List of top Mathematics Questions asked in AP EAPCET

If \[ A=\begin{bmatrix} x & 2 & 1\\ 2 & x & 1\\ 2 & 1 & 0 \end{bmatrix} \] and \(\det(A^3)=125\), then \(x=\)

Let \(z\) and \(w\) be two complex numbers such that \[ \overline{z}+i\overline{w}=0 \] and \[ \operatorname{Arg}(zw)=\pi. \] Then \(\operatorname{Arg}(z)=\)

Let \[ A=\begin{bmatrix} 1 & 2\\ -2 & 1 \end{bmatrix} \] and \[ B^{-1}=\begin{bmatrix} 1 & 1\\ 0 & 2 \end{bmatrix} \] If \[ (AB^{-1})^{-1}=\begin{bmatrix} a & b\\ c & d \end{bmatrix}, \] then \(2b+5c+10d=\)

The domain of the real valued function \[ f(x)=\frac{\sqrt{\log_{0.5}(x-3)}}{\sqrt{x-1}} \] is

If a function \(f\) satisfies \(f(x+1)+f(x-1)=\sqrt{2}f(x)\), then \(f(x+2)+f(x-2)=\)

If \[ \cos\frac{y}{x}=A\log x+C \] is the general solution of \[ \left(x\sin\frac{y}{x}\right)dy=\left(y\sin\frac{y}{x}-x\right)dx, \] then \(A=\)

Every curve represented by the general solution of \[ \frac{dy}{dx}-\frac{x\log x}{y^3e^{y^2-5}}=0 \] cuts every curve represented by the general solution of \[ \frac{dy}{dx}+\frac{y^3e^{y^2-5}}{x\log x}=0 \] at angle \(\theta\). Then \[ 4\theta-\frac{\pi}{2}= \]

If \(f\) is a continuous function and \(f(x+T)=f(x), \forall x\in R\), it is given that \[ \int_0^{NT} f(t)\,dt=N\int_0^T f(t)\,dt \] \((N\) is a natural number). Then \[ \int_0^{50\pi}\sqrt{1-\cos 2x}\,dx= \]

\(a,b,c,d\) are real numbers. The general solution of \[ \frac{dy}{dx}=\frac{ax+b}{cy+d} \] represents a family of straight lines, when

Assertion (A): \[ \int_{2}^{e}\left(\frac{1}{\log_e x}-\frac{1}{(\log_e x)^2}\right)\,dx = e-2\log_2 e \] Reason (R): \[ \int_{a}^{b} e^x\left(f(x)+f'(x)\right)\,dx = e^bf(b)-e^af(a) \]

If \[ \int_0^\pi \frac{dx}{1+2\sin^2x}=k, \] then greatest integer less than or equal to \(k\) is

Evaluate \[ \int_0^{\pi^2/4}\left(2\sin\sqrt{x}+\sqrt{x}\cos\sqrt{x}\right)\,dx \]

Evaluate \[ \int \frac{2\cos x+1}{(2+\cos x)^2}\,dx-\frac{\sin x}{2+\cos x} \]

If \[ \int \frac{1}{\cos 4x \cos 2x}\,dx = \frac{1}{4\sqrt{2}}\log\left|\frac{1+f(x)}{1-f(x)}\right| -\frac{1}{2}\log g(x)+C, \] then \[ g\left(\frac{\pi}{6}\right)-\sqrt{2}f\left(\frac{\pi}{6}\right)= \]

Evaluate \[ \int \sqrt{1+2\cot x(\cot x+\cosec x)}\,dx \]

Evaluate \[ \int \frac{\cos^4x}{\left(\sin^2x+\sin^{-3}x\cos^5x\right)^3}\,dx \]

For a particle moving on a straight line, it is observed that the distance \(S\) at time \(t\) is given by \[ S=6t-\frac{t^3}{2} \] The maximum velocity during the motion is

\(a,b,c,d,e,f,g,h\) are distinct elements in the set \[ \{-7,-5,-3,-2,2,4,6,13\} \] The minimum value of \[ (a+b+c+d)^2+(e+f+g+h)^2 \] is

Let \[ f(x)= \begin{cases} |x|, & -\infty\lt x\lt 2 \\ |2x-4|, & 2\leq x\leq 20 \end{cases} \] \(x=a\) is a point where \(f(x)\) is continuous but not differentiable and \(x=b\) is a point where \(f(x)\) is not differentiable \((a\neq b)\). Then \(a+b=\)

The normal to the curve \[ x=a(1+\cos\theta), \quad y=a\sin\theta \] at \(\theta\) always passes through a fixed point, then the fixed point is

The angle between the tangents drawn at \((0,0)\) to the curves \[ y^3-x^2y+5y-2x=0 \] and \[ x^4-x^3y^2+5x+2y=0 \] is

If \[ x\sin(\alpha+y)=\sin y \] and \[ y=\frac{m}{x^2+2nx+1}, \] then \(m^2=\)

Two sides of a triangle are given. If the area of the triangle is maximum, then the angle between the given sides is

\([\,]\) represents the greatest integer function. At \(x=-1\), \[ \frac{d}{dx}\sin \pi [x] \] is

If \(n\gt 0\) and \[ \lim_{x\to 0}\frac{((a-n)nx-\tan x)\sin nx}{x^2}=0, \] then minimum value of \(a\) is