}}= \]

If \(y(x)=x^x,\ x>0\), then \[ y''(2)-2y'(2)= \]

If \[ z=x^2y^3+e^y\sin x, \] then \[ \frac{\partial^2 z}{\partial x\partial y}= \]

If \[ 2^x+2^y=2^{x+y}, \] then \[ \frac{dy}{dx}= \]

If \[ y+\sin^{-1}(1-x^2)=e^x, \] then \[ \frac{dy}{dx}= \]