Three charges e, e and - 2e are placed at the corners of the triangle as shown. The net dipole moment of the system is

A mass is attached to one end of a spring of spring constant k. The spring is stretched and then released such that its amplitude of oscillation is A. For a displacement y from the mean position, if the kinetic energy is 44% of its potential energy, then y in terms of A is

At a given instant there are 25% of undecayed radioactive nuclei in a sample. After 20s, the number of undecayed nuclei reduces to 12.5%. The extra time required in which the number of undecayed nuclei will further reduce to 3.125% of the sample is-

The escape velocity for an atmospheric particle 2000 km above the earth's surface is (Radius of the earth = 6.4 x 10⁶ m and g = 10 m s^{- 2} )

A circular disc of radius r and thickness r/6 has moment of inertia I about an axis passing through its centre and perpendicular to its plane. It is melted and recasted to a solid sphere. The moment of inertia of the sphere about its diameter as axis of rotation is

When an UV light of 10¹⁵ Hz and intensity 2 W/m² is directed at a metal surface, photoelectrons emitted were found to have a maximum kinetic energy of 1.6 eV. If the work functions for different materials are as follows: Potassium 2.2 eV, Sodium 2.3 eV, Lithium 2.5 eV and Calcium 3.2 eV, identify the metal in the given problem.

Two sources of sound S₁ and S₂ each emitting waves of wavelength A are kept symmetrically on either side of the centre 0 of a circle ABCD such that S₁O = S₂O = K . When the detector is moved along the circumference of the circle, the number of maxima recorded by the detector in one revolution is

A boat capable of a speed v in still water wants to cross a river of width d. The speed of the water current increases linearly from zero at either bank to a maximum of u at the middle of the river. When the boat is rowed at right angles to the bank, its downstream drift is

Figure shows the plot of a potential energy function of a conservative system U versus x. Which of the following statements is correct ?

A sphere with some cavity has outer radius R. It rolls down an inclined plane without slipping and attains a speed v at the bottom. When this sphere slides down without rolling on the frictionless inclined plane of same height its speed at the bottom is 5v/4. The radius of gyration of the sphere is

The antenna current of an AM transmitter is 8 A when only carrier wave is sent but the current increases to 8.88 A when the carrier wave is sinusoidally modulated. The percentage of modulation is

A square metal wire loop of side 20 cm and resistance 1 Ω is moved with a constant velocity Vo in a uniform magnetic field of induction B = 4 Wb/m². The magnetic field lines are perpendicular to the plane of the loop and directed inwards. The loop is connected to a network of resistors each of value 2 Ω . The resistance of load wires AB and CD are negligible. To get a current of 2 mA in the loop, the speed of motion of the loop is

Four identical hollow cylindrical columns of steel, support a big structure of mass 60,000 kg. The inner and outer radii of each column are 40 cm and 50 cm respectively. When the load distribution is uniform, the compressional strain on each column is (Young’s modulus of steel is 2 x 10¹¹ Pa)

A steel ball of mass 60 g falls from a height 0.8 m on the horizontal surface of a massive slab. The coefficient of restitution between the ball and the slab is e = 0.4; the total momentum imparted to the slab by the ball after numerous bounces is

In nuclear reaction, energy released per fission is 200 MeV. When uranium 235 is used as nuclear fuel in a reactor having a power level of 1 MW, the amount of fuel needed in 30 days will be

The temperature at which the speed of sound in oxygen will be same as the speed of sound in nitrogen at 25 °C-

An alternating voltage having frequency of 50 cycles/sec and maximum voltage 220 V is supplied to a circuit containing a pure inductance of 0.02 H and a pure resistance of 10 Ω in series. The value of maximum current in circuit is-

A beam of light traveling in water strikes a glass plate which is also immersed in water. When the angle of incidence is 50 ° the reflected beam is found to be plane polarised. The refractive index of water is 4/3. The refractive index of the glass plate is (Given tan 50 ° = 1.198)

A reversible heat engine converts one fourth of heat input into work. When the temperature of the sink is reduced by 200 K, its efficiency is doubled. The temperature of the source is

A man pulls a loaded sledge of mass 60 kg along a horizontal surface at constant velocity as shown in figure. The coefficient of kinetic friction between the sledge and the surface is 0.15. The tension in the rope during pulling when it makes an angle of cp = 40 ° with the horizontal is (cos 40 0 = 0.766, sin 40 ° = 0.643 and g = 10 ms'2)

Gravitational acceleration on the surface of planet is where  is the gravitational acceleration on the surface of earth. The average mass density of the planet is 2/3 times that of the earth. If escape speed on the surface of the earth is taken to be 11kms^–1, escape speed on the surface of the planet in kms^–1, will be:

A point object ‘O’ is placed in a medium of refractive index μ₁ = 1.4. S₁ and S₂ are two concentric spherical surfaces of radii 1m and 2m. To the right of ‘O’ contains a medium of refractive index μ₂ = 1.5 between the interfaces S₁ and S₂. Find the object distance of O form S₁ (in meter) so that an image of ‘O’ as seen by observer from air, coincides with O.

