List of top Questions asked in AP EAMCET

The angle made by the resultant vector of two vectors \( 2\hat{i} + 3\hat{j} + 4\hat{k} \) and \( 2\hat{i} - 7\hat{j} - 4\hat{k} \) with the x-axis is:
If the longest wavelength of the spectral line of the Paschen series of \( \text{Li}^{2+} \) ion spectrum is \( x \) Å, then the longest wavelength (in Å) of the Lyman series of the hydrogen spectrum is:
Let \( A(2, 3), B(1, -1) \) be two points. If \( P \) is a variable point such that \( \angle APB = 90^\circ \), then the locus of \( P \) is
The charge \( q \) (in coulombs) passing through a \( 10 \Omega \) resistor as a function of time \( t \) (in seconds) is given by: \[ q = 3t^2 - 2t + 6 \] The potential difference across the ends of the resistor at time \( t = 5 \) s is:

The percentage error in the measurement of mass and velocity are 3% and 4% respectively. The percentage error in the measurement of kinetic energy is:

A → P is a first order reaction. The following graph is obtained for this reaction. (x-axis = time; y-axis = conc. of A). The instantaneous rate of the reaction at point C is
first order reaction
If \( \alpha, \beta, \gamma \) are the roots of the determinant equation: \[ \begin{vmatrix} 1-x & -2 & 1
-2 & 4-x & -2
1 & -2 & 1-x \end{vmatrix} = 0 \] then \( \alpha \beta + \beta \gamma + \gamma \alpha \) is:

If \( L, M, N \) are the midpoints of the sides PQ, QR, and RP of triangle \( \Delta PQR \), then \( \overline{QM} + \overline{LN} + \overline{ML} + \overline{RN} - \overline{MN} - \overline{QL} = \):

In the ground state of hydrogen atom, electron absorbs 1.5 times energy than the minimum energy \( (2.18 \times 10^{-18} J)\) to escape from the atom. The wavelength of the emitted electron (in m) is \((m_e = 9 \times 10^{-31} kg)\)
Aniline on direct nitration at 288 K gives 51% (A), 47% (B) and 2% (C). ‘B’ on diazotisation, followed by reaction with CuCN | KCN gives a compound X. The percentage of nitrogen in X is:
If the coefficients of \(x^5\) and \(x^6\) are equal in the expansion of \( \left( a + \frac{x}{5} \right)^{65} \), then the coefficient of \(x^2\) in the expansion of \( \left( a + \frac{x}{5} \right)^4 \) is:
Given \[ A = \begin{bmatrix} 0 & 1 & 2 \\ 4 & 0 & 3 \\ 2 & 4 & 0 \end{bmatrix} \] \(\quad B \text{ is a matrix such that }\) \(AB = BA. \text{ If } AB \text{ is not an identity matrix, then the matrix that can be taken as } B \text{ is:} \)
The de Broglie wavelength of an electron with kinetic energy of \( 2.5 \) eV is (in m): \[ (1 \text{ eV} = 1.6 \times 10^{-19} \text{ J}, \quad m_e = 9 \times 10^{-31} \text{ kg}) \]
A soccer ball of mass 250 g is moving horizontally to the left with a speed of 22 m/s. This ball is kicked towards right with a velocity 30 m/s at an angle 53° with the horizontal in upward direction. Assuming that it took 0.01 s for the collision to take place, the average force acting is:
Two satellites of masses \( m \) and \( 1.5m \) are revolving around the Earth with different speeds in two circular orbits of heights \( R_E \) and \( 2R_E \) respectively, where \( R_E \) is the radius of the Earth. The ratio of the minimum and maximum gravitational forces on the Earth due to the two satellites is
Given the equation: \[ y = (\tan^{-1} 2x)^2 + (\cot^{-1} 2x)^2, \] find the expression: \[ (1+4x^2)^2 y'' - 16. \]
Which of the following sets are correctly matched?
(i) B2H6- electron deficient hydride
(ii) NH3- electron precise hydride
(iii) H2O- electron rich hydride
If the line through the point \( P(5,3) \) meets the circle \( x^2 + y^2 - 2x - 4y + \alpha = 0 \) at \( A(4, 2) \) and \( B(x_1, y_1) \), then \( PA \times PB = \):
Size of the antenna for a carrier wave of frequency 3 MHz is:
The range of the real valued function \( f(x) = \frac{x^2 + 2x - 15}{2x^2 + 13x + 15} \) is:
The diffraction pattern of a crystalline solid gave a peak at \( 2\theta = 60^\circ \). What is the distance (in cm) between the layers that gave this peak? \[ \text{(Given: Wavelength } \lambda = 1.544\text{ Å, } \sin 30^\circ = 0.5, \sin 60^\circ = 0.866, n=1) \]

A hydrocarbon containing C and H has 92.3% C. When 39 g of hydrocarbon was completely burnt in O2, x moles of water and y moles of CO2 were formed. x moles of water is sufficient to liberate 0.75 moles of H2 with Na metal. What is the weight (in g) of oxygen consumed?

RMS velocity of one mole of an ideal gas was measured at different temperatures. A graph of \( (u_{\text{rms}})^2 \) (on y-axis) and \( T/K \) (on x-axis) gave a straight line passing through the origin, and its slope is \( 249 \, \text{m}^2 \text{s}^{-2}\text{K}^{-1} \). What is the molar mass (in kg mol\(^{-1}\)) of the ideal gas? \(( R = 8.3 \, \text{J mol}^{-1} \text{K}^{-1} )\)
If the points with position vectors \[ (\mathbf{a}i + 10j + 13k), \quad (6i + 11j + 11k), \quad \left(\frac{9}{2}i + \beta j - 8k\right) \] are collinear, then evaluate \( (19a - 6\beta)^2 \).
Evaluate the sum: \[ \sin^2 18^\circ + \sin^2 24^\circ + \sin^2 36^\circ + \sin^2 42^\circ + \sin^2 78^\circ + \sin^2 90^\circ + \sin^2 96^\circ + \sin^2 102^\circ + \sin^2 138^\circ + \sin^2 162^\circ. \]