Find the distance of the image from object O, formed by the combination of lenses in the figure :

Curved surfaces of a plano-convex lens of refractive index $$\mu$$1 and a plano-concave lens of refractive index $$\mu$$2 have equal radius of curvature as shown in figure. Find the ratio of radius of curvature to the focal length of the combined lenses.

An object is placed at the focus of concave lens having focal length f. What is the magnification and distance of the image from the optical centre of the lens?

Two plane mirrors M1 and M2 are at right angle to each other shown. A point source 'P' is placed at 'a' and '2a' meter away from M1 and M2 respectively. The shortest distance between the images thus formed is : (Take $$\sqrt{5}$$ = 2.3)

A glass tumbler having inner depth of 17.5 cm is kept on a table. A student starts pouring water ($$\mu$$ = 4/3) into it while looking at the surface of water from the above. When he feels that the tumbler is half filled, he stops pouring water. Up to what height, the tumbler is actually filled?

A current through a wire depends on time as i = $$\alpha$$0t + $$\beta$$t2 where $$\alpha$$0 = 20 A/s and $$\beta$$ = 8 As$$-$$2. Find the charge crossed through a section of the wire in 15 s.

A cell E1 of emf 6V and internal resistance 2$$\Omega$$ is connected with another cell E2 of emf 4V and internal resistance 8$$\Omega$$ (as shown in the figure). The potential difference across points X and Y is :

Five equal resistances are connected in a network as shown in figure. The net resistance between the points A and B is :

A wire of 1$$\Omega$$ has a length of 1 m. It is stretched till its length increases by 25%. The percentage change in resistance to the nearest integer is :

A conducting wire of length 'l', area of cross-section A and electric resistivity $$\rho$$ is connected between the terminals of a battery. A potential difference V is developed between its ends, causing an electric current. If the length of the wire of the same material is doubled and the area of cross-section is halved, the resultant current would be :

A resistor develops 500 J of thermal energy in 20 s when a current of 1.5A is passed through it. If the current is increased from 1.5A to 3A, what will be the energy developed in 20 s.

A current of 10A exists in a wire of cross-sectional area of 5 mm2 with a drift velocity of 2 $$\times$$ 10$$-$$3 ms$$-$$1. The number of free electrons in each cubic meter of the wire is ___________.

Two cells of emf 2E and E with internal resistance r1 and r2 respectively are connected in series to an external resistor R (see figure). The value of R, at which the potential difference across the terminals of the first cell becomes zero is

The four arms of a Wheatstone bridge have resistances as shown in the figure. A galvanometer of 15$$\Omega$$ resistance is connected across BD. Calculate the current through the galvanometer when a potential difference of 10V is maintained across AC.

In the experiment of Ohm's law, a potential difference of 5.0 V is applied across the end of a conductor of length 10.0 cm and diameter of 5.00 mm. The measured current in the conductor is 2.00 A. The maximum permissible percentage error in the resistivity of the conductor is :

A current of 5 A is passing through a non-linear magnesium wire of cross-section 0.04 m2. At every point the direction of current density is at an angle of 60$${}^{\circ }$$ with the unit vector of area of cross-section. The magnitude of electric field at every point of the conductor is : (Resistivity of magnesium $$\rho$$ = 44 $$\times$$ 10$$-$$8 $$\Omega$$m)

The value of current in the 6 $$\Omega$$ resistance is :

A Copper (Cu) rod of length 25 cm and cross-sectional area 3 mm2 is joined with a similar Aluminium (Al) rod as shown in figure. Find the resistance of the combination between the ends A and B. (Take Resistivity of Copper = 1.7 $$\times$$ 10$$-$$8 $$\Omega$$m and Resistivity of Aluminium = 2.6 $$\times$$ 10$$-$$8 $$\Omega$$m)

In the given figure, there is a circuit of potentiometer of length AB = 10 m. The resistance per unit length is 0.1 $$\Omega$$ per cm. Across AB, a battery of emf E and internal resistance 'r' is connected. The maximum value of emf measured by this potentiometer is :

In the given potentiometer circuit arrangement, the balancing length AC is measured to be 250 cm. When the galvanometer connection is shifted from point (1) to point (2) in the given diagram, the balancing length becomes 400 cm. The ratio of the emf of two cells, {{{\varepsilon _1}} \over {{\varepsilon _2}}} is :