List of top Questions asked in AP EAMCET

If the coefficients of the \( (2r + 6)^{th \) and \( (r - 1)^{th} \) terms in the expansion of \( (1 + x)^{21} \) are equal, then the value of \( r \) is:}
The number of different ways of preparing a garland using 6 distinct white roses and 6 distinct red roses such that no two red roses come together is:
The orthogonal projection vector of \( \bar{a} = 2\bar{i} + 3\bar{j} + 3\bar{k} \) on \( \bar{b} = \bar{i} - 2\bar{j} + \bar{k} \) is:
For a dataset, if the coefficient of variation is 25 and the mean is 44, find the variance.
Let \( \mathbf{a}, \mathbf{b} \) be two unit vectors. If \( \mathbf{c} = \mathbf{a} + 2\mathbf{b} \) and \( \mathbf{d} = 5\mathbf{a} - 4\mathbf{b} \) are perpendicular to each other, find the angle between \( \mathbf{a} \) and \( \mathbf{b} \).
If the vectors \(a\bar{i} + \bar{j} + \bar{k}\), \(\bar{i} + b\bar{j} + \bar{k}\), \(\bar{i} + \bar{j} + c\bar{k}\) (\(a \ne b \ne c \ne 1\)) are coplanar, then \(\frac{1}{1 - a} + \frac{1}{1 - b} + \frac{1}{1 - c} =\)
The general solution of \( \cot \frac{x}{2} - \cot x = \csc \frac{x}{2} \) is:
An electron is moving with a velocity \( (2\hat{i} + 3\hat{j}) \) m/s in an electric field \( (3\hat{i} + 6\hat{j} + 2\hat{k}) \) V/m and a magnetic field \( (2\hat{j} + 3\hat{k}) \) T. The magnitude and direction (with x-axis) of the Lorentz force acting on the electron is
If \( \mathbf{f}, \mathbf{g}, \mathbf{h} \) are mutually orthogonal vectors of equal magnitudes, then find the angle between the vectors \( \mathbf{f} + \mathbf{g} + \mathbf{h} \) and \( \mathbf{h} \).
The molar specific heat capacity of a diatomic gas at constant pressure is \( C \). The molar specific heat capacity of a monatomic gas at constant volume is
The origin is shifted to the point \( (2, 3) \) by translation of axes and then the coordinate axes are rotated about the origin through an angle \( \theta \) in the counter-clockwise sense. Due to this if the equation \( 3x^2 + 2xy + 3y^2 - 18x - 22y + 50 = 0 \) is transformed to \( 4x^2 + 2y^2 - 1 = 0 \), then the angle \( \theta = \):
Taxonomic keys are based on
If \( (a, b) \) is the midpoint of the chord \( 2x - y + 3 = 0 \) of the circle \( x^2 + y^2 + 6x - 4y + 4 = 0 \), then \( 2a + 3b = \):
If the eleventh term in the binomial expansion of \( (x + a)^n \) is the geometric mean of the eighth and twelfth terms, then the greatest term in the expansion is:
A spring of \( 5 \times 10^3 \) Nm\(^{-1} \) spring constant is stretched initially by 10 cm from the unstretched position. The work required to stretch it further by another 10 cm is
The set of all real values of \( a \) such that the function \( f(x) = x^3 + 2ax^2 + 3(a+1)x + 5 \) is strictly increasing in its entire domain is:
The length of the tangent drawn at the point \( P \left( \frac{\pi}{4} \right) \) on the curve \( x^{2/3} + y^{2/3} = 2^{2/3} \) is:
If A, B, C are the angles of a triangle, then \(\frac{\sin A + \sin B + \sin C}{\sin^2 \frac{A}{2} + \sin^2 \frac{B}{2} + \sin^2 \frac{C}{2} - 1} =\)
Evaluate the limit: \[ \lim_{x \to 0} \frac{1 - \cos x \cos 2x}{\sin^2 x} \]
If the distance between the planes \( 2x + y + z + 1 = 0 \) and \( 2x + y + z + \alpha = 0 \) is 3 units, then the product of all possible values of \( \alpha \) is:
The complex conjugate of \( (4 - 3i)(2 + 3i)(1 + 4i) \) is:
A running man has half the kinetic energy of a boy of half his mass. The man speeds up by \(1 \, {m/s}^{-1}\) to have the same kinetic energy as the boy. The initial speed of the man is:
The line \( x - 2y - 3 = 0 \) cuts the parabola \( y^2 = 4ax \) at points P and Q. If the focus of this parabola is \( \left(\frac{1}{4}, k\right) \), then PQ is:
Heat is supplied at constant pressure to a diatomic gas. The part of this heat that was utilized to increase its internal energy is:
A student writes an exam with 8 true/false questions. He passes if he answers at least 6 correctly. Find the probability that he fails.