Q: A gas mixture consists of 2 moles of O2 and 4 moles of Ar at temperature T. Neglecting all vibrational modes, the total internal energy of the system is:

UU=n12f1RT+n22f2RT=2×25RT+4×23RT=5RT+6RT=11RT

Q: Radioactive material 'A' has decay constant '8λ′ and material 'B' has decay constant ' λ '. Initially they have same number of nuclei. After what time, the ratio of number of nuclei of material 'B' to that 'A' will be e1 ?

No option is correctIf we take NBNA=e1ThenNBNA=e−λte−8λt e1−1t=e−7λt=−7λt=7λ1

Q: A∪ tube with both ends open to the atmosphere, is partially filled with water. Oil, which is immiscible with water, is poured into one side until it stands at a distance of 10 mm above the water level on the other side. Meanwhile the water rises by65 mm from its original level (see diagram). The density of the oil is:

. hoil ρoil g140×ρoil ρoil ρoil =hwater ρwater g=130×ρwater =1413×1000 kg/m3=928 kg m−3

Q: A 250 -Turn rectangular coil of length 2.1 cm and width 1.25 cm carries a current of 85μA and subjected to a magnetic field of strength 0.85 T. Work done for rotating the coil by 180∘ against the torque is:

W=MB(cosθ1−cosθ2) When it is rotated by angle 180∘ thenWW=2MB=2(NIA)B=2×250×85×10−6[1.25×2.1×10−4]×85=9.1μJ

Q: The de-Broglie wavelength of a neutron in thermal equilibrium with heavy water at a temperature T (Kelvin) and mass m, is:

De-Broglie wavelengthλλ=mvh=2m(KE)h=2m(23kT)h=3mkTh

Q: One end of a string of length l is connected to a particle of mass ' m ' and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in circle with speed ′v′ , the net force on the particle (directed towards center) will be ( T represents the tension in the string):

Centripetal force (lmv2) is provided by tension so the net force will be equal to tension i.e., T.

Q: The x and y coordinates of the particle at any time are x=5t−2t2 and y=10 t respectively, where x and y are in meters and t in seconds. The acceleration of the particle at t=2 s is:

x=5t−2t2 y=10t dtdx=5−4tvx=5−4tdtdvx=−4ax=−4dtdy=10vy=10dtdvy=10ay=0 Acceleration of particle at t=2 s is =−4 m/s2 .

Q: Suppose the charge of a proton and an electron differ slightly. One of them is -e, the other is (e+Δe). If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distance d (much greater than atomic size) apart is zero, then Δe is of the order of :[Given mass of hydrogen mh=1.67×10−27 kg].

Fe=Fg 4πε01d2Δe2=d2Gm29×109(Δe2)=6.67×10−11×1.67×10−27×1.67×10−27Δe2=96.67×1.67×1.67×10−74Δe=10−37

Q: Two rods A and B of different materials are welded together as shown in figure. Their thermal conductivities are K1 and K2. The thermal conductivity of the composite rod will be:

Thermal current,H=H1+H2=dK1A(T1−T2)+dK2A(T1−T2)dKEQ2A(T1−T2)=dA(T1−T2)[K1+K2]KEQ=[2K1+K2]

Question 1

A potentiometer is an accurate and versatile device to make electrical measurements of E.M.F, because the method involves :

Accepted Answer

Reading of potentiometer is accurate because during taking reading it does not draw any current from the circuit.

Question 2

A gas mixture consists of 2 moles of O2​ and 4 moles of Ar at temperature T. Neglecting all vibrational modes, the total internal energy of the system is:

Accepted Answer

UU​=n1​2f1​​RT+n2​2f2​​RT=2×25​RT+4×23​RT=5RT+6RT=11RT​

Question 3

Radioactive material 'A' has decay constant '8λ′  and material 'B' has decay constant ' λ  '. Initially they have same number of nuclei. After what time, the ratio of number of nuclei of material 'B' to that 'A' will be e1​  ?

Accepted Answer

No option is correctIf we take NB​NA​​=e1​ThenNB​NA​​=e−λte−8λt​ e1​−1t​=e−7λt=−7λt=7λ1​​

Question 4

A∪  tube with both ends open to the atmosphere, is partially filled with water. Oil, which is immiscible with water, is poured into one side until it stands at a distance of 10 mm  above the water level on the other side. Meanwhile the water rises by65 mm  from its original level (see diagram). The density of the oil is:

Accepted Answer

. hoil ​ρoil ​g140×ρoil ​ρoil ​ρoil ​​=hwater ​ρwater ​g=130×ρwater ​=1413​×1000 kg/m3=928 kg m−3​

Question 5

A 250 -Turn rectangular coil of length 2.1 cm  and width 1.25 cm  carries a current of 85μA  and subjected to a magnetic field of strength 0.85 T. Work done for rotating the coil by 180∘ against the torque is:

Accepted Answer

W=MB(cosθ1​−cosθ2​) When it is rotated by angle 180∘  thenWW​=2MB=2(NIA)B=2×250×85×10−6[1.25×2.1×10−4]×85=9.1μJ​

Question 6

The de-Broglie wavelength of a neutron in thermal equilibrium with heavy water at a temperature T (Kelvin) and mass m, is:

Accepted Answer

De-Broglie wavelengthλλ​=mvh​=2m(KE)​h​=2m(23​kT)​h​=3mkT​h​​

Question 7

One end of a string of length l is connected to a particle of mass ' m ' and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in circle with speed ′v′ ,  the net force on the particle (directed towards center) will be ( T represents the tension in the string):

Accepted Answer

Centripetal force (lmv2​)  is provided by tension so the net force will be equal to tension i.e., T.

