The phase difference between the alternating current and emf is π/2. Which of the following cannot be the constituent of the circuit?

A radar has a power of 1 kW and is operating at a frequency of 10 GHz. It is located on a mountain top of height 500 m. The maximum distance up to which it can detect an object located on the surface of Earth is: (Radius of Earth = 6.4 × 10⁶ m)

A spherical shell, made of a material of electrical conductivity 10⁹/π (Ω m)^-1, has thickness t = 2 mm and radius R = 10 cm. In an arrangement, its inside surface is kept at a lower potential than its outside surface. The resistance offered by the shell is equal to

The following question contains statement-1 and statement-2. Of the four choices given, choose the one that best describes the two statements.

Statement-1: For a mass M kept at the centre of a cube of side a, the flux of gravitational field passing through its sides is 4πGM.
Statement-2: If the direction of a field due to a point source is radial and its dependence on the distance r from the source is given as 1/r², its flux through a closed surface depends only on the strength of the source enclosed by the surface and not on the size or shape of the surface.

A solid conducting sphere of radius 10 cm is enclosed by a thin metallic shell of radius 20 cm. A charge q = 20 μC is given to the inner sphere. What is the heat generated in the process when the inner sphere is connected to the shell by a conducting wire?

When the current in the portion of the circuit, shown in the figure, is 2 A and is increasing at the rate of 1 A/s, then the measured potential difference V_ab is 8 V. However, when the current is 2 A and is decreasing at the rate of 1 A/s, the measured potential difference V_ab is 4V. The values of R and L are

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An electromagnetic wave in vacuum has the electric and magnetic fields , which are always perpendicular to each other. The direction of polarisation is given by  and that of wave propagation by . Then,

Identify the wrong statement.

If C_P and C_V denote the specific heats of nitrogen per unit mass at constant pressure and constant volume, respectively, then

A particle of mass m is at rest at the origin at time t = 0. It is subjected to a force F(t) = F₀e^-bt in the x direction.

Which of the following curves depicts its speed v(t)?

There is a circular tube in a vertical plane. Two immiscible liquids having densities d₁ and d₂ are filled in the tube. Each liquid subtends 90° angle at the centre. The radius joining their interface makes an angle α with the vertical.
The ratio d¹/d² is equal to

A wire elongates by l mm when a load W is hanged from it. If the wire goes over a pulley and two weights W each are hung at the two ends, the elongation of the wire will be (in mm)

A 2 m wide truck is moving with a uniform speed v₀ = 8 m/s along a straight horizontal road. A pedestrian starts to cross the road with a uniform speed v when the truck is 4 m away from him. The minimum value of v so that he can cross the road safely is

Two particles, A and B, of equal masses are suspended from two massless springs of spring constants k₁ and k₂, respectively. If the maximum velocities, during oscillations, are equal, then the ratio of amplitudes of A and B is

The |u| - |v| graph for a concave mirror is as shown in figure. Here, |u| > |f|. If a line passing through the origin of slope 1 cuts the graph at point P, then the co-ordinates of point P are

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At some instant, a particle is moving along a straight line 2x - 3y = 2 and its co-ordinates on that line are (4, 2). Now, at another instant, the same particle is moving along a straight line 3x + 4y = 7 and its co-ordinates are (1, 1). Find the co-ordinates of that axis about which it is in pure rotation.

A solid cylinder of mass M and radius R is mounted on a frictionless horizontal axle, so that it can freely rotate about this axis. A string of negligible mass is wrapped round the cylinder and a body of mass m is hung from the string as shown in the figure. The mass is released from rest.

The acceleration with which the mass will fall is

The amplitude of wave disturbance propagating in the positive x-axis is given by y = 1/1+x² at t = 0 and y =  at t = 2s, where x and y are in metres. The shape of the disturbance does not change during the propagation. The velocity of the wave is

A particle of mass m is moving in a circular path of constant radius r, such that its centripetal acceleration a_c is varying with time t as a_c = k² rt², where k is a constant. The power delivered to the particle by the force acting on it is

A battery of internal resistance 4Ω is connected to the network of resistances as shown. In order that the maximum power can be delivered to the network, the value of R in Ω should be

