A charge Q is uniformly distributed over a long rod AB of length L as shown in the figure. The electric potential at the point O, lying at a distance L from the end A, is

Materials suitable for making electromagnets should have

A radio transmitter operates at a frequency of 880 kHz and a power of 10 kW. What is the approximate number of photons emitted per second?

A parallel plate capacitor is made of two circular plates separated by a distance of 5 mm and with a dielectric of dielectric constant 2.2 between them. When the electric field in the dielectric is 3 × 10⁴ V/m, the charge density of the positive plate will be close to

An infinite number of charges, each equal to q, are placed along the x-axis at x = 1, x = 2, x = 4, x = 8, and so on. If the consecutive charges have opposite signs, then the electric field at x = 0 would be

A circular loop of radius 0.3 cm lies parallel to a much bigger circular loop of radius 20 cm. The centre of the small loop is on the axis of the bigger loop. The distance between their centres is 15 cm. If a current of 2.0 A flows through the smaller loop, then the flux linked with bigger loop is

Brakes of automobiles do not work well during rainy season because

A thin wire of length L and mass M is bent to form a semicircle. What is the magnitude of gravitational field at the centre?

A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats γ. It is moving with speed v and is suddenly brought to rest. Assuming no heat is lost to the surroundings, its temperature increases by

Two cars of masses m₁ and m₂ are moving in circles of radii r₁ and r₂, respectively. Their speeds are such that they make complete circles in the same time t. The ratio of their centripetal acceleration is

For a paramagnetic material, the dependence of magnetic susceptibility X on absolute temperature is given by the relation

Assume that a drop of liquid evaporates by decrease in its surface energy, so that its temperature remains unchanged. What should be the minimum radius of the drop for this to be possible?
(The surface tension is T, density of liquid is ρ and L is its latent heat of vaporisation)

For a given velocity, a projectile has the same range 'R' for two angles of projection. If 't₁' and 't₂' are the times of flight in the two cases, then

A wooden wheel of radius R is made of two semicircular parts (see figure).

The two parts are held together by a ring made of a metal strip of cross-sectional area S and length L. L is slightly less than 2πR. To fit the ring on the wheel, it is heated so that its temperature rises by ΔT and it just steps over the wheel. As it cools down to surrounding temperature, it presses the semi-circular parts together. If the coefficient of linear expansion of the metal is α and its Young's modulus is Y, the force that one part of the wheel applies on the other part is

Simple harmonic vibrations x₁ = 8 sin ωt, x₂ = 6 sin (ωt + π/2), x₃ = 4 sin (ωt + π) and x₄ = 2 sin (ωt + 3π/2) are superimposed on one another. The resulting amplitude and its phase difference with x₁ are

Three rods of copper, brass and steel are welded together to form a Y-shaped structure. Area of cross-section of each rod = 4 cm². End of copper rod is maintained at 100°C whereas ends of brass and steel are kept at 0°C. Lengths of the copper, brass and steel rods are 46, 13 and 12 cm, respectively. The rods are thermally insulated from surroundings, except at ends. Thermal conductivities of copper, brass and steel are 0.92, 0.26 and 0.12 CGS units, respectively. Rate of heat flow through copper rod is

Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are 3% each, then error in the value of resistance of the wire is

A pipe of length 85 cm is closed from one end. Find the number of possible natural oscillations of air column in the pipe whose frequency lie below 1250 Hz.
(The velocity of sound in air is 340 m s^-1)

This question has Statement 1 and Statement 2. Of the four choices given after the statements, choose the one that best describes the two statements.

If two springs S₁ and S₂ of force constants k₁ and k₂, respectively, are stretched by the same force, then it is found that more work is done on spring S₁ than on spring S₂.

Statement 1: If stretched by the same amount, work done on S₁ will be more than that on S₂.
Statement 2: k₁ < k₂

In a large building, there are 15 bulbs of 40 W, 5 bulbs of 100 W, 5 fans of 80 W and 1 heater of 1 kW. The voltage of the electric main is 220 V. The minimum capacity of the main fuse of the building will be (Key in the integral value, in Amperes)

Assume that a neutron breaks into a proton and an electron. The energy released during this process is (Answer up to two decimal places, in MeV)
(Mass of neutron = 1.6725 × 10^-27 kg, mass of proton = 1.6725 × 10^-27 kg and mass of electron = 9 × 10^-31 kg)

The resistance of a wire is 5 ohm at 50°C and 6 ohm at 100°C. The resistance of the wire at 0°C will be (in ohm)

A particle of mass m moves along line PC with velocity v as shown. The angular momentum of the particle about P is nmvr. What is the value of n?

