The velocity of an object moving in a straight line path is given as a function of time by \(v=6 t-3 t^2\), where \(v\) is in \(\mathrm{ms}^{-1}, t\) is in \(\mathrm{s}\). The average velocity of the object between, \(t=0\) and \(t=2 \mathrm{~s}\) is

A string of length \(1 \mathrm{~m}\) and mass \(490 \mathrm{~g}\) is put under a tension of \(25 \mathrm{~N}\). A wave of frequency \(120 \mathrm{~Hz}\) is sent along it. The speed of this wave is

As shown in the figure, two infinitely long straight parallel wires \(P\) and \(Q\) carrying equal currents in opposite directions are arranged parallel to \(\mathrm{Y}\)-axis. If the magnetic field due to wire \(\mathrm{P}\) at the origin ' \(\mathrm{O}\) ' of the co-ordinate system is B, then match the resultant magnetic fields at various points given in column \(A\) with the points given in column \(B\).
\(\begin{array}{ll}
\text{Column A} & \text{Column B} \\
\text{A)} \frac{B}{4} & \text{i)} (0,0) \\
\text{B)} \frac{B}{2} & \text{ii)} (a, 0) \\
\text{C)} \frac{2 \mathrm{~B}}{3} & \text{iii)} (2a, 0) \\
\text{D)} 2 \mathrm{~B} & \text{iv)} (3 \mathrm{a}, 0) \\
\end{array}\)


The correct answer is

The difference between the radii of \(n^{\text {th }}\) and \((n+1)^{\text {th }}\) orbits of hydrogen atom is equal to the radius of \((n-1)^{\text {th }}\) orbit of hydrogen. The angular momentum of the electron in the \(n^{\text {th }}\) orbit is _________ ( \(h\) is Planck's constant).

Two metal plates $P$ and $Q$ of same material are arranged as shown in the figure. If both the plates are uniformly heated through same range of temperature, then

A photon incident on a metal of work function 2 eV produced photo electron of maximum kinetic energy of 2 eV . The wavelength associated with the photon is

An object moving along $x$-axis with a uniform acceleration has velocity $\overrightarrow{v}=\left(12 \mathrm{cm} {\mathrm{s}}^{-1}\right) \hat{\mathrm{i}}$ at $x=3 \mathrm{cm}$. After $2 \mathrm{s}$ if it is at $x=-5 \mathrm{cm}$, then its acceleration is,

In a triangle ABC, if \(\mathrm{r}_1=3, \mathrm{r}_2=4, \mathrm{r}_3=6\), then \(\mathrm{b}=\)

The sum of number of angular nodes and radial nodes for 4 d orbital is

If 27 charged water droplets, each of radius \(10^{-3} \mathrm{~m}\) and charge \(10^{-12} \mathrm{C}\) coalesce to form a single big spherical drop, then the potential of the big drop is

The value \(c\) of Lagrange's mean value theorem for \(f(x)=e^{\mathrm{x}}+24\) in \([0,1]\) is

A circular film of a liquid has an area of \(10 \mathrm{~cm}^2\). If the work done in making its radius two times the initial radius is \(8 \times 10^{-3} \mathrm{~J}\). the surface tension of the liquid is \(\left(1+\frac{1}{\alpha}\right) \mathrm{Nm}^{-1}\). The value of \(\alpha\) is

For a particle executing simple harmonic motion, the ratio of kinetic and potential energies at a point where displacement is one half of the amplitude is