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Shown below is a distribution of charges. The flux of electric field due to these charges through the surface S is:
The second overtone of an open organ pipe has the same frequency as the first overtone of a closed pipe $L$ metre long. The length of the open pipe will be
An ideal gas undergoes four different processes from the same initial state as shown in the figure below. Those processes are adiabatic, isothermal, isobaric, and isochoric. The curve which represents the adiabatic process among $1$, $2$, $3$ and $4$ is:
The magnetic flux linked with a coil (in Wb) is given by the equation $\phi = 5t^2 + 3t + 60$. The magnitude of induced emf in the coil at $t = 4$ s will be:
A wheel with 20 metallic spokes, each 1 m long, is rotated with a speed of 120 rpm in a plane perpendicular to a magnetic field of 0.4 G. The induced emf between the axle and rim of the wheel will be: (1 G = 10⁻⁴ T)
An air column, closed at one end and open at the other, resonates with a tuning fork when the smallest length of the column is $50 \text{ cm}$. The next larger length of the column resonating with the same tuning fork is
Sound waves travel at $350 \text{ m/s}$ through warm air and at $3500 \text{ m/s}$ through brass. The wavelength of a $700 \text{ Hz}$ acoustic wave as it enters brass from warm air:
A coil of resistance $400\Omega$ is placed in a magnetic field. If the magnetic flux $\phi\;(\text{Wb})$ linked with the coil varies with time $t\;(\text{sec})$ as $\phi=50t^2+4$. The current in the coil at $t=2\text{s}$ is:
A conducting circular loop is placed in a uniform magnetic field $0.04\text{ T}$ with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at $2\text{ mm/s}$. The induced emf in the loop when the radius is $2\text{ cm}$ is:
A source of sound S emitting waves of frequency $100 \text{ Hz}$ and an observer O are located at some distance from each other. The source is moving with a speed of $19.4 \text{ m/s}$ at an angle of $60^{\circ}$ with the source-observer line as shown in the figure. The observer is at rest. The apparent frequency observed by the observer (velocity of sound in air $330 \text{ m/s}$), is:
A Carnot engine has an efficiency of $50\%$ when its source is at a temperature $327^\circ \mathrm{C}$. The temperature of the sink is:
If we study the vibration of a pipe open at both ends, then the following statement is not true:
A wooden stick of length $3l$ is rotated about an end with constant angular velocity $\omega$ in a uniform magnetic field $B$ perpendicular to the plane of motion. If the upper one third of its length is coated with copper, the potential difference across the whole length of the stick is:
An ideal gas goes from state $A$ to state $B$ via three different processes, as indicated in the $P$-$V$ diagram. If $Q_1, Q_2, Q_3$ indicates the heat absorbed by the gas along the three processes and $\Delta U_1, \Delta U_2, \Delta U_3$ indicates the change in internal energy along the three processes respectively, then:
The most reactive compound among the following toward electrophilic aromatic substitution reaction is:
Light with an energy flux of $25 \times 10^4$ Wm$^{-2}$ falls on a perfectly reflecting surface at normal incidence. If the surface area is 15 cm$^2$, then the average force exerted on the surface is:
If c is the velocity of light in free space, the correct statements about photons among the following are: (A) The energy of a photon is E = hν. (B) The velocity of a photon is c. (C) The momentum of a photon, p = hν/c. (D) In a photon-electron collision, both total energy and total momentum are conserved. (E) Photon possesses a positive electric charge.
Goblet cells of alimentary canal are modified from
A uniform rope of length $L$ and mass $m_1$ hangs vertically from a rigid support. A block of mass $m_2$ is attached to the free end of the rope. A transverse pulse of wavelength $\lambda_1$ is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is $\lambda_2$. The ratio $\frac{\lambda_2}{\lambda_1}$ is:
A plano-convex lens of unknown material and unknown focal length is given. With the help of a spherometer, we can measure the: