List of top Mathematics Questions asked in AP EAPCET

If the rank of the matrix \[ A= \begin{bmatrix} 1 & 2 & 1 & -1 \\ -1 & 2 & 3 & 5 \\ 0 & 1 & k & k \end{bmatrix} \] is \(2\) and \(k\) is a real number, then \(k\) is a root of the following quadratic equation:

If \(b\) and \(c\) are non-zero real numbers, \[ A= \begin{bmatrix} 1 & b & c\\ b & 2 & 3\\ c & 3 & 4 \end{bmatrix} \quad \text{and} \quad B= \begin{bmatrix} 0 & b & c\\ -b & 0 & 2\\ -c & -2 & 0 \end{bmatrix}, \] then \(\det(A+B)=\)

Evaluate \[ \sum_{k=1}^{6}\sin\left(\frac{2\pi k}{7}\right) -i\cos\left(\frac{2\pi k}{7}\right) \]

The range of the real valued function \(f(x)=\dfrac{x^2+x+1}{x}\) is

If a function \(f:\mathbb{R}-\{l\}\to \mathbb{R}-\{m\}\) defined by \[ f(x)=\frac{x+3}{x-2} \] is a bijection, then \(3l+2m=\)

Assertion (A): Order of the differential equations of a family of circles with constant radius is two.
Reason (R): An algebraic equation having two arbitrary constants is general solution of a \(2^{\text{nd}}\) order differential equation.

Let \(T\gt 0\) be a fixed number. If \(f:\mathbb{R}\to\mathbb{R}\) is a continuous function such that \[ f(x+T)=f(x),\qquad x\in \mathbb{R}. \] If \[ I=\int_0^T f(x)\,dx, \] then \[ \int_0^{5T} f(2x)\,dx= \]

The general solution of the differential equation \[ \frac{dy}{dx}=\cos^2(3x+y) \] is \[ \tan^{-1}\left(\frac{\sqrt{3}}{2}\tan(3x+y)\right)=f(x). \] Then \(f(x)=\)

If \[ \int_1^3 x\sqrt[n]{x^2-1}\,dx=6, \] then \(n=\)

If \([\,\,]\) represents greatest integer function, then \[ \int_{-1}^{1}\left(x[1+\sin \pi x]+1\right)dx= \]

If \[ \lim_{n\to\infty} \left[ \frac{n}{(n+1)\sqrt{2n+1}} + \frac{n}{(n+2)\sqrt{2(2n+2)}} + \frac{n}{(n+3)\sqrt{3(2n+3)}} +\cdots+n\ \text{terms} \right] = \int_0^1 f(x)\,dx, \] then \(f(x)=\)

If the general solution of the differential equation \[ \cos^2x\frac{dy}{dx}+y=\tan x \] is \[ y=\tan x-1+Ce^{-\tan x} \] and it satisfies \[ y\left(\frac{\pi}{4}\right)=1, \] then \(C=\)

Evaluate \[ \int \frac{e^{\tan^{-1}x}}{1+x^2} \left[ \left(\sec^{-1}\sqrt{1+x^2}\right)^2+ \cos^{-1}\left(\frac{1-x^2}{1+x^2}\right) \right]dx \]

Evaluate \[ \int \frac{dx}{(x-3)^{4/5}(x+1)^{6/5}} \]

If \[ \int \frac{3x+4}{x^3-2x+4}\,dx=\log f(x)+C, \] then \(f(3)=\)

If \(a,b\gt 0\), then minimum value of \[ y=\frac{b^2}{a-x}+\frac{a^2}{x}, \qquad 0\lt x\lt a \] is

The point on the curve \[ y=x^2+4x+3 \] which is closest to the line \[ y=3x+2 \] is

If \[ y=x^3-ax^2+48x+7 \] is an increasing function for all real values of \(x\), then \(a\) lies in the interval

If \[ I_n=\int(\cos^n x+\sin^n x)\,dx \] and \[ I_n-\frac{n-1}{n}I_{n-2} = \frac{\sin x\cos x}{n}f(x), \] then \(f(x)=\)

If \[ x=f(\theta) \] and \[ y=g(\theta), \] then \[ \frac{d^2y}{dx^2}= \]

Assertion (A): \[ \frac{d}{dx}\left(\frac{x^2\sin x}{\log x}\right) = \frac{x^2\sin x}{\log x} \left(\cot x+\frac{2}{x}-\frac{1}{x\log x}\right) \] Reason (R): \[ \frac{d}{dx}\left(\frac{uv}{w}\right) = \frac{uv}{w} \left[ \frac{u'}{u}+\frac{v'}{v}-\frac{w'}{w} \right] \]

Evaluate \[ \lim_{x\to 0}\frac{3|x|-x}{|x|-2x} - \lim_{x\to 0}\frac{\log(1+x^3)}{\sin^3 x} \]

If the normal drawn at a point \(P\) on the curve \[ 3y=6x-5x^3 \] passes through \((0,0)\), then the positive integral value of the abscissa of the point \(P\) is

The line joining the points \((0,3)\) and \((5,-2)\) is a tangent to the curve \[ y=\frac{C}{x+1} \] then \(C=\)

If \[ 3f(\cos x)+2f(\sin x)=5x, \] then \[ f'(\cos x)+f'(\sin x)= \]