STAGE-1 TEST PAPERS-2 (PHYSICS)
STAGE
TEST PAPERS (PHYSICS)
1
SCREENING EXAMINATION
Time : 1.00 Hr Max. Marks : 84
GENERAL INSTRUCTIONS
1. This question paper has 28 objective type questions. Each question has four choices (A), (B), (C) and (D) out of which only one is correct.
2. For each question you will be awarded 3 Marks if you give the correct answer and zero Mark if no answer is given. In all other cases, minus one (–1) Mark will be awarded.
Directions : Select the most appropriate alternative A, B, C and D in questions 1-35.
1. In the relation ;
Z
P = e k
P is pressure, Z is distance, k is Boltzman constant and is the temperature. The dimensions of will be:
(A) [M0 L2 T0] (B) [ML2 T]
(C) [ML0 T–1] (D) [M0 L2 T–1]
2. A wire has a mass (0.3 ± 0.003)g, radius (0.5 ± 0.005)mm and length (6 ± 0.006)cm. The maximum percentage error in the measurement of its density is :
(A) 1 (B) 2
(C) 3 (D) 4z
3. A particle starts from rest. Its acceleration (a) versus time (t) is shown in the figure. The maximum speed of the particle will be :
(A) 110 m/s (B) 55 m/s
(C) 550 m/s (D) 660 m/s
a 10m/s2
11 t(s)
4. A small block slides down an inclined plane without friction starting from rest. Let sn be the distance travelled
Sn
from t = n – 1 to t = n. Then Sn1
2n 1
is :
2n 1
(A)
2n
2n 1
(B)
2n 1
2n
(C) 2n 1 (D) 2n 1
5. A block P of mass m is placed on a horizontal frictionless plane. A second block of same mass m is placed on it and is connected to a spring of spring constant k, the two blocks are pulled by distance A. Block Q oscillates without slipping. What is the maximum value of frictional force between the two block?
(A) kA/2 (B) kA
(C) mg (D) zero
6. A particle is placed at the origin and a force F = kx is acting on it (where k is a positive constant). If U(0) = 0, the graph of U(x) versus x will be (where U is the potential energy function) :
x
(A)
x
(B)
U(x)
(C)
x x
(D)
7. A disc is rolling (without slipping) on a horizontal surface. C is its centre and Q and P are two points equidistant from C. Let vP, vQ and vC be the magnitude of velocities of points P,Q and C respectively, then:
(A) vQ > vC > vP (B) vQ < vC < vP
(C) vQ
= vP
1
, vC = 2 P
(D) vQ
< vC
, vC
> vP
8. A child is standing with folded hands at the centre of a plateform rotating about its central axis. The kinetic energy of the system is K. The child now stretches his arms so that the moment of inertia of the system doubles. The kinetic energy of the system now is :
(A) 2K (B) K/2
(C) K/4 (D) 4K
9. A source of sound of frequency 600 Hz is placed inside water. The speed of sound in water is 1500 m/s and in air it is 300 m/s. The frequency of sound recorded by an observer who is standing in air is :
(A) 200 Hz (B) 3000 Hz
(C) 120 Hz (D) 600 Hz
10. A closed organ pipe of length L and an open organ pipe contain gases of densities and respectively. The
1 2
compressibility of gases are equal in both the pipe. Both the pipes are vibrating in their first overtone with same frequency. The length of the open organ pipe is :
L
(A) 3
4L 1
4L
(B) 3
4L 2
(C) 3 2 (D) 3 1
11. Liquid oxygen at 50K is heated to 300 K at constant pressureof 1atm. The rate of heating is constant. Which of the following graphs represents the variation of temperature with time ?
Temp.
Temp.
Temp.
Temp.
