The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5% and 1%, the maximum error in determining the density is:

The relative error in the determination of the surface area of sphere is $$\alpha$$. Then the relative error in the determination of its volume is :

The relative uncertainly in the period of a satellite orbiting around the earth is 10-2. If the relative uncertainty in the radius of the orbit is negligible, the relative uncertainty in the mass of the earth is :

The percentage errors in quantities P, Q, R and S are 0.5%, 1%, 3% and 1.5% respectively in the measurement of a physical quantity A = {{{P^3}{Q^2}} \over {\sqrt R S}}. The maximum percentage error in the value of A will be :

A convergent doublet of separated lenses, corrected for spherical aberration, has resultant focal length of 10 cm. The separation between the two lenses is $$2$$ cm. The focal lengths of the component lenses are :

A particle is oscillating on the $$X$$-axis with an amplitude $$2$$ $$cm$$ about the point $$x_0=10cm,$$ with a frequency $$\omega$$. A concave mirror of local length $$5$$ $$cm$$ is placed at the origin (see figure). Identify the correct statements.

A planoconvex lens becomes an optical system of $$28$$ $$cm$$ focal length when its plane surface is silvered and illuminated from left to right as shown in Fig-A. If the same lens is instead silvered on the curved surface and illuminated from other side as in Fig-B, it acts like an optical system of focal length $$10$$ $$cm.$$ The refractive index of the material of lens is :

A ray of light is incident at an angle of 60o on one face of a prism of angle 30o. The emergent ray of light makes an angle of 30o with incident ray. The angle made by the emergent ray with second face of prism will be :

A galvanometer with its coil resistance 25 $$\Omega$$ requires a current of 1 mA for its full deflection. In order to construct an ammeter to read upto a current of 2 A, the approximate value of the shunt resistance should be :

On interchanging the resistances, the balance point of a meter bridge shifts to the left by 10 cm. The resistance of their series combination is 1 k$$\Omega$$. How much was the resistance on the left slot before interchanging the resistances?

Two batteries with e.m.f 12 V and 13 V are connected in parallel across a load resistor of 10 $$\Omega$$. The internal resistances of the two batteries are 1 $$\Omega$$ and 2 $$\Omega$$ respectively. The voltage across the load lies between :

A heating element has a resistance of 100 $$\Omega$$ at room temperature. When it is connected to a supply of 220 V, a steady current of 2 A passes in it and temperature is 500oC more than room temperature. what is the temperature coefficient of resistance of the heating element ?

In a potentiometer experiment, it is found that no current passes through the galvanometer when the terminals of the cell are connected across 52 cm of the potentiometer wire. If the cell is shunted by a resistance of 5 $$\Omega$$, a balance is found when the cell is connected across 40 cm of the wire. Find the internal resistance of the cell.

In a meter bridge, as shown in the figure, it is given that resistance $$Y=12.5\Omega$$ and that the balance is obtained at a distance $$39.5$$ $$cm$$ from end $$A$$ (by Jockey J). After interchanging the resistances $$X$$ and $$Y$$, a new balance point is found at a distance $$l_2$$ from end $$A.$$ What are the value of $$X$$ and $$l_2$$ ?

In the given circuit all resistances are of value $$R$$ $$ohm$$ each. The equivalent resistance between $$A$$ and $$B$$ is :

A copper rod of cross-sectional area A carries a uniform current I through it. At temperature T, if the volume charge density of the rod is $$\rho$$, how long will the changes take to travel a distance d ?

A constant voltages is applied between two ends of a metallic wire. If the length is halved and the radius of the wire is doubled, the rate of heat developed in the wire will be :

In a circuit for finding the resistance of a galvanometer by half deflection method, a 6 V battery and a high resistance of 11 k$$\Omega$$ are used. The figure of merit of the galvanometer is 60 $$\mu A/$$division. In the absence of shunt resistance, the galvanometer produces a deflection of $$\theta$$ = 9 divisions when current flows in the circuit. The value of the shunt resistance that can cause the deflection of $$\theta /2,$$ is closest to :

A proton of mass m collides elastically with a particle of unknown mass at rest. After the collision, the proton and the unknown particle are seen moving at an angle of 90o with respect to each other. The mass of unknown particle is :

The mass of a hydrogen molecule is 3.32 $$\times$$ 10-27 kg. If 1023 hydrogen molecules strike, per second, a fixed wall of area 2 cm2 at an angle of 45o to the normal, and rebound elastically with a speed of 103 m/s, then the pressure on the wall is nearly: