List of top Questions asked in AP EAPCET

Which of the following orders are correct against the stated property?
I) NaO$_2 < KO$_2 < RbO$_2 < CsO$_2$ — stability
II) Mg(OH)$_2 < Ca(OH)$_2 < Sr(OH)$_2$ — basic strength
III) MgCO$_3 < CaCO$_3 < SrCO$_3$ — thermal stability

Consider the following
Statement-I: During isothermal expansion of an ideal gas its enthalpy decreases.
Statement-II: When 2.0 L of an ideal gas expands isothermally into vacuum, $\Delta U = 0$.

Which of the following statements are correct? (only correct)
I) The energy of hydrogen atom in its ground state is -13.6 eV.
II) On the basis of Bohr's model, the radius of the 3$^{rd}$ orbit of hydrogen atom is 158.7 pm.
III) The order of radius of the first orbit of H, He$^+$, Li$^{2+}$ and Be$^{3+}$ is H > He$^+$ > Li$^{2+}$ > Be$^{3+}$

Two concentric loops $A$ and $B$ of same radius $2\pi~\text{cm$ are placed at right angles to each other. If the currents flowing through $A$ and $B$ are $3~\text{A}$ and $4~\text{A}$ respectively, then the net magnetic field at their common center is}

A Carnot engine having efficiency $60%$ receives heat from a source at temperature $600~\text{K$. For the same sink temperature, to increase its efficiency to $80%$, the temperature of the source is}

Ratio of angular velocity of hour hand of a watch and the angular velocity of rotation of earth is

The bob of a simple pendulum of length $200~\text{cm}$ is released from horizontal position.
If $10%$ of its initial energy is lost to air resistance, then the speed of bob at the mean position is
(Acceleration due to gravity $= 10~\text{m/s}^2$)

The area of the region (in sq. units) enclosed between the curves \( y = |x| \), \( y = [x] \) and the ordinates \( x = -1, x = 0, x = 1 \) is

Evaluate the integral \[ \int_{\frac{1}{2}}^{\frac{\sqrt{3}}{2}} \frac{1}{\left(x + \sqrt{1 - x^2}\right) \cdot \left(1 - x^2\right)} \, dx = \]

Evaluate the integral $\displaystyle \int_0^{\frac{\pi{2}} \log(\tan x + \cot x)\, dx$}

Evaluate the integral \[ \int_{0}^{\pi} x \cdot \sin x \cdot \int_{x}^{5} \frac{\cos x}{x} \cdot dx = \]

If \( \int \frac{dx}{(x-1)^2(x-3)^2 = \sqrt{f(x)} + c \), then \( f(-1) - f(0) = \)}

If \(y = (ax + b)\cos x\), then \(y_2 + y_1 \sin 2x + y(1 + \sin^2 x) = \)

If \(x^2 + y^2 = \dfrac{1}{t} \text{ and } x^4 + y^4 = t^2 + \dfrac{1}{t^2},\) then \(\dfrac{dy}{dx} =\)

If a function defined by \[ f(x) = \begin{cases} \dfrac{1 - \cos 4x}{x^2}, & x<0
a, & x = 0
\dfrac{\sqrt{x}}{\sqrt{16 + \sqrt{x} - 4}}, & x>0 \end{cases} \] is continuous at \(x = 0\), then \(a =\)