List of top Questions asked in AP EAMCET

A balloon carrying some sand of mass \( M \) is moving down with a constant acceleration \( a_0 \). The mass \( m \) of sand to be removed so that the balloon moves up with double the acceleration \( a_0 \) is:
If \( Q(h, k) \) is the inverse point of \( P(1,2) \) with respect to the circle \( x^2 + y^2 - 4x + 1 = 0 \), then \( 2h + k \) is:
The general solution of the differential equation: $$ x \, dy - y \, dx = \sqrt{x^2 + y^2} \, dx. $$ 
If \( \theta \) is the angle between the tangents drawn from the point \( (2,3) \) to the circle \( x^2 + y^2 - 6x + 4y + 12 = 0 \), then \( \theta \) is:
If five-digit numbers are formed from the digits 0, 1, 2, 3, 4 using every digit exactly only once, then the probability that a randomly chosen number from those numbers is divisible by 4 is
At 27°C, the degree of dissociation of HA (weak acid) in 0.5 M of its solution is 1%. The concentrations of H\(_3\)O\(^+\), A\(^-\), and HA at equilibrium (in mol L\(^{-1}\)) are respectively:
If \( \vec{a} = \hat{i} - \hat{j} + \hat{k} \), \( \vec{b} = 2\hat{i} + \hat{j} + \hat{k} \) are two vectors and \( \vec{c} \) is a unit vector lying in the plane of \( \vec{a} \) and \( \vec{b} \), and if \( \vec{c} \) is perpendicular to \( \vec{b} \), then \( \vec{c} \cdot (\hat{i} + 2\hat{k}) = \):
Evaluate: \[ \cosh^{-1} 2 \]
The masses of a solid cylinder and a hollow cylinder are 3.2 kg and 1.6 kg respectively. Both the solid cylinder and hollow cylinder start from rest from the top of an inclined plane and roll down without slipping. If both the cylinders have equal radius and the acceleration of the solid cylinder is \( 4 { ms}^{-2} \), the acceleration of the hollow cylinder is:
In \( \triangle ABC \), evaluate: \[ \frac{r_2 (r_1 + r_3)}{\sqrt{r_1 r_2 + r_2 r_3 + r_3 r_1}}. \]
If the system of equations: $$ a_1 x + b_1 y + c_1 z = 0, \quad a_2 x + b_2 y + c_2 z = 0, \quad a_3 x + b_3 y + c_3 z = 0 $$ has only the trivial solution, then the rank of the matrix:  \[\left[ \begin{array}{ccc} a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3 \end{array} \right] \] is
Evaluate \( \cosh (\log 4) \):
Given the partial fraction decomposition: \[ \frac{4x^2 + 5}{(x - 2)^4} = \frac{A}{(x - 2)} + \frac{B}{(x - 2)^2} + \frac{C}{(x - 2)^3} + \frac{D}{(x - 2)^4} \] then the value of \[ \sqrt{\frac{A}{C} + \frac{B}{C} + \frac{D}{C}} \] is:
The range of the real-valued function \( f(x) = \sin^{-1} \left( \frac{1 + x^2}{2x} \right) + \cos^{-1} \left( \frac{2x}{1 + x^2} \right) \) is:
In a triangle ABC, if \( r : R = 1 : 3 : 7 \), then \( \sin(A + C) + \sin B = \)
2.644 g of metal (M) was deposited when 8040 coulombs of electricity was passed through molten MF\(_2\) salt. What is the atomic mass of M? (F = 96500 C mol\(^{-1}\))
The set of all values of \(k\) for which the inequality \(x^2 - (3k+1)x + 4k^2 + 3k - 3>0\) is true for all real values of \(x\) is
If \(\sec \theta + \tan \theta = \frac{1}{3}\), then the quadrant in which \(2\theta\) lies is:
In a triangle ABC, if \( r_1 = 2r_2 = 3r_3 \), then \(\sin A\): \(\sin B\): \(\sin C\) = Options:
Among the 4-digit numbers formed using the digits \( 0, 1, 2, 3, 4 \) when repetition of digits is allowed, the number of numbers which are divisible by 4 is:
At 300 K, \( \Delta_r G^\circ \) for the reaction \( A(g) \rightleftharpoons B(g) \) is \( -11.5 \) kJ mol\(^{-1}\). The equilibrium constant at 300 K is approximately: \((R = 8.314 \text{ J mol}^{-1} \text{ K}^{-1})\)
A slab consists of two identical plates of copper and brass. The free face of the brass is at \( 0^\circ C \) and that of copper at \( 100^\circ C \). If the thermal conductivities of brass and copper are in the ratio \( 1:4 \), then the temperature of the interface is:

If

 
and \( AA^T = I \), then \( \frac{a}{b} + \frac{b}{a} = \):

125 identical charged small spheres coalesce to form a big charged sphere. If the electric potential on each small sphere is 60 mV, then the electric potential on the bigger sphere formed is:
In a region, the electric field is \( (30\hat{i} + 40\hat{j}) \) NC\(^{-1}\). If the electric potential at the origin is zero, the electric potential at the point (1 m, 2 m) is