In the circuit shown in the following figure,the value of $Y$ is

$A$ ball is allowed to fall from a height of $10\, m$. If there is $40\%$ loss of energy due to impact,then after one impact,the ball will rise to a height of ......... $m$.

Which of the following factors increase the heart rate?
$(a)$ Sympathetic nerve signals
$(b)$ Parasympathetic nerve signals
$(c)$ Adrenal medullary hormones
$(d)$ Vagus nerve
$(e)$ Thyroxine hormone
$(f)$ Acetylcholine

If the area of the auxiliary circle of the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ $(a > b)$ is twice the area of the ellipse,then the eccentricity of the ellipse is

An earthquake generates both transverse $(S)$ and longitudinal $(P)$ waves in the earth. The speed of $S$ waves is about $4.5 \, km/s$ and that of $P$ waves is about $8.0 \, km/s$. $A$ seismograph records $P$ and $S$ waves from an earthquake. The first $P$ wave arrives $4.0 \, min$ before the first $S$ wave. The epicenter of the earthquake is located at a distance of about ..... $km$.

$A$ wheel which is initially at rest is subjected to a constant angular acceleration about its axis. It rotates through an angle of $15^{\circ}$ in time $t \ s$. The increase in angle through which it rotates in the next $2t \ s$ is (in $^{\circ}$)