List of top Mathematics Questions asked in AP EAPCET

By multiplying with \[ e^{\int Pdx} \] on both sides of the equation \[ \frac{dy}{dx}+P(x)y=Q(x), \] the left side of the equation turns in the form \[ \frac{d}{dx}\left(yf(x)\right), \] then \[ f(x)= \] is:

If the slope of the tangent at a point \((x,y)\) on a curve is \[ \frac{y-4}{x-3} \] and the curve passes through \((4,3)\), then the point where it cuts the line \[ y=x \] is:

Evaluate \[ \int_{-\pi}^{\pi}\frac{2x(1+\sin x)}{1+\cos^2x}\,dx \] is:

Evaluate \[ \int_{-1}^{1}\frac{\sin x-x^2}{3-|x|}\,dx = \]

The integrating factor of the linear differential equation \[ \frac{dy}{dx}+P(x)y=Q(x) \] is a solution of the differential equation:

\([\,.\,]\) represents a greatest integer function. If \[ \int_{\sqrt{3}}^{\sqrt{18}}[x]\,dx=a+b\sqrt{2}+c\sqrt{3}, \] then \[ a+b+c= \] is:

Evaluate \[ \int_{0}^{4}\frac{x+2}{\sqrt{4x-x^2}}\,dx \] is:

There exists \(\theta\) such that \[ a\gt |\sec\theta|, \] then \[ \int \frac{dx}{1+a\cos x} = \] is:

Evaluate \[ \int \frac{x^2}{x^3\sqrt{x^2-1}}\,dx = \]

If the line \[ ax+by+c=0 \] is a normal to the curve \[ xy=1, \] then:

If \(a,b,c,d\neq 0\) and \[ f\left(\frac{at+b}{ct+d}\right)=t, \] then \[ \int f(x)\,dx= \] is:

In the interval \[ (7,\infty), \] the function \[ f(x)=|x-5|+2|x-7| \] is:

Let \[ f(x)=\int \frac{e^{3x}}{4+8e^{2x}+e^{4x}}\,dx \] and \[ g(x)=\int \frac{2\,dx}{e^{3x}+8e^x+4e^{-x}}, \] then \[ f(x)-g(x)= \] is:

\(f:\mathbb{R}\to\mathbb{R}\) is a function such that \[ |f(x)-f(y)|\leq \frac{1}{2}|x-y| \quad \forall x,y\in \mathbb{R} \] and \[ f'(x)\geq \frac{1}{2}\quad \forall x\in \mathbb{R},\quad f(1)=\frac{1}{2} \] Then the number of points of intersection of the curve \(y=f(x)\) and the curve \[ y=x^2-2x-5 \] is:

If \[ \frac{d^n y}{dx^n}=y_n \] and \[ y=e^{\sqrt{x}}+e^{-\sqrt{x}}, \] then \[ 4xy_2+2y_1= \]

The area of the triangle formed by the tangent to the curve \[ xy=a^2 \] at \((x_1,y_1)\) on it and the axes is

If the slope of the line through \((0,0)\) which is tangent to the curve \[ y=x^2+x+16 \] is \(m\), then the value of \[ m-4 \] is:

If the two curves \[ y=a^x \] and \[ y=b^x \] intersect at angle \(\alpha\), then \[ \tan\alpha= \] is:

Evaluate \[ \lim_{n\to\infty}\sqrt{2} \left[ \frac{(2+\sqrt{2})^n+(2-\sqrt{2})^n} {(2+\sqrt{2})^n-(2-\sqrt{2})^n} \right] \]

If \(a\gt 0\), \([\,]\) denotes greatest integer function and \[ \lim_{x\to a} \left( \frac{[x]^3}{a}-\left[\frac{x}{a}\right]^3 \right)=k, \] \[ \lim_{x\to a} \left( \frac{[x]^5}{a}-\left[\frac{x}{a}\right]^3 \right)=l, \] then

Evaluate \[ \lim_{n\to\infty}\frac{A+e^{nx}}{x+Ae^{nx}} \]

If \[ -2,\ \frac{4}{3},\ -\frac{4}{5} \] are the intercepts made by a plane on \(X,Y,Z\)-axes respectively, then the direction cosines of a normal to this plane are:

If \[ f(x)= \begin{cases} \dfrac{1-\sin^3 x}{3\cos^2 x}, & x\lt \dfrac{\pi}{2} \\[6pt] \alpha, & x=\dfrac{\pi}{2} \\[6pt] \dfrac{\beta(1-\sin x)}{(\pi-2x)^2}, & x\gt \dfrac{\pi}{2} \end{cases} \] is continuous at \(x=\dfrac{\pi}{2}\), then \(\alpha\beta=\)

If the centroid of triangle whose vertices are \[ (a,1,3),\ (-2,b,-5)\ \text{and}\ (4,7,c) \] be the origin, then \[ a^2+b^2+c^2= \] is:

If \(\alpha,2\alpha,3\alpha\) are angles made by a ray with \(OX\), \(OY\), \(OZ\) axes respectively, then all the possible values of \(\alpha\) are: