An object is projected with a velocity of $20 \ m/s$ making an angle of $45^\circ$ with the horizontal. The equation for the trajectory is $h = Ax - Bx^2$,where $h$ is height,$x$ is horizontal distance,and $A$ and $B$ are constants. The ratio $A : B$ is $(g = 10 \ m/s^2)$.

$A$ whistle revolves in a circle with an angular speed of $20\, rad/s$ using a string of length $50\, cm$. If the frequency of sound from the whistle is $385\, Hz$,then what is the minimum frequency heard by an observer,who is far away from the centre in the same plane? (Speed of sound is $340\, m/s$)

Which one of the following is not an iso-electronic pair?

Consider the following statements. Which of the following statements are correct?
$(i)$ Froth floatation technique is used to concentrate sulphide ore.
$(ii)$ Froth floatation technique is based upon differential wettability of ore and impurity in water.
$(iii)$ Red Bauxite is concentrated by Bayer’s process.
$(iv)$ Carbon is used as reducing agent during extraction of zinc from zinc blende.

$A$ monoatomic ideal gas,initially at temperature $T_1$,is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature $T_2$ by releasing the piston suddenly. If $L_1$ and $L_2$ are the lengths of the gas columns before and after the expansion respectively,then the ratio $\frac{T_2}{T_1}$ is:

The current flowing through an inductor of self-inductance $L$ is continuously increasing at a constant rate. The variation of induced e.m.f. $(e)$ versus $dI/dt$ is shown graphically by which graph?