In an AC circuit, the voltage applied is E = E₀ sin ωt. The resulting current in the circuit is I = I₀ sin . The power consumption in the circuit will be (in Watt)

An excess of AgNO₃ is added to 100 mL of a 0.01 M solution of dichlorotetraaquachromium (III) chloride. The number of moles of AgCl precipitate would be

The compressibility of a gas is less than unity at STP. Therefore,

When beryllium is bombarded with α-particles, extremely penetrating radiations which cannot be deflected by electrical or magnetic field are given out. These are

If an electron is transferred from A to B forming ions A⁺ and B^-, then the reaction is possible when

For the reaction X₂O₄(ℓ) → 2XO₂(g), ΔU = 2.1 kcal and ΔS = 20 cal K^-1 at 300 K. Hence, ΔG is

At temperature 327°C and concentration C, the osmotic pressure of a solution is P. The same solution at concentration C/2 and temperature 427°C shows the osmotic pressure of 2 atm. What will be the value of P?

In the table, 1 litre each of the two solutions X and Y is given and to coagulate each one of them, the numbers of millimoles of NaCl and MgCl₂ are also shown.

From the options, choose the value which is not reasonable for the amount of other salt required to cause precipitation.

If four moles of electrons are transferred from anode to cathode in an experiment on electrolysis of water, then the total volume of the two gases produced at STP will be

The decomposition of dinitrogen pentaoxide following the first order kinetics is given by

N₂O₅ → 4NO₂ (g) + O₂ (g)

0.2 mole of N₂O₅ is taken in a vessel of 1 L capacity and heated to a certain temperature (K) at which reaction begins. The concentration of N₂O₅ is measured at different intervals of time by withdrawing samples of reaction mixture. A plot of ln [N₂O₅] v/s time is shown in figure below:

If the value of rate constant k is determined from slope of linear plot and the slope of straight line is -5 × 10^-2 min^-1, then what is the half-life of the reaction?

Which of the following will have the highest coagulating power for a ferric hydroxide solution?

To an aqueous solution of AgNO₃, some NaOH (aq) is added till a brown precipitate is obtained. To this, H₂O₂ is added drop-wise. The precipitate turns black with the evolution of O₂. The black precipitate is

On hydrolysis, (Me)₂SiCI₂ will produce

[X] + H₂SO₄ → [Y], a colourless gas with irritating smell.
[Y] + K₂Cr₂O₇ + H₂SO₄ → Green solution.
[X] and [Y] are

Among the following complexes, the one which shows zero crystal field stabilisation energy (CFSE) is

Photochemical smog formed in congested metropolitan cities mainly consists of

The hybridisation of nitrogen I and that of nitrogen II in the following compound are:

Electrophile E^⊕ attacks benzene ring to generate the intermediate σ-complex. Which of the following σ-complexes is of lowest energy?

 Identify Z in the following reaction series.

Identity Z in the following sequence of reactions.

CH₂CH₂CH=CH₂ Z

Which of the following are substituted purines?

a. Adenine
b. Uracil
c. Guanine
d. Cytosine

What should be the molarity of the solution of sodium acetate to be added to a 0.1 M solution of CH₃COOH to give a solution of pH = 5.5?
(pK_a of CH₃COOH = 4.5)
The answer should be expressed in two significant figures.

CaC₂O₄ (Molecular weight = 128), on dissolving in distilled water, forms a saturated solution?
[K_sp(CaC₂O₄) = 2.5 x 10^-9 mol²L^-2]
The mass of CaC₂O₄ in 1L of the saturated solution = M × 10^-5 g
The value of 'M' is

Consider the following reaction that follows the first order kinetics:

[Given: Initial pressure of CH₃CHO = 80 mm of Hg and total pressure at the end of 20 min = 120 mm of Hg]
The rate constant for the reaction = Y × 10^-3 min^-.
The value of 'Y' (upto two decimal places) is

If 58 ml of   is used to neutralise ammonia given by 1 g of an organic compound, then the percentage of nitrogen in the compound is

Boiling point of a solution of 0.11 g of a substance in 15 g of ether was found to be 0.1°C higher than that of pure ether. The molecular weight of the substance(closest whole number value in g mol^-1) will be
(K_b = 2.16 K kg mol^-1)