List of top Questions asked in AP EAMCET

If the roots of the equation \(x^3 + ax^2 + bx + c = 0\) are in arithmetic progression, then:
If \( z = x+iy \), \( x^2+y^2 = 1 \) and \( z_1 = e^{i\theta} \), then the expression \( \frac{z_1^{2n-1} - 1}{z_1^{2^n-1} + 1} \) simplifies to:
If \( \frac{3 - 2i \sin \theta}{1 + 2i \sin \theta}\) is a purely imaginary number, then \( \theta \) is:
If \( z_1 = 10 + 6i \), \( z_2 = 4 + 6i \) and \( z \) is any complex number such that the argument of \( \frac{z-z_1}{z-z_2} \) is \( \frac{\pi}{4} \), then the value of \( |z - 7 - 9i| \) is:
If \( A = [a_{ij}]\) where \( 1 \leq i, j \leq n \) with \( n \geq 2 \) and \( a_{ij} = i + j \) is a matrix, then the rank of \( A \) is:
Let \( A, B, C, D, \) and \( E \) be \( n \times n \) matrices, each with non-zero determinant. If \( ABCDE = I \), then \( C^{-1} \) is:
If \(2.4^{2n+1} + 3^{3n+1}\) is divisible by \(k\) for all \(n \in \mathbb{N}\), then \(k\) is:
The domain of the real valued function \( f(x) = \sqrt{2 + x} + \sqrt{3 - x} \) is:
Let \( f: \mathbb{R} \rightarrow \mathbb{R} \) be defined by \( f(x + y) = f(x) + 12y \), for all \( x, y \in \mathbb{R} \). If \( f(1) = 6 \), then the value of \( \sum_{r=1}^n f(r) \) is:
When 100 J of heat is supplied to a gas, the increase in the internal energy of the gas is 60 J. Then the gas is/can

What are X and Y respectively in the following reaction sequence? 

Identify the amino acid which has: 

The correct sequence of reactions involved in the following conversion is: 

Given the function:

\[ f(x) = \begin{cases} \frac{(2x^2 - ax +1) - (ax^2 + 3bx + 2)}{x+1}, & \text{if } x \neq -1 \\ k, & \text{if } x = -1 \end{cases} \]

If \( a, b, k \in \mathbb{R} \) and \( f(x) \) is continuous for all \( x \), then the value of \( k \) is:

Given the function:

\[ f(x) = \begin{cases} \frac{2x e^{1/2x} - 3x e^{-1/2x}}{e^{1/2x} + 4e^{-1/2x}}, & \text{if } x \neq 0 \\ 0, & \text{if } x = 0 \end{cases} \]

Determine the differentiability of \( f(x) \) at \( x = 0 \).

A magnet suspended in a uniform magnetic field is heated so as to reduce its magnetic moment by 19%. By doing this, the time period of the magnet approximately

A Carnot heat engine has an efficiency of 10%. If the same engine is worked backward to obtain a refrigerator, then the coefficient of performance of the refrigerator is

Match the following physical quantities with their respective dimensional formulas.

An object is projected such that it has to attain maximum range, while another body is projected to reach maximum height. If both objects reached the same maximum height, then find the ratio of their initial velocities.

Three blocks of masses 2 m, 4 m and 6 m are placed as shown in figure. If \( \sin 37^\circ = \frac{3}{5} \), \( \sin 53^\circ = \frac{4}{5} \), the acceleration of the system is:

For a particle executing simple harmonic motion, match the following statements (conditions) from column I to statements (shapes of graph) in column II.

In a Carnot engine, the absolute temperature of the source is 25% more than the absolute temperature of the sink. The efficiency of the engine is

In a potentiometer, the area of cross-section of the wire is 4 cm\(^2\), the current flowing in the circuit is 1 A, and the potential gradient is 7.5 Vm\(^{-1}\). Then the resistivity of the potentiometer wire is

A current-carrying coil experiences a torque due to a magnetic field. The value of the torque is 80% of the maximum possible torque. The angle between the magnetic field and the normal to the plane of the coil is

If the current through an inductor increases from 2 A to 3 A, the magnetic energy stored in the inductor increases by