List of top Questions asked in AP ECET ME

A carnot engine having an efficiency of $\frac{1}{10}$ as heat engine, is used as a refrigerator. If the work done on the system is $10 \text{ J}$, the amount of energy absorbed from the reservoir at lower temperature is

A rigid diatomic ideal gas undergoes an adiabatic process at room temperature. The relation between temperature and volume of this process is $TV^x = \text{constant}$. Then $x$ is

The specific heat at constant volume for a monoatomic gas is $0.075\text{ cal/kg}\cdot\text{K}$ and its gram molecular specific heat is $3\text{ cal/mol}\cdot\text{K}$. Then mass of one atom of that gas is

During the free expansion of an ideal gas, which of the following physical quantity remains constant

If the pressure of an ideal gas contained in a closed vessel is increased by $0.5\%$, the increase in temperature is $2^\circ\text{C}$. The initial temperature of the gas is

If $A = \begin{bmatrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{bmatrix}$ then $(A^{-1}) =$

To have a good sound effect inside a hall

A source of sound producing wavelength of $50 \text{ cm}$ is moving away from stationary observer with $\frac{1}{5}\text{th}$ speed of sound. The wavelength of the sound heard by the observer is

Bernoulli's equation is of the form

The necessary and sufficient condition for the differential equation $Mdx + Ndy = 0$ to be exact is

Transform $dx + xdy = e^{-y} \sec^2 y \, dy$ into linear form

The integrating factor of $\frac{dy}{dx} + 3x = 2y$ is

The Order of the differential equation $\left[ \frac{d^2y}{dx^2} + \left(\frac{dy}{dx}\right)^3 \right]^{6/5} = 6y$ is

If $S = 12t - 3t^2$ then $\frac{dS}{dt} =$

If $u(x, y) = \sin^{-1} \frac{x}{y} + \tan^{-1} \frac{y}{x}$ then $xu_x + yu_y =$

$\frac{d}{dx} \left( e^{3 \log x} \right) =$

If $u = e^x \sin y$ then first partial derivative of $u$ with respect to $y$ is

If $y = \cos x$ then $\frac{d^2y}{dx^2} =$

If $4x - 7y + 15 = 0$ then derivative of $y$ with respect to $x$ is

When $a \gt 0$, $\lim_{x \to 0} \frac{a^x - 1}{x} =$

$\frac{d}{dx} [e^x(x^2 + 1)] =$

The eccentricity of $x^2 + 2y^2 = 3$ is

The equation of the Parabola, whose focus is $(0, -2)$ and the vertex is $(0, 0)$, is

The length of the latus rectum of the parabola $y^2 = 12x$ and the focal distance of the point $(3, -6)$ is

Equation of the circle with centre $(-3, 2)$ and radius 4 is