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QUESTION: 1

Four identical particles of mass M are located at the corners of a square of side ‘a’. What should be their speed if each of them revolves under the influence of others’gravitational field in a circular orbit circumscribing the square?

Solution:

QUESTION: 2

Two particles move at right angle to each other. Their de Broglie wavelengths are λ_{1 } and λ_{2} respectively. The particles suffer perfectly inelastic collision. The de Broglie wavelength λ , of the final particle, is given by:

Solution:

QUESTION: 3

In SI units, the dimensions of

Solution:

QUESTION: 4

A particle moves in one dimension from rest under the influence of a force that varies with the distance travelled by the particle as shown in the figure. The kinetic energy of the particle after it has travelled 3 m is:

Solution:

Final K.E.=6.5 J

QUESTION: 5

An alternating voltage volt is applied to a purely resistive load of 50Ω . The time taken for the current to rise from half of the peak value to the peak value is:

Solution:

QUESTION: 6

A boy's catapult is made of rubber cord which is 42 cm long, with 6 mm diameter of cross-section and of negligible mass. The boy keeps a stone weighing 0.02 kg on it and stretches the cord by 20 cm by applying a constant force. When released, the stone flies off with a velocity of 20 ms-1. Neglect the change in the area of crosssection

of the cord while stretched. The Young's modulus of rubber is closest to:

Solution:

QUESTION: 7

The reverse breakdown voltage of a Zener diode is 5.6 V in the given circuit.

The current I_{z} through the Zener is:

Solution:

Current through 800

Current through 200

Then current I_{z} is 10 mA.

QUESTION: 8

Two identical beakers A and B contain equal volumes of two different liquids at 60°C each and left to cool down. Liquid in A has density of 8 x10^{2} kg/ m^{3} and specific heat of 2000J kg^{-1} K^{-}1 while liquid in B has density of 10^{3} kg m-3 and specific heat of 4000J kg^{-1}K^{-1}. Which of the following best describes their temperature versus time graph schematically? (Assume the emissivity of both the beakers to be the same)

Solution:

QUESTION: 9

A plane electromagnetic wave travels in free space along the x-direction. The electric field component of the wave at a particular point of space and time is E = 6 Vm^{-1} along y-direction. Its corresponding magnetic field component, B would be:

Solution:

Along z-direction

QUESTION: 10

A wire of length 2L, is made by joining two wires A and B of same length but different radii r and 2r and made of the same material. It is vibrating at a frequency such that the joint of the two wires forms a node. If the number of antinodes in wire A is p and that in B is q then the ratio p: q is:

Solution:

QUESTION: 11

Radiation coming from transitions n =2 to n=1 of hydrogen atoms fall on He+ ions in n=1 and n=2 states. The possible transition of helium ions as they absorb energy from the radiation is:

Solution:

For hydrogen,

For He^{+},

2 → 4 transition.

QUESTION: 12

For the circuit shown, with and the

potential difference between the points ’a' and ‘b’ is approximately (in V) :

Solution:

QUESTION: 13

Voltage rating of a parallel plate capacitor is 500 V. Its dielectric can withstand a maximum electric field of 10^{6} V/ m. The plate area is 10^{-4} m^{2}. What is the dielectric constant if the capacitance is 15 pF ?

Solution:

QUESTION: 14

A solid conducting sphere, having a charge Q, is surrounded by an uncharged conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be V. If the shell is now given a charge of -4 Q, the new potential difference between the same two surfaces is :

Solution:

Potential difference doesn’t change.

QUESTION: 15

A thin strip 10 cm long is on a U shaped wire of negligible resistance and it is connected to a spring of spring constant 0.5 Nm^{-1} (see figure). The assembly is kept in a uniform magnetic field of 0.1 T. If the strip is pulled from its equilibrium position and released, the number of oscillations it performs before its amplitude decreases by a factor of e is N. If the mass of the strip is 50 grams, its resistance 10 Ω . and air drag negligible, N will be close to :

Solution:

Force on oscillating wire if it’s speed v is

Time period T is

No. of oscillations is and t is given by

QUESTION: 16

An upright object is placed at a distance of 40 cm in front of a convergent lens of focal length 20 cm. A convergent mirror of focal length 10 cm is placed at a distance of 60 cm on the other side of the lens. The position and size of the final image will be:

Solution:

Actual final image (3^{rd} image) is formed at object itself with same size but according to the options best answer is taken for second image.