Ultraviolet light of wavelength 300 nm and intensity 1.0 Wm^-2 falls on the surface of a photosensitive material. If one percent of the incident photons produce photoelectrons, then the number of photoelectrons emitted from an area of 1.0 cm² of the surface is nearly p × 10¹² s-1. The value of p is (Answer up to one decimal place)

In a transformer, the number of turns in the primary coil is 140 and that in the secondary coil is 280. If current in the primary coil is 4 A, then that in the secondary coil is

The electrical conductivity of a semiconductor increases when electromagnetic radiation of wavelength shorter than 2480 nm is incident on it. The band gap (in eV) for the semiconductor is (Answer up to one decimal place)

A Carnot engine, whose efficiency is 40%, takes in heat from a source maintained at a temperature of 500 K. It is desired to have an engine of efficiency 60%. Then, the intake temperature for the same exhaust (sink) temperature (in K) must be

1 L mixture of C₃H₈ and C₅H₁₂ is completely reacted with O₂ to produce 3.5 L of CO₂. Find the respective volumes of C₃H₈ and C₅H₁₂ in the mixture, when all the volumes are measured under similar conditions of temperature and pressure.

The ionisation energy of hydrogen in ground state is X kJ. The energy required for an electron to jump from the second orbit to the third orbit is

Which of the following nuclear reactions can be represented as p-d type reaction?

Consider the different types of hybridisations listed below.

dsp², sp³d, dsp³ and sp³d²

They have at least one 90° angle between the bond pair-bond pair electrons involved in the respective structures.

Which of the following hybridisations has the maximum number of 90° angles between its bond pair-bond pair electrons?

At 25°C, the solubility product of Mg(OH)₂ is 1.0 × 10^-11. At which pH will Mg²⁺ ions start precipitating in the form of Mg(OH)₂ from a solution of 0.001 M Mg²⁺ ions?

For the coagulation of ferric hydroxide solution, what will be the increasing order of effectiveness of the given electrolytes?

(a) SnCl₄
(b) CaSO₄
(c) AlPO₄
(d) K₄Fe(CN)₆

Which of the following statements is incorrect?

During the separation of Group IV metal ions as insoluble carbonates by adding a saturated solution of (NH₄)₂CO₃ to the solution of the sample in an ammoniacal medium containing excess of NH₄Cl, Mg²⁺ is not precipitated either as Mg(OH)₂ or as MgCO₃ because

Sulphur reacts with chlorine in the ratio 1 : 2 and forms X. Hydrolysis of X gives a sulphur compound Y. What are the structure and hybridisation of anion of Y?

Smog is essentially caused by the presence of

In the following reaction, what is X?

Which of the following sequences of reactions (reagents) can be used for the conversion of C₆H₅CH₂CH₃ into C₆H₅CH=CH₂?

The increasing order of the rates of HCN addition to compounds A - D is

(A) HCHO
(B) CH₃COCH₃
(C) PhCOCH₃
(D) PhCOPh

Compound 'A', on heating with ammonia, gives compound 'B' which on treating with conc. H₂SO₄ gives compound 'C'. This compound 'C' on reduction gives ethyl amine. What is compound 'A'?

Which of the following orders of amine in terms of basic nature in aqueous solution is correct?

Which of the following statements are true?

(A) Sucrose is a non-reducing sugar.
(B) Glucose is oxidised by bromine water.
(C) Glucose rotates plane polarised light in the clockwise direction.
(D) Fructose is oxidised by bromine water.

The number of P-O-P bridges in the structures of phosphorus pentoxide and phosphorus trioxide is

Consider a titration of potassium dichromate solution with acidified Mohr's salt solution using diphenylamine as indicator. The number of moles of Mohr's salt required per mole of dichromate is

Mixture X containing 0.02 mol of [Co(NH₃)₅SO₄]Br and 0.02 mol of [Co(NH₃)₅Br]SO₄ was prepared in 2 litre of solution.

1 litre of mixture X + Excess AgNO₃ → Y
1 litre of mixture X + Excess BaCl₂ → Z

Total number of moles of Y and Z are

Find out mole % of C in CH₄

5 mole of an ideal gas at 100 K (C_v,m = 28 J/mol/K) is heated to 200K.
R = 8 J K^-1 mol^-1.

The value of ΔU (in kJ) for the process is

The value of keq for the above reaction is 10^x The value of x is