List of top Mathematics Questions asked in AP EAPCET

If \[ A = \begin{bmatrix}0 & 1 & 2 & 3 \\ 0 & 2 & 4 & 8 \\ 0 & 0 & 4 & 8\end{bmatrix}, \text{ then the rank of } A \text{ is:} \]

If \[ A= \begin{bmatrix} 1 & -3 & 2\\ -2 & 1 & 3\\ 3 & 2 & -1 \end{bmatrix} \] then \(A^2\operatorname{Adj}A=\)

If the system of simultaneous linear equations \[ x+y+z = \lambda, \quad 5x - y + \mu z = 10, \quad 2x + 3y - z = 6 \] has a unique solution, then:

Let \(f(x)=\sqrt{\frac{x+1}{x+3}}\) and \(g(x)=\sqrt{\frac{2-x}{x+3}}\) be two real valued functions. Then the domain of \(\frac{f}{g}\) is:

If the function \(f:\mathbb{R}\to\mathbb{R}\) is defined as \(f(x)=x^2-2x-3\), then \(f\) is:

For the parabola represented in the parametric form \[ x=t^2+t+1 \] \[ y=t^2-t+1, \] the length of latus rectum is:

An integrating factor of the differential equation \[ (x^2+1)\frac{dy}{dx}+xy=x^3 \] is

If the general solution of \[ \frac{dy}{dx}=\frac{y^2}{xy-y^2-x^2} \] is \[ \tan^{-1}\left(\frac{y}{x}\right)=f(y)+C, \] then \(f(e^3)=\)

Evaluate \[ \int_{-\pi/4}^{\pi/4}\cos^{-8}x\,dx \]

Evaluate \[ \int_{a-1}^{a}\frac{e^x(a-x)}{(x-a+1)^2}\,dx \]

For \(n\in N\), if \[ I_n=\int \frac{\sin nx}{\sin x}\,dx = \frac{2}{n-1}\sin(n-1)x+I_{n-2} \] and \[ \int_0^\pi \frac{\sin nx}{\sin x}\,dx=\frac{k\pi}{2}, \] then \(k=\)

If \[ f(x)=\sin(\tan^{-1}x), \] then \[ \int_0^1 xf''(x)\,dx= \]

If \[ \int \frac{\sin\left(x-\frac{\pi}{4}\right)}{2+\sin 2x}\,dx = -\frac{1}{\sqrt2}\tan^{-1}(f(x))+C, \] then \(f(x)=\)

If \(a\) and \(b\) are respectively the order and degree of the differential equation \[ y^2(y'')^2+3x(y')^{1/3}+x^2y^2=\sin x, \] then

Evaluate \[ \int \sqrt{x+\sqrt{x^2+2}}\,dx \]

If \[ \int \frac{x^8+4}{x^4-2x^2+2}\,dx=Ax^5+Bx^3+Cx+K, \] then \(5A+3B+C=\)

Evaluate \[ \int \frac{dx}{(1+\sqrt{x})^{2022}} \]

If an open cylinder of given surface area has maximum volume, then its radius is

If \[ x+y=k,\quad x\gt 0,\quad y\gt 0, \] then \(x^2+y^2\) is minimum, if

Assertion (A): \[ f(x)=|x| \] is differentiable at \(x=a\neq 0\) and continuous but not differentiable at \(x=0\). Reason (R): If a function is differentiable at a point, then it is continuous at that point. But the converse is not true.

Equation of tangent to the curve \[ y=x+\frac{4}{x^2} \] which is parallel to \(x\)-axis is

The normal to the curve \(y=f(x)\) at the point \((3,4)\) makes an angle \(\frac{3\pi}{4}\) with positive \(x\)-axis, then \(f'(3)=\)

The minimum distance of a point on the curve \[ y=x^2-4 \] from the origin is

If \[ \frac{d}{dx}\left(\frac{x^2+1}{(x^2+5)(x^2+9)}\right) = \frac{2x(x^2+1)}{(x^2+5)(x^2+9)} \left[ \frac{1}{f(x)}-\frac{1}{g(x)}-\frac{1}{h(x)} \right], \] then \(2h(x)-f(x)-g(x)=\)

If \[ \lim_{x\to -a}\frac{x^7+a^7}{x+a}=7, \] then \(a=\)