QUESTION: 17

A steel wire having a radius of 2.0 mm, carrying a load of 4 kg, is hanging from a ceiling. Given that g=3.1 πms^{-2} what will be the tensile stress that would be developed in the wire?

Solution:

QUESTION: 18

A thermally insulated vessel contains 150 g of water at 0°C. Then the air from the vessel is pumped out adiabatically. A fraction of water turns into ice and the rest evaporates at 0°C itself. The mass of evaporated water will be closest to: (Latent heat of vaporization of water = 2.10 x 10^{6}J kg^{-1} and Latent heat of Fusion of water =3.36x 10^{5}J kg^{-1})

Solution:

QUESTION: 19

A thin circular plate of mass M and radius R has its density varying as with as constant and r is the distance from its center. The moment of Inertia of the circular plate about an axis perpendicular to the plate and passing through its edge is

The value of the coefficient a is:

Solution:

QUESTION: 20

A 20 Henry inductor coil is connected to a 10 ohm resistance in series as shown in figure. The time at which rate of dissipation of energy (Joule's heat) across resistance is equal to the rate at which magnetic energy is stored in the inductor, is:

Solution:

QUESTION: 21

Four particles A, B, C and D with masses m_{A}=m, m_{B}=2m, m_{C}=3m and m_{D}=4m are at the corners of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles is:

Solution:

QUESTION: 22

A circular coil having N turns and radius r carries a current I. It is held in the XZ plane in a magnetic field The torque on the coil due to the magnetic field is:

Solution:

QUESTION: 23

If 10^{22} gas molecules each of mass 10^{-26} kg collide with a surface (perpendicular to it) elastically per second over an area 1 m^{2} with a speed 10^{4} m/s, the pressure exerted by the gas molecules will be of the order of :

Solution:

Pressure = 2Nm^{-2}

QUESTION: 24

In figure, the optical fiber is l=2 m long and has a diameter of d =20 μm. If a ray of light is incident on one end of the fiber at angle the number of reflections it makes before emerging from the other end is close to : (refractive index of fiber is 1.31 and sin 40^{0}= 0.64)

Solution:

x=d / tanθ_{2}

No. of collisions

QUESTION: 25

A 200Ω resistor has a certain color code. If one replaces the red color by green in

the code, the new resistance will be :

Solution:

In the given resistance 200Ω , 2 stands for red. If it is replaced by green, then the resistance becomes 500Ω .

QUESTION: 26

The bob of a simple pendulum has mass 2 g and a charge of 5.0μ C. It is at rest in a uniform horizontal electric field of intensity 2000 V/ m. At equilibrium, the angle that the pendulum makes with the vertical is (take g = 10 m/s^{2})

Solution:

QUESTION: 27

Ship A is sailing towards north-east with velocity where points east and north. Ship B is at a distance of 80 km east and 150 km north of Ship A and is sailing towards west at 10 km/hr. A will be at minimum distance from B in:

Solution:

Velocity of A w.r.t B is

QUESTION: 28

In an interference experiment the ratio of amplitudes of coherent waves is The ratio of maximum and minimum intensities of fringes will be:

Solution:

QUESTION: 29

Water from a pipe is coming at a rate of 100 liters per minute. If the radius of the pipe is 5 cm, the Reynolds number for the flow is of the order of : (density of water =1000 kg/m^{3}, coefficient of viscosity of water= 1 mPas)

Solution:

QUESTION: 30

The wavelength of the carrier waves in a modern optical fiber communication network is close to:

Solution:

Wavelength used for communication are 1300nm and 1500nm.

