A circuit has a resistance of $$12$$ $$ohm$$ and an impedance of $$15$$ $$ohm$$. The power factor of the circuit will be

The diagram shows the energy levels for an electron in a certain atom. Which transition shown represents the emission of a photon with the most energy?

A nuclear transformation is denoted by $$X\left(n,\alpha \right)\text{matrix}7\text{cr}3\text{cr}Li.$$ Which of the following is the nucleus of element $$X$$ ?

If radius of the $$\text{matrix}27\text{cr}13\text{cr}$$ $$Al$$ nucleus is estimated to be $$3.6$$ fermi then the radius of $$\text{matrix}125\text{cr}52\text{cr}Te$$ nucleus is estimated to be nearly

Starting with a sample of pure {}^{66}Cu,{7 \over 8} of it decays into $$Zn$$ in $$15$$ minutes. The corresponding half life is

The intensity of gamma radiation from a given source is $$L$$. On passing through $$36$$ $$mm$$ of lead, it is reduced to {{\rm I} \over 8}. The thickness of lead which will reduce the intensity to {{\rm I} \over 2} will be

A gaseous mixture consists of $$16$$ $$g$$ of helium and $$16$$ $$g$$ of oxygen. The ratio {{Cp} \over {{C_v}}} of the mixture is

The temperature-entropy diagram of a reversible engine cycle is given in the figure. Its efficiency is

The figure shows a system of two concentric spheres of radii $$r_1$$ and $$r_2$$ are kept at temperatures $$T_1$$ and $$T_2$$, respectively. The radial rate of flow of heat in a substance between the two concentric spheres is proportional to

A system goes from $$A$$ to $$B$$ via two processes $$I$$ and $$II$$ as shown in figure. If $$\Delta U_1$$ and $$\Delta U_2$$ are the changes in internal energies in the processes $$I$$ and $$II$$ respectively, then

Which of the following is incorrect regarding the first law of thermodynamics?

Two thin wire rings each having a radius $$R$$ are placed at a distance $$d$$ apart with their axes coinciding. The charges on the two rings are $$+q$$ and $$-q.$$ The potential difference between the centres of the two rings is

A charged ball $$B$$ hangs from a silk thread $$S,$$ which makes angle $$\theta$$ with a large charged conducting sheet $$P,$$ as shown in the figure. The surface charge density $$\sigma$$ of the sheet is proportional to f

Two point charges $$+8q$$ and $$-2q$$ are located at $$x=0$$ and $$x=L$$ respectively. The location of a point on the $$x$$ axis at which the net electric field due to these two point charges is zero is

A particle is moving eastwards with a velocity of 5 m/s. In 10 seconds the velocity changes to 5 m/s northwards. The average acceleration in this time is

A car starting from rest accelerates at the rate f through a distance S, then continues at constant speed for time t and then decelerates at the rate {f \over 2} to come to rest. If the total distance traversed is 15 S, then

The relation between time t and distance x is t = ax2 + bx where a and b are constants. The acceleration is

A parachutist after bailing out falls $$50$$ $$m$$ without friction. When parachute opens, it decelerates at $$2m/s^2.$$ He reaches the ground with a speed of $$3$$ $$m/s$$. At what height, did he bail out?

If the kinetic energy of a free electron doubles, it's deBroglie wavelength changes by the factor

A photocell is illuminated by a small bright source placed $$1$$ $$m$$ away. When the same source of light is placed {1 \over 2} $$m$$ away, the number of electrons emitted by photo-cathode would