If force (F), velocity (V) and time (T) are taken as fundamental units, the dimensions of mass are

A projectile is fired from the surface of the earth with a velocity of $5 ms^{-1}$ and angle $\theta$ with the horizontal. Another projectile fired from another planet with a velocity of $3 ms^{-1}$ at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is (given, $g = 9.8$ m/s$^2$)

A particle is moving such that its position coordinates $(x, y)$ are:$\newline (2m, 3m)$ at time $t = 0, \newline (6m,7m)$

A system consists of three masses $m_1, m_2$ and $m_3$ connected by a string passing over a pulley P. The mass

The force $F$ acting on a particle of mass $m$ is indicated by the force-time graph. The change in momentum of the particle over the time interval from zero to 8 s is

A balloon with mass $m$ is descending down with an acceleration $a$ (where $a < g$). How much mass should be removed from it so that it starts moving up with an acceleration $a$?

A body of mass $4m$ is lying in the x-y plane at rest. It suddenly explodes into three pieces. Two pieces, each of mass $m$ move perpendicular to each other with equal speeds $v$. The total kinetic energy generated due to explosion is

The oscillation of a body on a smooth horizontal surface is represented by the equation,$\newline x = A \cos(\omega t) \newline$Which one of the following graphs correctly shows the variation of acceleration $a$ with time $t$?

A solid cylinder of mass $50$ kg and radius $0.5$ m is free to rotate about a horizontal axis. A massless string is wound around the cylinder with one end attached to it and the other hanging freely. The tension in the string required to produce an angular acceleration of $2$ rev/s$^2$ is

The ratio of the acceleration for a solid sphere (mass $m$ and radius $R$) rolling down an incline of angle $\theta$ without slipping and slipping down the incline without rolling is

A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would Earth (mass = $5.98 \times 10^{24}$ kg) have to be compressed to be a black hole?

Dependence of intensity of gravitational field (E) of Earth with distance (r) from the center of Earth is correctly represented by

Copper of fixed volume $V$ is drawn into wire of length $l.$ When this wire is subjected to a constant force $F,$ the extension produced in the wire is $\Delta l.$ Which of the following graph is a straight line?

A certain number of spherical drops of a liquid of radius $r$ coalesce to form a single drop of radius $R$ and volume $V.$ If $T$ is the surface tension of the liquid, then

Steam at $100^{\circ}C$ is passed into $20g$ of water at $10^{\circ}C.$ When water acquires a temperature of $80^{\circ}C,$

Certain quantity of water cools from $70^{\circ}C$ to $60^{\circ}C$ in the first $5$ min and to $54^{\circ}C$

A monoatomic gas at a pressure $P,$ having a volume $V$ expands isothermally to a volume $2V$ and then adiabatically to a volume $16V.$ The final pressure of the gas is (take $\gamma = \frac{5}{3}$

A thermodynamic system undergoes cyclic process ABCDA as shown in the figure. The work done by the system in the cycle is

The mean free path of molecules of a gas (radius $r$) is inversely proportional to

If $n_1, n_2, n_3$ are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency $n$

The number of possible natural oscillations of an air column in a pipe closed at one end of length $85$ cm whose frequencies lie below $1250$ Hz are (velocity of sound $= 340$ m/s)

A speeding motorcyclist sees traffic jam ahead of him. He slows down to $36$ km/h. He finds that traffic has eased and a car moving ahead of him at $18$ km/h is honking at a frequency of $1392$ Hz. If the speed of sound is $343$ m/s, the frequency of the horn as heard by him will be

Two thin dielectric slabs of dielectric constants $K_1$ and $K_2$ ($K_1 < K_2$

A conducting sphere of radius $R$ is given a charge $Q.$ The electric potential and the electric field at the center of the sphere respectively are

In a region the potential is represented by $V(x, y, z) = 6x - 8xy - 8y + 6yz.$ The electric force experienced by a charge of 2 C situated at point $(1,1,1)$

Two cities are $150$ km apart. Electric power is sent from one city to another city through copper wires. The fall of potential per km is $8$ V and the average resistance per km is $0.5 \Omega.$ The power loss in the wire is

The resistance in the two arms of the meter bridge are $5 \Omega$ and $R \Omega$, respectively. When the resistance $R$ is shunted with an equal resistance, the new balance point is at $1.6 l_1.$

A potentiometer circuit has been set up for finding the internal resistance of a given cell. The main battery, used across the potentiometer wire, has an emf of $2.0 V$ and a negligible internal resistance. The potentiometer wire itself is $4$ m long. When the resistance $R$ is connected across the given cell, it has values of$\newline (a) \infty \quad (b) 9.5 \Omega \newline$

Following figures show the arrangement of bar magnets in different configurations. Each magnet has magnetic dipole moment $\vec{m}.$ Which configuration has highest net magnetic dipole moment?

In an ammeter $0.2\%$ of main current passes through the galvanometer. If resistance of galvanometer is $G,$ the resistance of ammeter will be

Two identical long conducting wires $AOB$ and $COD$ are placed at right angles to each other, with one above the other such that $O$ is their common point. The wires carry currents $I_1$

A thin semicircular conducting ring (PQR) of radius $r$ is falling with its plane vertical in a horizontal magnetic field $B.$ The potential difference developed across the ring when its speed is $v,$ is

A transformer having efficiency of $90\%$ is working on $200$ V and $3$ kW power supply. If the current in the secondary coil is $6$ A, the voltage across the secondary coil and the current in the primary coil respectively are

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$^2,$

A beam of light of $\lambda = 600$ nm from a distant source falls on a single slit $1$ mm wide and the resulting diffraction pattern is observed on a screen $2$ m away. The distance between first dark fringes on either side of the central bright fringe is

In the Young’s double slit experiment, the intensity of light at a point on the screen where the path difference is $\lambda$ is $K$ ($\lambda$ being the wavelength of light used). The intensity at a point where the path difference is $\lambda/4$ will be

If the focal length of the objective lens is increased, then magnifying power of

The angle of a prism is $A.$ One of its refracting surfaces is silvered. Light rays falling at an angle of incidence $2A$ on the first surface return back through the same path after suffering reflection at the silvered surface. The refractive index $\mu$ of the prism is

When the energy of the incident radiation is increased by $20\%$, the kinetic energy of the photoelectrons emitted from a metal surface increased from $0.5$ eV to $0.8$ eV. The work function of the metal is

If the kinetic energy of the particle is increased to $16$ times its previous value, the percentage change in the de Broglie wavelength of the particle is

Hydrogen atom in ground state is excited by a monochromatic radiation of $\lambda = 975$ Å$.$ Number of spectral lines in the resulting spectrum emitted will be

The Binding energy per nucleon of $^7_3$Li and $^4_2$He are $5.60$

A radio isotope $X$ with a half-life $1.4 \times 10^9$ years decays to $Y$ which is stable. A sample of the rock from a cave was found to contain $X$ and $Y$

The given graph represents V-I characteristic for a semiconductor device.$\newline$Which one of the following statements is correct?

The barrier potential of a p-n junction depends on$\newline (a)$ type of semiconductor material.$\newline (b)$ amount of doping.$\newline (c)$ temperature.$\newline$Which one of the following is correct?