IIT-JEE 2006

Match the following columns.

.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px;
overflow:hidden;padding:10px 5px;word-break:normal...

Initially, the capacitor was uncharged. Now, switch $S_1$ is closed and $S_2$ is kept open. If time constant of this circuit is $\tau$, then

If the total charge stored in the LC circuit.is $\mathrm{Q}_0$, then for $t \geq 0$,

After the capacitor gets fully charged, $\mathrm{S}_1$ is opened and $S_2$ is closed so that the inductor is connected in series with the capacitor. Then,

In hydrogen-like atom $(z=11)$, $n$th line of Lyman series has wavelength A equal to the de Broglie's wavelength of electron in the level from which it originated. What is the value of $n$ ?

\(\text { Match the following Columns. }\)


.tg {border-collapse:collapse;border-spacing:0;}

.tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px;

overflow:hidden;padding:10px 5p...

In the following circuits, it is given that $\mathrm{R}_1=1 \Omega, \mathrm{R}_2=2 \Omega, \mathrm{C}_1=2 \mu \mathrm{~F}$ and $\mathrm{C}_2=4 \mu \mathrm{~F}$.The time constants (in $\mu \mathrm{s}$ ) for the circuits I, II, III are, rcspe...

In the given diagram, a line of force of a particular force field is shown. Out of the following options, it can never represent

Consider a cylindrical element as shown in the figure. The current that flows through the element is I and resistivity of material of the cylinder is $\rho$. Choose the correct option out the following

The graph between $\frac{1}{\lambda}$ and stopping potential (V) of three metals having work functions $\phi_1, \phi_2$, and $\phi_3$ in an experiment of photoelectric effect is plotted as shown in the figure. Which of the following stateme...

What is the advantage of this system?

What is the disadvantage of this system?

Which force causes the train to elevate upwards

The electrostatic potential $\left(\phi_r\right)$ of a spherical symmetric system, kept at origin, is shown in the adjacent figure, and given as
$$ \begin{array}{ll} \phi_r=\frac{q}{4 \pi \epsilon_0 r} & \left(r \geq \mathrm{R}_0\right) \\ ...

A simple telescope used to view distant objects has eyepiece and objective lens of focal lengths $f_e$ and $f_0$, respectively. Match Column I with Column II:
.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;borde...

Graph of position of image versus position of point object from a convex lens is shown. Then, the focal length of the lens is

A biconvex lens of focal length $f$ forms a circular image of sun of radius $r$ in focal plane. Then

A point object is placed at a distance of 20 cm from a thin plano-convex lens of focal length 15 cm , if the plane surface is silvered. The image will form at

A system of binary stars of masses $m_{\mathrm{A}}$ and $m_{\mathrm{B}}$ are moving in circular orbits of radii $r_{\mathrm{A}}$ and $r_R$, respectively. If $\mathrm{T}_A$ and $\mathrm{T}_B$ are the time periods of masses $m_A$ and $m_B$ re...

In a dark room with ambient temperature $\mathrm{T}_0$, a black body is kept at a temperature T . Keeping the temperature of the black body constant (at T), sunrays are allowed to fall on the black body through a hole in the roof of the dar...

In an insulated vessel, 0.05 kg steam at 373 K and 0.45 kg of ice at 253 K are mixed. Then, find the final temperature of the mixture.

Heat given to the processes is positive. Match Column I with Column II:

.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px;
overflo...

Two blocks A and B of masses $2 m$ and $m$, respectively, are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in the figure. The magnitudes of acceleration of A and B, immediately...

A circular disc with a groove along its diameter is placed horizontally. A block of mass 1 kg is placed as shown. The coefficient of friction between the block and all surfaces of groove in contact is $\mu=\frac{2}{5}$. The disc has an acce...

\(\text { Match the following Columns. }\)
.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px;
overflow:hidden;padding:10px 5px;wo...

An infinite current-carrying wire passes through point O and in perpendicular to the plane containing a current-carrying loop ABCD as shown in the figure. Choose the correct option(s):

If the height $h_2$ of water level is further decreased, then

If the level of liquid starts decreasing slowly when the level of liquid is at a height $h_1$ above the cylinder, the block just starts moving up. Then, the value of $h_1$ is:

Let the cylinder is prevented from moving up, by applying a force and water level is further decreased. Then, the height of water level ( $h_2$ in the figure) for which the cylinder remains in original position without application of force ...

A solid sphere of radius $R$ has moment of inertia $I$ about its geometrical axis. If it is melted into a disc of radius $r$ and thickness $t$. If its moment of inertia about the tangential axis (which is perpendicular to plane of the disc)...

A solid cylinder of mass m and radius $r$ is rolling on rough inclined plane of inclination $\theta$. The coefficient of friction between the cylinder and incline is $\mu$. then

Function $x=\mathrm{A} \sin ^2 \omega t+\mathrm{B} \cos ^2 \omega t+\mathrm{C} \sin \omega t \cos \omega t$ represents SHM

In a screw gauge, the zero of main scale coincides with the fifth division of circular scale in figure (i).The circular division of screw gauge is 50. It moves 0.5 mm on main scale in one rotation.The diameter of the ball in figure (ii) is

A student performs an experiment for determination of $g\left(=\frac{4 \pi^2 l}{\mathrm{~T}^2}\right), l=1 m$, and he commits an error of $\Delta l$. For T , he takes the time of $n$ oscillations with the stop watch of least count $\Delta \...

Find the number of times the intensity is maximum in the time interval of 1 sec.

Find the wave velocity of louder sound.

Find the number of times $y_1+y_2=0$ at $x=0$ in $1 s$.

A massless rod is suspended by two identical strings AB and CD of equal length. A block of mass $m$ is suspended from point $O$ such that BO is equal to $x$. Further, it is observed that the frequency of 1st harmonic (fundamental frequency)...

A ball moves over a fixed track as shown in the figure. From $A$ to $B$, the ball rolls without slipping. Surface $B C$ is frictionless. $K_A, K_B$ and $K_c$ are kinetic energies of the ball at $A, B$ and C , respectively. Then

There is a rectangular plate of mass M kg of dimensions ( $a \times b$ ). The plate is held in horizontal position by striking $n$ small balls each of mass m per unit area per unit time. These are striking in the shaded half region of the p...