Question 8

The x and y coordinates of the particle at any time are x=5t−2t2  and y=10  t respectively, where x and y are in meters and t in seconds. The acceleration of the particle at t=2 s  is:

Accepted Answer

x=5t−2t2 y=10t dtdx​=5−4tvx​=5−4tdtdv​x=−4ax​=−4​dtdy​=10vy​=10dtdv​y=10ay​=0​ Acceleration of particle at t=2 s  is =−4 m/s2 .

Question 9

Suppose the charge of a proton and an electron differ slightly. One of them is -e, the other is (e+Δe).  If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distance d (much greater than atomic size) apart is zero, then Δe  is of the order of :[Given mass of hydrogen mh​=1.67×10−27 kg].

Accepted Answer

Fe​=Fg​ ​4πε0​1​d2Δe2​=d2Gm2​9×109(Δe2)=6.67×10−11×1.67×10−27×1.67×10−27Δe2=96.67×1.67×1.67​×10−74Δe=10−37​

Question 10

Two rods A and B of different materials are welded together as shown in figure. Their thermal conductivities are K1​  and K2​. The thermal conductivity of the composite rod will be:

Accepted Answer

Thermal current,​H=H1​+H2​=dK1​A(T1​−T2​)​+dK2​A(T1​−T2​)​dKEQ​2A(T1​−T2​)​=dA(T1​−T2​)​[K1​+K2​]KEQ​=[2K1​+K2​​]​

Question 11

The diagrams below show regions of equipotentials.A positive charge is moved from A to B in each diagram.

Accepted Answer

Work done w=qΔV ΔV  is same in all the cases so work is done will be same in all the cases.

Question 12

The ratio of wavelengths of the last line of Balmer series and the last line of Lyman series is:

Accepted Answer

For last Balmer series​λb​1​=R[221​−∞21​]λb​=R4​​ For last Lyman seriesλI​1​=R[121​−∞21​] λl​=R1​ λl​λb​​=R1​R4​​ λl​λb​​=4

Question 13

Young's double slit experiment is first performed in air and then in a medium other than air. It is found that 8th   bright fringe in the medium lies where 5th   dark fringe lies in air. The refractive index of the medium is nearly:

Accepted Answer

X1​=X5 th dark ​=(2×5−1)2dλD​ ​X2​=X8th bright ​=8μdλD​X1​=X2​29​dλD​=8μdλD​μ=916​=1.78​

Question 14

A particle executes linear simple harmonic motion with an amplitude of 3 cm . When the particle is at 2 cm  from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then its time period in seconds is:

Accepted Answer

v=ωA2−x2​ ​a=xω2v=aωA2−x2​=xω2(3)2−(2)2​=2(T2π​)5​=T4π​T=5​4π​​

Question 15

Thermodynamic processes are indicated in the following diagram.Match the following

Accepted Answer

Process I = Isochoric,∥∥IV​= Adiabatic = Isothermal = Isobaric ​

Question 16

A capacitor is charged by a battery. The battery is removed and another identical uncharged capacitor is connected in parallel. The total electrostatic energy of resulting system.

Accepted Answer

Uf​​=21​C(2V​)2+21​C(2V​)2=4CV2​​  Loss of energy =Ui​−Uf​ =4CV2​ i.e. decreases by a factor (2)

Question 17

The photoelectric threshold wavelength of silver is 3250×10−10 m.  The velocity of the electron ejected from a silver surface by ultraviolet light of wavelength 2536×10−10 m  is:(Given h=4.14×10−15eVs  and c=3×108 ms−1 )

Accepted Answer

​ I. λ0​=3250×10−10 mλ=2536×10−10 mϕ=325 nm1242eV−nm​=3.82eVhv=253.6 nm1242eV−nm​=4.89eVKEmax​=(4.89−3.82)eV=1.077eV21​mv2=1.077×1.6×10−19v=9.1×10−312×1.077×1.6×10−19​​v=0.6×106 m/s​

Question 18

A physical quantity of the dimensions of length that can be formed out of c, G and4πε0​e2​  is :[c is velocity of light, G is universal constant of gravitation and e is charge]

Accepted Answer

Let 4πε0​e2​=A=ML3T−2 ​I=CxGy(A)zL=[LT−1]x[M−1L3T−2]y[ML3T−2]z−y+z=0⇒y=zx+3y+3z=1−x−4z=0​ From (i), (ii) \& (iii)z=y=21​,x=−2

Question 19

Two cars moving in opposite directions approach each other with speed of 22 m/s and 16.5 m/s respectively. The driver of the first car blows a horn having a frequency 400 Hz. The frequency heard by the driver of the second car is [velocity of sound 340 m/s] .

Accepted Answer

fA​=f[v−vs​v+vo​​] ​=400[340−22340+16.5​]fA​=448 Hz​

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