List of top Questions asked in AP EAPCET

In quadrilateral ABCD, $\vec{AB} = \vec{a},\ \vec{BC} = \vec{b},\ \vec{DA} = \vec{a} - \vec{b}$. M is midpoint of BC and X lies on DM such that $\vec{DX} = \dfrac{4}{5}\vec{DM}$. Then the points A, X and C:
In a triangle \( ABC \), if \( a : b : c = 4 : 5 : 6 \), the ratio of radius of the circumcircle to that of the incircle is:
Which of the following compounds do not have sp$^3$ carbon atom(s)?
I. Acetone\quad II. Acetic acid\quad III. Buta-1,3-diene\quad IV. Propyne\quad V. Naphthalene
Identify the ortho and para directing groups towards aromatic electrophilic substitution reactions from the following list: -OH, -CN, COOH, -OCH3, -NHCOCH3, -CHO
If $(1 + \tan1^\circ)(1 + \tan2^\circ)\dots(1 + \tan45^\circ) = 2^n$, then $n =$ ?
An iron block A of volume \( 0.25\ \text{m}^3 \) stretches a spring by 0.2 m. A new block B of volume \( 0.75\ \text{m}^3 \) is kept on a frictionless incline (30°) using same spring. Find equilibrium distance along incline.
An iron block A of volume 0.25 m3
A stick of length $r$ units slides with its ends on coordinate axes. Then the locus of the midpoint of the stick is a curve whose length is
For $\alpha \in \left[0, \dfrac{\pi}{2} \right]$, the angle between the lines represented by
$[x \cos\theta - y] \left[ (\cos\theta + \tan\alpha)x - (1 - \cos\theta \tan\alpha)y \right] = 0$ is
The straight line passing through \( (0, 0) \) and the foot of the perpendicular from \( (2, 4) \) onto the line \( x + y - 1 = 0 \) is:
If the point \( P(\sin\alpha, \cos\alpha) \) lies inside the triangle formed by the vertices \( (0, 0), \left(\frac{\sqrt{3}}{2}, 0\right), (0, \frac{\sqrt{3}}{2}) \), then \( \alpha \) lies in the interval:
The ratio of the largest and shortest distances from the point $(2, -7)$ to the circle $x^2 + y^2 - 14x - 10y - 151 = 0$ is
Find the least distance from the point $ (10, 7) $ to the circle: $$ x^2 + y^2 - 4x - 2y - 20 = 0 $$
A bulb of power 660 W radiates uniformly in all directions. The pressure exerted by the radiation on the surface at a distance of 5 m is
\( \int_{a-1}^{a} \frac{e^x(a-x)}{(x-a+1)^2} dx = \)
A block of mass \(5\,\text{kg}\) starts up a \(45^\circ\) incline with an initial kinetic energy of \(100\,\text{J}\). The coefficient of friction is \(0.5\). The distance it travels before coming to rest is:
In a triangle ABC, let \(\angle C = \pi/2\). If r and R are respectively inradius and circumradius of ABC, then R + r =
A hydrogen atom is excited to \( n = 4 \). Find the potential energy of the electron in excited state.
Given: $$ \frac{2x^2 + 1}{x^3 - 1} = \frac{A}{x - 1} + \frac{Bx + C}{x^2 + x + 1} $$ Find the value of $ 7A + 2B + C $
A light from Paschen series of hydrogen atom is able to eject photoelectrons from a metal. Then the work function of the metal is
Identify the major product formed from the following:
the major product formed from the following
The rms speed of oxygen at room temperature is about \(500 \, \text{m/s}\). The rms speed of hydrogen at the same temperature is about
x% (w/v) solution of urea is isotonic with 4% (w/v) solution of non-volatile solute of molar mass 120 g mol-1. The value of x is
Let \( A = \begin{bmatrix} n & 0 & 0 \\ 0 & n & 0 \\ 0 & 0 & n \end{bmatrix} \) and \( B = \begin{bmatrix} 0 & 0 & n \\ 0 & n & 0 \\ n & 0 & 0 \end{bmatrix} \). Then \( A^2 + B^2 + AB = \)
Find the distance between the point \( (6, 4\sqrt{3}) \) and the focus of the parabola \( y^2 = 8x \)
If $\displaystyle \lim_{x \to 0} \dfrac{|x|}{\sqrt{x^4 + 4x^2 + 5}} = k$, $\displaystyle \lim_{x \to 0} x^4 \sin\left(\dfrac{1}{3\sqrt{x}}\right) = l$, Then $k + l = $