List of top Mathematics Questions asked in AP EAPCET

If \(a,b,c\) are respectively the \(5^{th}, 8^{th}, 13^{th}\) terms of an arithmetic progression, then \[ \begin{vmatrix} a & 5 & 1\\ b & 8 & 1\\ c & 13 & 1 \end{vmatrix} = \]

Let \[ A= \begin{bmatrix} -2 & x & 1\\ x & 1 & 1\\ 2 & 3 & -1 \end{bmatrix} \] If the roots of the equation \[ \det(A)=0 \] are \(l,m\), then \[ l^3-m^3= \]

If \[ A=\begin{bmatrix} 2 & -3\\ -4 & 1 \end{bmatrix}, \] then \[ (A^T)^2+(12A)^T= \]

The set \[ \left\{x \in \mathbb{R} \,/\, \frac{\sqrt{|x|^2-2|x|-8}} {\log(2-x-x^2)} \text{ is a real number} \right\} \] is equal to:

The domain of the real valued function \[ f(x)=\sin\left(\log\left(\frac{\sqrt{4-x^2}}{1-x}\right)\right) \] is:

If the solution of \(\dfrac{dy}{dx}=\dfrac{y^3\cos\sqrt{x}}{\sqrt{x}e^{1/y^2}}\), \(y(0)=1\), is \(\dfrac{1}{y^2}=\log_e(f(x))\), then \(f(x)=\)

Suppose that \(f(x,y)\) and \(g(x,y)\) are homogeneous functions of same order. If \(x=Vy\) reduces the equation \(\dfrac{dy}{dx}=\dfrac{f(x,y)}{g(x,y)}\) to the form \(\dfrac{dV}{dy}=\dfrac{1}{y}(F(V))\), then \(F(V)=\)

The general solution of \(xdy-ydx=xy\,dy\) is

\(\displaystyle \int_{-1}^{2}\left[\tan^{-1}\left(\frac{x}{x^2+1}\right)+\tan^{-1}\left(\frac{x^2+1}{x}\right)\right]dx=\)

\(\displaystyle \int_{-\pi/2}^{2\pi}\sin^{-1}(\sin x)\,dx=\)

If \(\displaystyle \int_{9}^{x}\frac{f(y)}{y^2}\,dy=2\sqrt{x}-6\), then \(f(x)=\)

\(\displaystyle \int \left(\sqrt{x+\sqrt{12x-36}}+\sqrt{x-\sqrt{12x-36}}\right)\,dx=\)

If \(\displaystyle \int \frac{x\,dx}{\sqrt[15]{(1+x^2)^{12}(2+x^2)^{18}}}=\alpha\left(\frac{1+x^2}{2+x^2}\right)^{1/n}+C\), then \(\dfrac{n}{\alpha}=\)

\(\displaystyle \int (\log x)^2 x^3\,dx=\dfrac{x^4}{32}f(x)+C \Rightarrow f(x)=\)

\(\displaystyle \int_{0}^{\infty}\left(x^{12}+x^{-12}\right)\frac{\log x}{x}\,dx=\)

If \(\displaystyle \int \frac{3e^x-7e^{-x}}{7e^x+3e^{-x}}\,dx=Kx+L\log\left(e^{-2x}+\frac{7}{3}\right)+C\), then \(K+L=\)

If the angle between the curves \(y^2=4x\) and \(y=e^{-x/2}\) is \(\theta\), then \(\cosec^2\left(\dfrac{\theta}{2}\right)\) is

The least intercept made by a tangent to the ellipse \(\dfrac{x^2}{64}+\dfrac{y^2}{49}=1\) with coordinate axes is

If \(0<x<\dfrac{\pi}{2}\), then

If \(f(x)=\sqrt{3\sin x-\cos x-2ax+b}\) decreases for all values of \(x\), then

If \[ y=\frac{\log x}{x}, \] then \[ \frac{d^2y}{dx^2} at x=1 = \]

If \[ y=\sin\left(2\tan^{-1}\sqrt{\frac{1-x}{1+x}}\right), \quad x=\cos 2\theta, \] then \[ \frac{dy}{dx}= \]

If \[ f(x)=|x^2-3x+2|, \] then \[ \frac{df}{dx}= \]

Let \[ f(x)=\lim_{y\to\infty} y\left(x^{1/y}-1\right), \] and \[ 2022\,f\left(\frac{1}{x}\right)+P\,f(x)=f(x^2), \] then \(P=\)

The angle made by the tangent at \(\theta=\dfrac{\pi}{3}\) on the curve \(x=a(\theta+\sin\theta)\), \(y=a(1-\cos\theta)\) with \(x\)-axis is