QUESTION: 31

For the reaction the values of initial rate at different reactant concentrations are given in the table below. The rate law for the reaction is:

Solution:

⇒ a =1

⇒b = 2

Therefore,

QUESTION: 32

The major product of the following reaction is:

Solution:

QUESTION: 33

If solubility product of is denoted by KSP and its molar solubility is denoted by S, then which of the following relation between S and KSP is correct ?

Solution:

Let “s” be the solubility, then

QUESTION: 34

Maltose on treatment with dilute HCI gives:

Solution:

Maltose on treatment with dil.HCl gives D-glucose.

QUESTION: 35

The IUPAC name of the following compound is:

Solution:

3-hydroxy-4-methylpentanoic acid

QUESTION: 36

The quantum number of four electrons are given below:

The correct order of their increasing energies will be:

Solution:

lower (n +l) value, and followed by lower ‘n’ value (aufbau rule)

IV < II< III< I

(3p)(3d) (4p) (4d)

QUESTION: 37

Diborane (B_{2} H_{6}) reacts independently with O_{2} and H_{2}O to produce, respectively:

Solution:

Diborane burns in O_{2} forming B_{2}O_{3}

Diborane hydrolyses in water producing H_{2}BO_{3
}

QUESTION: 38

100 mL of a water sample contains 0.81 g of calcium bicarbonate and 0.73 g of magnesium bicarbonate. The hardness of this water sample expressed in terms of equivalents of CaCO_{3} is: (molar mass of calcium bicarbonate is 162 g mol^{-1} and magnesium bicarbonate is 146 g mol^{-1})

Solution:

100 ml sample contain 0.81g of i.e., equal to 5g of and 0.73 g of per 100ml is equal to 5g of per lit. total hardness is 10g per litre or 10,000 ppm

QUESTION: 39

The correct order of hydration enthalpies of alkali metal ions is:

Solution:

Hydration enthalpies of alkali metal ions decrease down two group

QUESTION: 40

For silver, If the temperature (T) of 3 moles of silver is raised from 300 K to 1000 K at 1 atm pressure, the value of ΔH will be close to :

Solution:

QUESTION: 41

The correct order of the spin-only magnetic moment of metal ions in the following low- spin complexes,

Solution:

configuration of which all the 3 are unpaired electrons,

configuration. On low spin the 4 electrons are arranged as one pair and 2 unpaired electrons,

configuration. In low spin the 5 electrons are arranged as 2 pairs ard 1 electron remain unpaired

configuration. In low spin complex all the six electrons are paired so no unpaired electrons

QUESTION: 42

Coupling of benzene diazonium chloride with 1-naphthol in alkaline medium will give:

Solution:

QUESTION: 43

Which of the following amines can be prepared by Gabriel phthalimide reaction ?

Solution:

Only primary amine can be prepared by Gabriel Pthalimide reaction with better S_{N}2.

QUESTION: 44

Given that

The strongest oxidizing agent is:

Solution:

Strongest oxidizing agent may have higher reduction potential in standard state

QUESTION: 45

Assertion : Ozone is destroyed by CFCs in the upper stratosphere.

Reason : Ozone holes increase the amount of UV radiation reaching the earth.

Solution:

Ozone is destroyed by due to which ozone holes are formed. Through these holes the amount u.v radiation reaching the earth increases

QUESTION: 46

Adsorption of a gas follows Freundlich adsorption isotherm. x is the mass of the gas adsorbed on mass m of the adsorbent. The plot of versus log p is shown in the given graph. is proportional to :

Solution:

QUESTION: 47

With respect to an ore, Ellingham diagram helps to predict the feasibility of its

Solution:

Ellingham diagrams are related to the values for the formation of oxides and can be used for the thermal reduction of ores

QUESTION: 48

The major product of the following reaction is:

Solution:

QUESTION: 49

In order to oxidise a mixture of one mole of each of andin acidic medium, the number of moles of KMnO_{4} required is:

Solution:

have valence factors as 3, 6, 1 and 0 and that of KMnO_{4} is 5. Therefore two moles of oxidizing agent is required

QUESTION: 50

The following ligand is

Solution:

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