List of top Questions asked in TS EAMCET

If the coefficients of three consecutive terms in the expansion of (1 + x)23 are in arithmetic progression, then those terms are ?
A wooden cube of side 10 cm floats at the interface between water and oil with its lower surface 3 cm below the interface. If the density of oil is 0.9 g/cm³, the mass of the wooden cube is:
Among the following four statements, the statement which is not true, for all \( n \in N \) is:
The half-life of a radioactive substance is 12 minutes. The time gap between 28\% decay and 82\% decay of the radioactive substance is:
A stone is thrown vertically up from the top end of a window of height 1.8 m with a velocity of 8 m/s\(^1\). The time taken by the stone to cross the window during its downward journey is:
(Acceleration due to gravity \( g = 10 \) ms\(^{-2}\))

The potential difference \( V \) across the filament of the bulb shown in the given Wheatstone bridge varies as \( V = i(2i + 1) \), where \( i \) is the current in ampere through the filament of the bulb. The emf of the battery (\( V_a \)) so that the bridge becomes balanced is:
 

The ratio of the wavelengths of radiation emitted when an electron in the hydrogen atom jumps from the 4th orbit to the 2nd orbit and from the 3rd orbit to the 2nd orbit is:
If \[ \frac{x^4}{(x^2+1)(x-2)} = f(x) + \frac{Ax+B}{x^2+1} + \frac{C}{x-2} \] then \( f(14) + 2A - B = \) ?
A particle of charge \( 2 C \) is moving with a velocity \( (3\hat{i} + 4\hat{j}) \) m/s in the presence of magnetic and electric fields. If the magnetic field is \( ( \hat{i} + 2\hat{j} + 3\hat{k} ) \) T and the electric field is \( (-2\hat{k}) \) NC\(^{-1}\), then the Lorentz force on the particle is:

According to Fajan's rules, which of the following is not correct about covalent character?

All the letters of the word 'COLLEGE' are arranged in all possible ways and all the seven letter words (with or without meaning) thus formed are arranged in the dictionary order. Then the rank of the word 'COLLEGE' is:
A body moving with uniform acceleration travels a distance of 25 m in the fourth second and 37 m in the sixth second. The distance covered by the body in the next two seconds is
If three sources of sound of frequencies \( (n-1), n, (n+1) \) are vibrated together, the number of beats produced and heard per second respectively are:

Calculate the determinant of the matrix:
 


 

If \( m_1 \) and \( m_2 \) are the slopes of the direct common tangents drawn to the circles \[ x^2 + y^2 - 2x - 8y + 8 = 0 \quad \text{and} \quad x^2 + y^2 - 8x + 15 = 0 \] then \( m_1 + m_2 \) is:
The general solution of the differential equation \[ (9x - 3y + 5) dy = (3x - y + 1) dx. \]
If the length of a string is \(P\) when the tension in it is 6 N and its length is \(Q\) when the tension in it is 8 N, then the original length of the string is:
If \( (2, -1) \) is the point of intersection of the pair of lines \[ 2x^2 + axy + 3y^2 + bx + cy - 3 = 0 \quad \text{then} \quad 3a + 2b + c = \]
Evaluate the integral: \[ \int \frac{dx}{9\cos^2 2x + 16\sin^2 2x} \]
If \( f(x) = ax^2 + bx + c \) is an even function and \( g(x) = px^3 + qx^2 + rx \) is an odd function, and if \( h(x) = f(x) + g(x) \) and \( h(-2) = 0 \), then \( 8p + 4q + 2r = \)?
If \( \theta \) is an acute angle and \( 2\sin^2 \theta = \cos^4 \frac{\pi}{8} + \sin^4 \frac{3\pi}{8} + \cos^4 \frac{5\pi}{8} + \sin^4 \frac{7\pi}{8} \), then \( \theta \) is:

Evaluate the integral: \[ \int \frac{\sec x}{3(\sec x + \tan x) + 2} \,dx \]

When the object and the screen are 90 cm apart, it is observed that a clear image is formed on the screen when a convex lens is placed at two positions separated by 30 cm between the object and the screen. The focal length of the lens is: 

In a triangle ABC, if \( r_1 = 6 \), \( r_2 = 9 \), \( r_3 = 18 \), then \( \cos A \) is:
The mean and variance of a binomial variate \(X\) are \(\frac{16}{5}\) and \(\frac{48}{25}\) respectively. Given that \(P(X \geq 1) = 1 - K \left(\frac{3}{5}\right)^7\), find \(5K\):