General Instructions
1. This test consists of 30 questions.
2. Each question is allotted 4 marks for correct response.
3. 1/4 marks will be deducted for indicating incorrect response of each question. No deduction from the total score will be made if no response is indicated in each question.
4. There is only one correct response for each question. Filling up more than one response in any question will be treated as wrong response and marks for wrong response will be deducted according as per instructions.
1.
The SI unit of energy is J =kgm s2 -2, that of speed v is ms- 1 and of acceleration a is ms- 2. Which one of the formula for kinetic energy given below is correct on the basis of dimensional arguments?[Given, m stands for mass of the body]
(a) K =m v2 2 (b) K=ma
(c) K =1mv +ma 2
2 (d) K=1mv
2
2
2.
A body of mass 5 10´ -3 kg is launched upon a rough inclined plane making an angle of 30° with the horizontal. Find the coefficient of friction between the body and the plane if the time of ascent is half of the time of descent.(a) 0.346 (b) 0.436 (c) 0.463 (d) 0.364
3.
A uniform chain of length L and mass M over hangs a horizontal table with its two-third part on the table.The friction coefficient between the table and the chain is m. The work done by the friction during the period, the chain slips off the table is
(a) -1
4m MgL (b) -2
9m MgL (c) -4
9m MgL (d) - 6 7m MgL
4.
A neutron travelling with velocity u and kinetic energy K collides head on elastically with the nucleus of an atom of mass number A at rest. The fraction of its kinetic energy retained by the neutron even after the collision is(a) 1 1 - 2
+ æ èç ö
ø÷ A
A (b) A A + -æ èç ö
ø÷ 1 1
2
(c) A A æ -èç ö
ø÷
1 2
(d) A A æ + èç ö
ø÷
1 2
5.
One end of a uniform rod of mass m1, uniform area of cross-section A is suspended from the roof and the mass m2 is suspended from the other end. What is the stress at the mid-point of the rod?(a) (m m) .g A
1+ 2 (b) (m m) .g
A
1- 2
(c) ( / ) )
m m .
A g
1 2 + 2
é ëê
ù
ûú (d) m m
A g
1+ 2 2
é ëê
ù ûú ( / )
.
6.
Two moles of an ideal monoatomic gas at 27°C occupies a volume of V. If the gas is expanded adiabatically to the volume 2V, then the work done by the gas will be Yæ = R=èç ö
ø÷
5
3, 8 31. J mol-K/
(a) + 2767.23 J (b) 2627.23 J (c) 2500 J (d) - 2500 J
7.
Use Moseley’s law with b= 1 to find the frequency of the Ka X-rays of La (Z= 57 if the frequency of) Ka X-rays of Cu(Z= 29 is known to be 188 10) . ´ 18Hz (a) 7.52 10 Hz´ 18 (b) 3.25 10 Hz´ 16(c) 8.51 10 Hz´ 19 (d) 9.1 10 Hz´ 15
8.
A small particle of mass m is projected at an angle q with the X-axis with an initial velocity v0 in the X-Y plane as shown in the figure. At a time t v< 0sing q, the angular momentum of the particle is
θ X
Y v0
(a) 1
9.
A ball falls on an inclined plane of inclination q from a height h above the point of impact and makes a perfectly elastic collision where will it hit the inclined plane again(a) 8h
sinq (b) 4h sinq (c) 8h sinq (d) 4h sinq
10.
A thin uniform annular disc of mass M has outer radius 4R and inner radius 2R. The work required to take a unit mass from point P on its axis to infinity is11.
Four rods of identical cross-sectional area and made from the same metal form the sides of square. The temperature of two diagonally opposite points are T and 2 T respectively, in the steady state. Assuming that only heat conduction takes place, what will be the temperature difference between other two points?12.
An object 2.4 m in front of a lens forms a sharp image on a film 12 cm behind the lens. A glass plate 1 cm thick of refractive index 1.50 is interposed between lens and film with its plane faces parallel to film. At what distance (from lens) should object shifted to be in sharp focus on film?(a) 7.2 (b) 2.4 (c) 3.2 (d) 5.6
13.
A sphere and a cube of same material and same volume. One heated upto the same temperature and allowed to cool in the same surroundings. The ratio of the amounts of radiation emitted will be(a) 1 : 1 (b) 4
14.
