List of top Questions asked in AP EAMCET

For \( a \in \mathbb{R} \setminus \{0\} \), if \( a \cos x + a \sin x + a = 2K + 1 \) has a solution, then \( K \) lies in the interval:
The equation \( x^4 - x^3 - 6x^2 + 4x + 8 = 0 \) has two equal roots. If \( \alpha, \beta \) are the other two roots of this equation, then \( \alpha^2 + \beta^2 = \):
If \( m, n \) are respectively the least positive and greatest negative integer values of such that \( (\frac{1-i}{1+i})^k = -i\), then \( m - n = \):
A block of mass 100 g is attached to the end of a string of unknown material of 50 cm long and cross-sectional area of \(2 \, {cm}^2\). When the block is whirled horizontally at a constant angular speed of 40 m/s, it moves along a circular path of radius 52 cm. Young's modulus of the material is:

A metal rod of 50 cm length is clamped at its midpoint and is set to vibrations. The density of that metal is \( 2 \times 10^3 \, {kg/m}^3 \).
Young's modulus of that metal is \( 8 \times 10^8 \, {Nm}^2 \). The fundamental frequency of the vibration is 
 

The element which is important in determining solute concentration and oxygen evolution:
Evaluate the integral \[ \int_{0}^{\frac{\pi}{4}} \frac{x^2}{(x \sin x + \cos x)^2} dx. \]
If the plane \[ x - y + z + 4 = 0 \] divides the line joining the points \[ P(2,3,-1) \quad {and} \quad Q(1,4,-2) \] in the ratio \( l:m \), then \( l + m \) is:
Let \( \vec{a} \times \vec{b} = 7\hat{i} - 5\hat{j} - 4\hat{k} \) and \( \vec{a} = \hat{i} + 3\hat{j} - 2\hat{k} \), if the length of projection of \( \vec{b} \) on \( \vec{a} \) is \( \frac{8}{\sqrt{14}} \), then \( |\vec{b}| \) is:
Two masses \( m_1 \) and \( m_2 \) are connected by a light string passing over a smooth pulley. When set free, \( m_1 \) moves downwards by 3 m in 3 s. The ratio of \( \frac{m_1}{m_2} \) is \((g = 10 \text{ m/s}^2)\).
A wheel of angular speed 600 rev/min is made to slow down at a rate of \( 2 \) rad/s\(^2\). The number of revolutions made by the wheel before coming to rest is

A hydrogen atom falls from nth higher energy orbit to first energy orbit (n = 1). 

The energy released is equal to 12.75 eV. The nth orbit is

The longest wavelength of light that can initiate photo electric effect in the metal of work function 9 eV is
An electromagnetic wave travels in a medium with a speed of \( 2 \times 10^8 \, \text{ms}^{-1} \). The relative permeability of the medium is 1. Then the relative permittivity is.
Magnetic field at a distance \(r\) from z axis is \( B = B_0 r \, \text{kt} \) present in the region. \( B_0 \) is constant and \(t\) is time. The magnitude of induced electric field at a distance \(r\) from z-axis is.
Which of the following hormones is responsible for preparing the uterus for implantation of a fertilized egg?
If \( (a, b) \) is the stationary point of the curve \( y = 2x - x^2 \), then the area bounded by the curves \( y = 2x - x^2 \), \( y = x^2 - 2x \), and \( x = a \) is:
Evaluate \( \int_{1}^{2} \frac{x^4 - 1}{x^6 - 1} dx \):
A body falling freely under gravity from rest from a certain height reaches the ground in \(5\) seconds. The distance travelled by the body in the last two seconds of its motion is:
100 mL of 0.1 M HA (weak acid) and 100 mL of 0.2 M NaA are mixed. What is the pH of the resultant solution? \((K_a \text{ of HA is } 10^{-5}, \log 2 = 0.3)\)
The real values of \( x \) that satisfy the equation \[ \tan^{-1}x + \tan^{-1}2x = \frac{\pi}{4} \] is:

Choose the incorrect statement related to life cycles: 
I. Sporophyte generation is represented by a single-celled zygote. 
II. Gametophyte is multicellular in Pteridophytes and Gymnosperms. 
III. Life cycle is diphlaplontic in Bryophytes. 
IV. Life cycle is haplodiplontic in Pteridophytes.

If a committee of 10 members is to be formed from 8 men and 6 women, then the number of different possible committees in which the men are in majority is:
10 g of a metal (M) reacts with oxygen to form 11.6 g of oxide. What is the equivalent weight of \( M \)?
The rms velocity (\( u_{\text{rms}} \)), mean velocity (\( u_{\text{av}} \)), and most probable velocity (\( u_{\text{mp}} \)) of a gas differ from each other at a given temperature. Which of the following ratios regarding them is correct?