An object is attached to the bottom of a light vertical spring and set vibrating. The maximum speed of the object is $15 ~cm/s$ and the period is $628 ~ms$. The amplitude of the motion in $cm$ is:

If $p \Rightarrow (q \vee r)$ is false,then the truth values of $p, q, r$ are respectively:

In order to eliminate the first degree terms from the equation $2x^2+4xy+5y^2-4x-22y+7=0$,the point to which the origin is to be shifted is

Two coherent narrow slits emitting light of wavelength $\lambda$ in the same phase are placed parallel to each other at a small separation of $3\lambda$. The light is collected on a screen $S$ which is placed at a distance $D$ from the slits. Find the smallest distance $x$ from the central point $O$ such that point $P$ is a maxima.

Two rigid boxes containing different ideal gases are placed on a table. Box $A$ contains one mole of nitrogen at temperature $T_0$,while box $B$ contains one mole of helium at temperature $(7/3) T_0$. The boxes are then put into thermal contact with each other,and heat flows between them until the gases reach a common final temperature (Ignore the heat capacity of boxes). Then,the final temperature of gases,$T_f$,in terms of $T_0$ is

$A$ galvanometer may be converted into an ammeter or a voltmeter. In which of the following cases will the resistance of the device so obtained be the largest?