A 50 $$\Omega $$ resistance is connected to a battery of 5 V. A galvanometer of resistance 100 $$\Omega $$ is to be used as an ammeter to measure current through the resistance, for this a resistance r_s is connected to the galvanometer. Which of the following connections should be employed if the measured current is within 1% of thecurrent without the ammeter in the circuit ?

Which of the following option correctly describes the variation of the speed v and acceleration ‘a’ of a point mass falling vertically in a viscous medium that applies a force F = − kv, where ‘k’ is a constant, on the body ? (Graphs are schematic and not drawn to scale)

Figure shows elliptical path abcd of a planet around the sun S such that the area of triangle csa is $${1 \over 4}$$ the area of the ellipse. (See figure) With db as the semimajor axis, and ca as the semiminor axis. If t₁ is the time taken for planet to go over path abc and t₂ for path taken over cda then :

To find the focal length of a convex mirror, a student records the following data :

Object Pin	Convex Lens	Convex Mirror	Image Pin
22.2 cm	32.2 cm	45.8 cm	71.2 cm

The focal length of the convex lens is f₁ and that of mirror is f₂. Then taking index correction to be negligibly small, f₁ and f₂ are close to :

A simple pendulum made of a bob of mass m and a metallic wire of negligible mass has time period 2 s at T=0^oC. If the temperature of the wire is increased and the corresponding change in its time period is plotted against its temperature, the resulting graph is a line of slope S. If the coefficient of linear expansion of metal is $$\alpha $$ then the value of S is :

A uniformly tapering conical wire is made from a material of Young’s modulus Y and has a normal, unextended length L. The radii, at the upper and lower ends of this conical wire, have values R and 3 R, respectively. The upper end of the wire is fixed to a rigid support and a mass M is suspended from its lower end. The equilibrium extended length, of this wire, would equal :

The truth table given in fig. represents :

A	B	Y
0	0	0
0	1	1
1	0	1
1	1	1

In Young’s double slit experiment, the distance between slits and the screen is 1.0 m and monochromatic light of 600 nm is being used. A person standing near the slits is looking at the fringe pattern. When the separation between the slits is varied, the interference pattern disappears for a particular distance d₀ between the slits. If the angular resolution of the eye is $$({{{1}} \over {60}})^o$$, the value of d₀ is close to :

Microwave oven acts on the principle of :

When photons of wavelength $${\lambda _1}$$ are incident on an isolated sphere, the corresponding stopping potential is found to be V. When photons of wavelength $${\lambda _2}$$ are used, the corresponding stopping potential was thrice that of the above value. If light of wavelength $${\lambda _3}$$ is used then find the stopping potential for this case :

A hydrogen atom makes a transition from n = 2 to n = 1 and emits a photon. This photon strikes a doubly ionized lithium atom (z = 3) in excited state and completely removes the orbiting electron. The least quantum number for the excited state of the ion for the process is :

The potential (in volts) of a charge distribution is given by.

V(z) = 30 $$-$$ 5x² for $$\left| z \right|$$ $$ \le $$ 1 m.
V(z) = 35 $$-$$ 10 $$\left| z \right|$$ for $$\left| z \right|$$ $$ \ge $$1 m.

V(z) does not depend on x and y. If this potential is generated by a constant charge per unit volume $${\rho _0}$$ (in units of $${\varepsilon _0}$$) which is spread over a certain region, then choose the correct statement.

A magnetic dipole is acted upon by two magnetic fields which are inclined to each other at an angle of 75^o. One of the fields has a magnitude of 15 mT. The dipole attains stable equilibrium at an angle of 30^o with this field. The magnitude of the other field (in mT ) is close to

Three capacitors each of 4 $$\mu $$F are to be connected in such a way that the effective capacitance is 6 $$\mu $$F. This can be done by connecting them :

Two particles are performing simple harmonic motion in a straight line about the same equilibrium point. The amplitude and time period for both particles are same and equal to A and I, respectively. At time t = 0 one particle has displacement A while the other one has displacement $${{ - A} \over 2}$$ and they are moving towards each other. If they cross each other at time t, then t is :

200 g water is heated from 40^oC to 60^oC. Ignoring the slight expansion of water, the change in its internal energy is close to (Given specific heat of water = 4184 J/kg/K) :

The ratio of work done by an ideal monoatomic gas to the heat supplied to it in an isobaric process is :

A cubical block of side 30 cm is moving with velocity 2 ms⁻¹ on a smooth horizontal surface. The surface has a bump at a point O as shown in figure. The angular velocity (in rad/s) of the block immediately after it hits the bump, is :

A car of weight W is on an inclined road that rises by 100 m over a distance of 1 km and applies a constant frictional force $${W \over 20}$$ on the car. While moving uphill on the road at a speed of 10 ms⁻¹, the car needs power P. If it needs power $${p \over 2}$$ while moving downhill at speed v then value of $$\upsilon $$ is :

In the following ‘I’ refers to current and other symbols have their usual meaning. Choose the option that corresponds to the dimensions of electrical conductivity :

A rocket is fired vertically from the earth with an acceleration of 2g, where g is the gravitational acceleration. On an inclined plane inside the rocket, making an angle $$\theta $$ with the horizontal, a point object of mass m is kept. The minimum coefficient of friction $$\mu $$_min between the mass and the inclined surface such that the mass does not move is :

A convex lens, of focal length 30 cm, a concave lens of focal length 120 cm, and aplane mirror are arranged as shown. For an object kept at a distance of 60 cm from the convex lens, the final image, formed by the combination, is a real image, at a distance of :

A series LR circuit is connected to a voltage source with
V(t) = V₀ sin$$\Omega $$t. After very large time, current I(t) behaves as
(t₀ >> $${L \over R}$$) :

An experiment is performed to determine the I - V characteristics of a Zener diode, which has a protective resistance of R = 100 $$\Omega $$, and a maximum power of dissipation rating of 1 W. The minimum voltage range of the DC source in the circuit is :

Consider a water jar of radius R that has water filled up to height H and is kept on astand of height h (see figure). Through a hole of radius r (r << R) at its bottom, the water leaks out and the stream of water coming down towards the ground has a shape like a funnel as shown in the figure. If the radius of the cross-section of water stream when it hits the ground is x. Then :

In the circuit shown, the resistance r is a variable resistance. If for r = fR, the heat generation in r is maximum then the value of f is :

To know the resistance G of a galvanometer by half deflection method, a battery of emf V_E and resistance R is used to deflect the galvanometer by angle $$\theta $$. If a shunt of resistance S is needed to get half deflection then G, R and S are related by the equation :