List of top Mathematics Questions asked in AP EAPCET

If \[ 4^x-3^{x-\frac{1}{2}}=3^{x+\frac{1}{2}}-2^{2x-1}, \] then \[ x= \]

If \[ A= \begin{bmatrix} 1 & 0 \\ 2 & 1 \end{bmatrix}, \quad B= \begin{bmatrix} 1 & 3 \\ 0 & 1 \end{bmatrix}, \] then \[ \det(A^4+B^6)= \]

The locus of a point \(z\) satisfying \[ |z|^2=\operatorname{Re}(z) \] is a circle with centre

Let \[ G(x)= \begin{bmatrix} \cos x & -\sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1 \end{bmatrix}. \] If \(x+y=0\), then \(G(x)G(y)=\)

By simplifying \[ i^{18}-3i^7+i^2(1+i^4)(i)^{22} \] we get

The values of \(x\) for which \[ \sin x+i\cos 2x \] and \[ \cos x-i\sin 2x \] are conjugate to each other are

If \[ A= \begin{bmatrix} 3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1 \end{bmatrix}, \] then \(AA^T\) is a

Let \(f:\mathbb{R}-\left\{-\frac{1}{2}\right\}\to \mathbb{R}\) be defined by \[ f(x)=\frac{x-2}{2x+1} \] If \(\alpha,\beta\) satisfy the equation \[ f(f(x))=-x, \] then \[ 4(\alpha^2+\beta^2)= \]

If \(AX=D\) represents the system of simultaneous linear equations \[ x+y+z=6, \] \[ 5x-y+2z=3, \] \[ 2x+y-z=5, \] then \((Adj\,A)D=\)

If \[ f(x)=\log \left(\frac{2x^2-3}{x}+\sqrt{\frac{4x^4-11x^2+9}{|x|}}\right) \] then \(f(x)\) is

\[ \frac{d}{dx}\left[ \lim_{y\to 2} \frac{1}{y-2} \left( \frac{1}{x} - \frac{1}{x+y-2} \right) \right] \]

If \[ 2x-y+c\log|x-2y-4|=k \] is the general solution of \[ \frac{dy}{dx}=\frac{2x-4y-5}{x-2y+2}, \] then \(c=\)

By eliminating the arbitrary constants from \[ y=(a+b)\sin(x-c)-de^{x+e+f}, \] the differential equation obtained is of order

If \(l\) and \(m\) are order and degree of a differential equation of all the straight lines at constant distance of \(P\) units from the origin, then \(lm^2+l^2m=\)

If \[ f(x)=\max\{\sin x,\cos x\} \] and \[ g(x)=\min\{\sin x,\cos x\}, \] then \[ \int_0^{\pi} f(x)\,dx+\int_0^{\pi} g(x)\,dx= \]

If \[ \int \frac{e^{\sqrt{x}}}{\sqrt{x}}(x+\sqrt{x})\,dx = e^{\sqrt{x}}\left[Ax+B\sqrt{x}+C\right]+K, \] then \(A+B+C=\)

If \[ \int \frac{1+\tan x}{\sin 2x}\,dx=A\log \tan x+B\tan x+C, \] then \(4A-2B=\)

Evaluate \[ \int \frac{1+\tan x\tan(x+a)}{\tan x\tan(x+a)}\,dx \]

If \[ I_n=\int_{0}^{\pi/4}\tan^n x\,dx, \] then \[ \frac{1}{I_2+I_4}+\frac{1}{I_3+I_5}+\frac{1}{I_4+I_6} \] is equal to

Evaluate \[ \int_{0}^{\pi/4} e^{\tan^2\theta}\sin^2\theta\tan\theta\,d\theta \]

Evaluate \[ \int_{\pi/4}^{5\pi/4}\left(|\cos t|\sin t+|\sin t|\cos t\right)\,dt \]

The number of those tangents to the curve \[ y^2-2x^3-4y+8=0 \] which pass through the point \((1,2)\) is

If the straight line \[ x\cos\alpha+y\sin\alpha=p \] touches the curve \[ \left(\frac{x}{a}\right)^n+\left(\frac{y}{b}\right)^n=2 \] at the point \((a,b)\) on it and \[ \frac{1}{a^2}+\frac{1}{b^2}=\frac{k}{p^2}, \] then \(k=\)

If \[ f(x)=\int x^2\cos^2x\left(2x\tan^2x-2x-6\tan x\right)\,dx \] and \(f(0)=\pi\), then \(f(x)=\)

Condition that 2 curves \[ y^2=4ax,\qquad xy=c^2 \] cut orthogonally is