List of top Questions asked in AP EAPCET

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
If \(A = \begin{bmatrix}x & 2 & 1 \\ 2 & x & 1 \\ 2 & 1 & 0\end{bmatrix}\) and \(\det(A) = 125\), then \(x =\)
In a triangle \( ABC \), if \( a : b : c = 4 : 5 : 6 \), the ratio of radius of the circumcircle to that of the incircle 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:
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:
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
A light from Paschen series of hydrogen atom is able to eject photoelectrons from a metal. Then the work function of the metal 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 major product formed from the following:
the major product formed from the following
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
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 hydrogen atom is excited to \( n = 4 \). Find the potential energy of the electron in excited state.
Identify the ortho and para directing groups towards aromatic electrophilic substitution reactions from the following list: -OH, -CN, COOH, -OCH3, -NHCOCH3, -CHO
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
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 $
Find the least distance from the point $ (10, 7) $ to the circle: $$ x^2 + y^2 - 4x - 2y - 20 = 0 $$
In a triangle ABC, let \(\angle C = \pi/2\). If r and R are respectively inradius and circumradius of ABC, then R + r =
\( \int_{a-1}^{a} \frac{e^x(a-x)}{(x-a+1)^2} dx = \)
If \( A = \begin{bmatrix} x & 0 \\ 1 & 1 \end{bmatrix} \) and \( B = \begin{bmatrix} 8 & 0 \\7 & 1 \end{bmatrix} \), and \( A^3 = B \), then \( x = \) ?
Suppose a point \( P \) moves such that: \[ BP^2 - AP^2 = 121 \] where \( A = (2, 5) \), \( B = (5, 11) \). Then the locus of \( P \) is a straight line. What is the slope of this line?
Find the distance between the point \( (6, 4\sqrt{3}) \) and the focus of the parabola \( y^2 = 8x \)
A ray makes angles \( \alpha, 2\alpha, 3\alpha \) with the coordinate axes OX, OY, OZ respectively. Then possible values of \( \alpha \) are:
Find the false statement for ideal gases:
In a triangle ABC, if $a \ne b$, then \[ \frac{a\cos A - b\cos B}{a\cos B - b\cos A} + \cos C = ? \]