A radioactive substance A decays in to B. It is known that only A is present at t = 0. Find the number of half lives at which the probability of getting B in the mixture is 15 times that of finding A, if we pick out randomly from the sample.

A single electron orbits round a stationary nucleus of charge Ze, where Z is a constant and - e is the electron charge. It is observed that it requires 47.2 eV to excite the electron from second Bohr orbit to third orbit. Then to ionise the atom from ground state, required wavelength of electromagnetic(EM) radiations is found to be 4nÅ. Find the value of n. [Take energy of electron in ground state of hydrogen atom is - 13.6 eV.]

An inductor L = 50 mH carrying an initial current l₀ = 2.5 amp is connected across a non linear resistor. The voltage across resistor is related to current as V = 10 l². After how much time (in ms) current through inductor becomes 1.25 amp.

Copper reduces  into NO and NO₂ depending upon concentration of HNO₃ in solution. Assuming  [Cu²⁺] = 0.1M, and P_NO = P_NO2 = 10^–3 bar. At which concentration of HNO₃, thermodynamic tendency for reduction of  into NO and NO₂ by copper is same?

A radioactive material (t_1/2 = 30 days) gets spilled over the floor of a room. If initial activity is ten times the permissible value, after how many days will it be safe to enter the room

A mixture of all possible stereoisomers from the above structure is subjected to fractional distillation, which of the following statements is correct

Which of the following about SF₄, SOF₄ and COF₂ molecules is correct?

B₂O₃ substitutes nonmetal oxides from several metal salts because

Which of these is most stable?

The correct statement regarding various types of molecular speeds are

The compounds that should be used to prepare glycine and β – alanine by Gabriel phthalimide synthesis are

In which of these compounds, Nitrogen can be estimated by Duma’s method?

A black mineral (A) in solid state is fused with KOH and KNO₃ and the mixture extracted with water to get a green coloured solution (B). On passing CO₂ gas through the solution the colour changes to pink with a black residue (C). Which of the following is/are correct

A is

Formation of “B” through the attack of first two reagents involve respectively

Product “C” is

A white substance (A) reacts with dilute H₂SO₄ to produce a colourless gas (B) and a colourless solution (C). The reaction between (B) and acidified K₂Cr₂O₇ solution produces a green solution and a slightly coloured precipitate (D). The substance (D) burns in air to produce a gas (E), which reacts with (B) to yield (D) and a colourless liquid. Anhydrous copper sulphate is turned blue on addition of this colourless liquid. Addition of aqueous NH₃ or NaOH to (C) produces first a precipitate which dissolves in the excess of the respective reagent to produce a clear solution in each case (B) and (D) are respectively

A white substance (A) reacts with dilute H₂SO₄ to produce a colourless gas (B) and a colourless solution (C). The reaction between (B) and acidified K₂Cr₂O₇ solution produces a green solution and a slightly coloured precipitate (D). The substance (D) burns in air to produce a gas (E), which reacts with (B) to yield (D) and a colourless liquid. Anhydrous copper sulphate is turned blue on addition of this colourless liquid. Addition of aqueous NH₃ or NaOH to (C) produces first a precipitate which dissolves in the excess of the respective reagent to produce a clear solution in each case

The precipitate obtained by addition of aqueous NH₃ or NaOH to (C) initially is _____ which dissolves in excess reagent to produce ________

Which of the following is correct regarding solutions of sodium metal in liquid ammonia.

For the given reaction the correct statement is

Choose the correct option

For the cell (at 1 bar H₂ pressure) Pt/H₂(g) H X (m₁), NaX(m₂), NaCl(m₃)/AgCl/Ag/Pt it is found that the value of E  approaches 0.2490 in the limit of zero concentration. Calculate  for the acid HX at 27°C. (R = 8.3 Jmole^–1K^–1, F = 96500C)

During the titration of 100 ml of a weak monobasic acid solution using 0.1 M NaOH, the solution became neutral at 40 mL addition of NaOH and equivalence point was obtained at 50 mL NaOH addition. The K_a of the acid is (log 2 = 0.3)

The sum of no of cyclic transition states and intermediates in the above reaction during the formation of product is/are....

How many carbon atoms (In A, B and (c) changed their hybridization till the formation of D? (Consider each reaction and do not consider stereoisomerism)

No of stereoisomers possible for X is

Index of hydrogen of the major product is….

No of 1° carbons in product is …..