List of top Questions asked in AP EAMCET

The de Broglie wavelength of a particle of mass 1 mg moving with a velocity of $ 10 $ ms$^{-1}$ is (h = $ 6.63 \times 10^{-34} $ Js)

If $ A = \left[\begin{array}{ccc} 83 & 74 & 41 \\ 93 & 96 & 31 \\ 24 & 15 & 79 \end{array} \right] $, then $\text{det} (A - A^T) = $:

If 7 and 8 are the lengths of two sides of a triangle and $ a $ is the length of its smallest side. The angles of the triangle are in AP and $ a $ has two values $ a_1 $ and $ a_2 $ satisfying this condition. If $ a_1<a_2 $, then $ 2a_1 + 3a_2 = $:

For $ \lambda, \mu \in \mathbb{R} $, the lines \[ (x - 2y - 1) + \lambda (3x + 2y - 11) = 0 \] and \[ (3x + 4y - 11) + \mu (-x + 2y - 3) = 0 \] represent two families of lines. If the equation of the line common to both families is given by \[ ax + by - 5 = 0, \] then $ 2a + b = $ ?

If real parts of $ \sqrt{-5 - 12i} $, $ \sqrt{5 + 12i} $ are positive values, the real part of $ \sqrt{-8 - 6i} $ is a negative value. If \[ a + ib = \frac{\sqrt{-5 - 12i} + \sqrt{5 + 12i}}{\sqrt{-8 - 6i}} \] then $ 2a + b $ is:

In $ \triangle ABC $, if $ a = 13 $, $ b = 14 $, and $ \cos \frac{C}{2} = \frac{3}{\sqrt{13}} $, then $ 2r_1 = $:

Evaluate the integral: \[ \int e^x \left( \frac{x + 2}{(x+4)} \right)^2 dx. \]

The number of ways of selecting 3 numbers that are in GP from the set $ \{1, 2, 3, \dots, 100\} $ is:

A hydrocarbon containing C and H has 92.3% C. When 39 g of hydrocarbon was completely burnt in O_2, x moles of water and y moles of CO₂were 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?

If $\int \frac{\log(1+x^4)}{x^3} dx = f(x) \log(\frac{1}{g(x)}) + \tan^{-1}(h(x)) + c$, then $h(x) [f(x) + f(\frac{1}{x})] =$

Initially the pressure of 1 mole of an ideal gas is $ 10^5 $ Nm$^2$ and its volume is 16 liters. When it is adiabatically compressed, its final volume is 2 liters. Work done on the gas is (molar specific heat at constant volume $ C_V = \frac{3R}{2} $):

A ball at point ‘O’ is at a horizontal distance of 7 m from a wall. On the wall, a target is set at point ‘C’. If the ball is thrown from ‘O’ at an angle $ 37^\circ $ with horizontal aiming the target ‘C’. But it hits the wall at point ‘D’ which is a vertical distance $ y_0 $ below ‘C’. If the initial velocity of the ball is 15 m/s, find $ y_0 $. (Given $ \cos 37^\circ = \frac{4}{5} $)