In Young’s double slit experiment, when violet light of a wavelength 4358 Å is used, then 84 fringes are seen in the field of view, but when sodium light of certain wavelength is used, then 62 fringes are seen in the field of view, the wavelength of a sodium light is (a) 6893 Å (b) 5904 Å (c) 5523 Å (d) 6429 Å15.
A transparent solid cylinderical rod has a refractive index of 2/ 3. Itis surrounded by air. A light ray is incident at the mid-point of one end of the rod as shown in the figure. The incident angle q for which the light ray grazes along the wall of the rod is
(a) sin- æ
16.
When two tunning forks (fork 1 and fork 2) are sounded simultaneously, 4 beat s- 1 are heard. Now, some tape is attached on the prong of the fork 2.When the tunning forks are sounded again, 6 beats s-1 are heard. If the frequency of fork 1 is 200 Hz, then what was the original frequency of fork 2?
(a) 200 Hz (b) 202 Hz
(c) 196 Hz (d) 204 Hz
17.
A particle of charge q and mass m starts moving from the origin under the action of an electric field, E=E0 $i and B B= 0 $i with a velocity, v v= 0 $j. The18.
The current in the primary circuit of a potentiometer is 0.2 A. The specific resistance and cross-section of the potentiometer wire are 4´10-7W m and 8´10-7m2, respectively. The potential gradient will be equal to(a) 0.2 V/m (b) 1 V/m
(c) 0.3 V/m (d) 0.1 V/m
19.
Two straight long conductors AOB and COD are perpendicular to each other and carry currents i1 and i2. The magnitude of the magnetic induction at a point P at a distance a from the point O in a direction perpendicular to the plane ABCD, is(a) m
20.
Two conductors have the same resistance of 0°C, but their temperature coefficients of resistance are a1and a2. The respective temperature, coefficients of their series and parallel combinations are nearly (a) (a1 a2)
21.
A parallel plate capacitor C with plates of unit area and the separation d is filled with a liquid of dielectric constantK= 2, the level of liquid is d/3, initially. Suppose, the liquid level decreases at a constant speed v, the time constant as a function of time t is
(a) 6
22.
A 10mF capacitor and a 20 mF capacitor are connected in series across 200 V supply line. The charged capacitors are then disconnected from the line and reconnected with their positive plates together and negative plates together and no external voltage is applied. What is the potential difference across each capacitor?(a) 800
9 V (b) 400 V (c) 800
3 V (d) 200 V
23.
A candidate connects a moving coil voltmeter V and a moving coil ammeter A and resistor R as shown in thefigure. If the voltmeter reads 10 V and the ammeter reads 2 A, then R is
(a) equal to 5W (b) greater than 5W (c) less than 5W
(d) greater or less than 5W depending upon its material
24.
A rectangular loop has a sliding connector PQ of length l and a resistance RW and it is moving with the speed v as shown.The set up is placed in the uniform magnetic field going into the plane of the paper. The three currents I1,I2 and I are
25.
A solid sphere of radius R has a charge q distributed in its volume with a charge density r = kra, where k and a are constants and r is the distance from its centre. If the electric field at r=R2 is 1
8 times that are r= , then the value of a isR
(a) 2 (b) 4 (c) 6 (d) 8
26.
Two positive charges of magnitude q are placed at the end of a side 1 of a square of side 2a. Two negative charges of the same magnitude are kept at the other corners. Starting from rest, if a charge q moves from the middle of side 1 to the centre of square, its kinetic energy at the centre of square is(a) 1 a time varying current flows as shown in the figure.
The ratio of current, i i
28.
A p-n junction (D) shown in the figure can act as a rectifier. An alternating current source ( )V is connected in the circuit.The current ( )I in the resistor ( )R can be shown by
29.
The graph given below represents the I-V characteristics of a Zener diode. Which part of the characteristic curve is most relevant for its operation as a voltage regulator?(a) ab (b) bc
(c) cd (d) de
30.
A fully charged capacitor C with initial charge q0 is connected to a coil of self-inductance L at t= 0. The time at which the equation is stored equally between the electric and magnetic field is(a) p