List of top Questions asked in TS EAMCET

Suppose \( \theta_1 \) and \( \theta_2 \) are such that \( (\theta_1 - \theta_2) \) lies in the 3rd or 4th quadrant. If \[ \sin\theta_1 + \sin\theta_2 = \frac{21}{65} \quad \text{and} \quad \cos\theta_1 + \cos\theta_2 = \frac{27}{65} \] then \[ \cos\left(\frac{\theta_1 - \theta_2}{2}\right) = \] 

Among the 5 married couples, if the names of 5 men are matched with the names of their wives randomly, then the probability that no man is matched with the name of his own wife is ?

If 2 cards drawn at random from a well shuffled pack of 52 playing cards are from the same suit, then the probability of getting a face card and a card having a prime number is:
The ratio of the radii of a planet and the earth is \( 1:2 \), the ratio of their mean densities is \( 4:1 \). If the acceleration due to gravity on the surface of the earth is \( 9.8 \, ms^{-2} \), then the acceleration due to gravity on the surface of the planet is?
If the tangents \( x + y + k = 0 \) and \( x + ay + b = 0 \) drawn to the circle \( S : x^2 + y^2 + 2x - 2y + 1 = 0 \) are perpendicular to each other and \( k, b \) are both greater than 1, then find \( b - k \).
If \(2\,\tan^{-1}x = 3\,\sin^{-1}x\) and \(x \neq 0\), then \(8x^2 +1 =\;?\)
If \[ \frac{x^4}{(x^2+1)(x-2)} = f(x) + \frac{Ax+B}{x^2+1} + \frac{C}{x-2} \] then \( f(14) + 2A - B = \) ?

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 \( S - k \).

A convex lens of focal length 20 cm is immersed in a liquid of refractive index 1.3. If the refractive index of the material of the lens is 1.5, then the focal length of the lens when immersed in the liquid is:
The question asks for an example of RNA-containing viruses.
A vessel contains hydrogen and nitrogen gases in the ratio 2:3 by mass. If the temperature of the mixture of the gases is 30°C, then the ratio of the average kinetic energies per molecule of hydrogen and nitrogen gases is:
Evaluate the integral: \[ \int \frac{dx}{9\cos^2 2x + 16\sin^2 2x} \]
The slope of a common tangent to the circles \( x^2 + y^2 - 4x - 8y + 16 = 0 \) and \( x^2 + y^2 - 6x - 16y + 64 = 0 \) is:
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
If \( dQ, dU, dW \) are heat energy absorbed, change in internal energy, and external work done respectively by a diatomic gas at constant pressure, then \( dW : dU : dQ \) 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 equations \(2x^2 + ax - 2 = 0\) and \(x^2 + x + 2a = 0\) have exactly one common root. If \(a \neq 0\), then one of the roots of the equation \(ax^2 - 4x - 2a = 0\) is:

Two logic gates are connected as shown in the figure. If the inputs are \( A = 1 \) and \( B = 0 \), then the values of \( y_1 \) and \( y_2 \) respectively are:
 

If the coefficients of three consecutive terms in the expansion of (1 + x)23 are in arithmetic progression, then those terms are ?
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: