List of top Questions asked in AP EAPCET

When a ball is dropped from a height it takes \(t\) sec to reach the ground. If the same experiment is done on a different planet having mass \(100\) times the earth's mass and radius \(10\) times the earth's radius, then the time it will take to cover the same height in the new planet 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:

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:

The dot product of unit vectors \(\hat{n}_1\) and \(\hat{n}_2\) that are parallel to \[ 5\hat{i}+12\hat{j} \] and \[ 3\hat{i}+4\hat{j} \] respectively is:

A sphere rolls down from the top of an inclined plane which makes an angle \(30^\circ\) with the horizontal roof. If the highest and lowest points of the inclined plane are \(8.75\,\text{m}\) and \(3.75\,\text{m}\) respectively from the ground, then the horizontal distance from the lower edge of the roof at which the sphere hits the ground is \((g=10\,\text{m/s}^2)\):

\([\,.\,]\) 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:

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:

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

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

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

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:

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

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

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

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

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:

\(f:\mathbb{R}\to\mathbb{R}\) 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:

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: