List of top Questions asked in TS EAMCET

For \( n \in \mathbb{N} \), the largest positive integer that divides \( 81^n + 20n - 1 \) is \( k \). If \( S \) is the sum of all positive divisors of \( k \), then find \( S - k \).

The question asks for an example of RNA-containing viruses.
If the ratio of the distances of a variable point \(P\) from the point \((1,1)\) and the line \(x - y + 2 = 0\) is \(1/\sqrt{2}\), then the equation of the locus of \(P\) is:

If water is poured into a cylindrical tank of radius 3.5 ft at the rate of 1 cubic ft/min, then the rate at which the level of the water in the tank increases (in ft/min) is:

The internal and external diameters of a hollow cylinder measured with vernier calipers are (5.73 \(\pm\) 0.01) cm and (6.01 \(\pm\) 0.01) cm respectively. Then the thickness of the cylinder wall is
Find the domain of the real valued function: \[ f(x) \;=\; \sqrt{\cos(\sin x)} + \cos^{-1}\left(\frac{1+x^2}{2x}\right). \]
The point \((p, q)\) is the point of intersection of a latus rectum and an asymptote of the hyperbola \(9x^2 - 16y^2 = 144\). If \(p>0\) and \(q>0\), then \(q = \ldots\)
If \( \log y = y^{\log x} \), then \( \frac{dy}{dx} \) is:
For the displacement current through the plates of a parallel plate capacitor of capacitance 30 µF to be 150 µA, the potential difference across the plates of the capacitor has to vary at the rate of:
The radii of two conducting spheres A and B of each charge +90 µC are 8 cm and 10 cm respectively. When the two spheres are connected by a conducting wire, then the charge flowing from sphere A to sphere B is:
The slope of a line L passing through the point \((-2, -3)\) is not defined. If the angle between the lines L and \( ax - 2y + 3 = 0 \) (where \( a>0 \)) is 45°, then the angle made by the line \( x + ay - 4 = 0 \) with positive X-axis in the anticlockwise direction is:
Identify the major product \((P)\) in the following reaction sequence: \[ (\text{CH}_3)_3\text{CBr} \xrightarrow[\Delta]{\text{Alcoholic KOH}} X \xrightarrow{\text{HBr}} P \]
Which one of the following corresponds to the wavelength of line spectrum of H atom in its Balmer series? (R = Rydberg constant)
Two particles each of mass \(m\) are separated by a distance \(d\). If the mass of one of the particles is doubled without changing the distance between the two particles, then the shift in the position of the center of mass is
A photoelectron emitted when a light of wavelength 2480 \(\mathring{A}\) falls on a metal, enters a uniform magnetic field of \( \frac{1}{4} \times 10^{-5} \) T perpendicular to it and moves in a circular path of maximum radius 1 m. The work function of the metal is nearly:

A, B, C, D are square matrices such that A + B is symmetric, A - B is skew-symmetric, and D is the transpose of C.

If

\[ A = \begin{bmatrix} -1 & 2 & 3 \\ 4 & 3 & -2 \\ 3 & -4 & 5 \end{bmatrix} \]

and

\[ C = \begin{bmatrix} 0 & 1 & -2 \\ 2 & -1 & 0 \\ 0 & 2 & 1 \end{bmatrix} \]

then the matrix \( B + D \) is:

If the expression \( 7 + 6x - 3x^2 \) attains its extreme value \( \beta \) at \( x = \alpha \), then the sum of the squares of the roots of the equation \( x^2 + ax - \beta = 0 \) is:
12 g of an element reacts with 32 g of oxygen. What is the equivalent weight of the element?
Four identical particles each of mass 'm' are kept at the four corners of a square of side 'a'. If one of the particles is removed, the shift in the position of the centre of mass is:

For a gas in a thermodynamic process, the relation between internal energy (U), the pressure (P), and the volume (V) is given by: \[ U = 3 + 1.5PV \] The ratio of the specific heat capacities of the gas at constant volume and constant pressure is: 

Match the following: 

List-1:                                  List-2:

A Physical barrier                  I Lysozyme
B Physiological barriers        II Interferons
C Cellular barriers                  III Monocytes
D Cytokine barriers               IV Colostrum
                                                V Mucus membrane

If \( A = \begin{pmatrix} x & y & y \\ y & x & y \\ y & y & x \end{pmatrix} \) and \( 5A^{-1} = \begin{pmatrix} -3 & 2 & 2 \\ 2 & -3 & 2 \\ 2 & 2 & -3 \end{pmatrix} \), then \( A^2 - 4A \) is:

When \( Q \) amount of heat is supplied to a monatomic gas, the work done by the gas is \( W \). When \( Q_1 \) amount of heat is supplied to a diatomic gas, the work done by the gas is \( 2W \). Then \( Q:Q_1 \) is: 

A boy standing on a platform observes the frequency of a train horn as it passes by. The change in the frequency noticed as the train approaches and recedes from him with a velocity of 108 km/h (speed of sound in air = 330 m/s) is:
The equation \( 16x^4 + 16x^3 - 4x - 1 = 0 \) has a multiple root. If \( \alpha, \beta, \gamma, \delta \) are the roots of this equation, then \( \frac{1}{\alpha^4} + \frac{1}{\beta^4} + \frac{1}{\gamma^4} + \frac{1}{\delta^4} = \)