12. An ideal gas expands isothermally from a volume V1 to V2 and then compressed to original volume V1 adiabatically. Initial pressure is P1 and final pressure is P3. The total work done by gas is W. Then :
(A) P3 > P1 ; W > 0 (B) P3 < P1 ; W > 0
(C) P3 > P1 ; W < 0 (D) P3 = P1 ; W = 0
13. Two identical conducting rods are first connected independently to two vessels, one containing water at 100ºC and the other containing ice at 0ºC. In the second case, the rods are joined at ends and connected to the same
vessels. Let q1
and q2
g/s be the rate of melting of ice in the two cases respectively. The ratio q1
q2
is :
(A) 1/2 (B) 2/1
(C) 4/1 (D) 1/4
14. Three discs, A,B and C having radii 2cm, 4cm and 6cm respectively are coated with carbon black on their outer surfaces. The wavelengths corresponding to maximum intensity are 300 nm, 400 nm and 500 nm in their radiation, respectively. The power radiated by them are QA, QB and QC respectively :
(A) QA is maximum (B) QB is maximum
(C) QC is maximum (D) QA = QB = QC
15. White light is incident on the interface of glass and air as shown in the figure. If green light is just totally intermally reflected then the emerging ray in air contains :
(A) yellow, orange, red (B) violet, indigo, blue
(C) all colours (D) all colours except green
16. A ray of light is incident on an equilateral glass prism placed on a horizon Q R
tal table. For minimum deviation which of the following is true ?
(A) PQ is horizontal (B) QR is horizontal P S
(C) RS is horizontal (D) Either PQ or RS is horizontal
17. A point object is placed at the centre of a glass sphere of radius 6cm and refractive index 1.5. The distance of the virtual image from the surface of the sphere is :
(A) 2cm (B) 4 cm
(C) 6 cm (D) 12 cm
18. In a YDSE bi–chromatic light of wavelength 400 nm and 560 nm are used. The distance between the slits is
0.1 mm and the distance between the plane of the slits and the screen is 1m. The minimum distance between two succesive regions of complete darkness is :
(A) 4 mm (B) 5.6 mm
(C) 14 mm (D) 28 mm
19. Six equal resistances are connected between points P,Q and R as shown in the figure. Then, the net resistance will be maximum between :
(A) P and Q (B) Q and R
(C) P and R (D) any two points
20. For the post office arrangement to determine the value of unknown resis tance, the unknown resistance should be connected between:
(A) B and C (B) C and D
(C) A and D (D) B1 and C1
21. A capacitor is charged using an external battery with a resistance x in se ries. The dashed line shows the variation of ln I with respect to time. If the resistance is changed to 2x, then new graph will be :
(A) P (B) Q
(C) R (D) S
P
Q R
B C D
22. Six charges, three positive and three negative of equal magnitude are to be placed at the vertices of a regular hexagon such that the electric field at O is double the
electric field when only one positive charge of same magnitude is placed at R. U R
Which of the following arrangements of charge is possible for, P,Q,R,S,T and U
respectively ? T S
(A) +, –,+, –, –, + (B) +, –,+, –, +, +
(C) +, +,–, +, –, – (D) –, +,+, –, +, –
23. Consider the charge configuration and a spherical Gaussian surface as shown in the figure. When calculat- ing the flux of the electric field over the spherical surface, the electric field will be due to :
(A) q2 (B) q1 and q2
(C) all the charges (D) zero.
24. An electron moving with a speed u along the positive x-axis at
y = 0 enters a region of uniform magnetic field → B kˆ
which exists to
the right to y–axis. The electron exits from the region after sometime with the speed v at co–ordinate y, then :
(A) v > u, y < 0 (B) v = u, y > 0
(C) v > u, y > 0 (D) v = u, y < 0
e– u
x
25. The variation of induced emf (e) with time (t) in a coil if a short bar magnet is slowly inserted inside a solenoid along its axis with a constant velocity is best represented as :
(A) (B)
t
(C)
t
(D)
t
26. The graph is showing the photocurrent with the applied voltage of a photoelectric effect experiment. Let ,
a b
and be the intensities and f , f and f be the frequencies for the curves A, B and C respectively, then
a b c
(A) fa = fb and o a b (B) fa = fc and o a = c
(C) fa = fb and o a = b (D) fb = fc and o b = c
27. A 280 days old radioactive substance shows an activity of 6000 disintegrations/second (d/s). Its activity decreases to 3000 d/s in the next 140 days. The original activity of the substance was
(A) 9000 d/s (B) 12000 d/s
(C) 20000 d/s (D) 24000 d/s
28. The kinetic energy E = 100 keV of a proton is equal to the energy of a photon, Let be the de-Broglie
1
wavelength of the proton and 2 be that of the photon. The ratio 2
(A) E–1/2 (B) E1/2
(C) E–1 (D) E
is proportional to
MAIN EXAMINATION
Time : 2.00 Hr Max. Marks : 60
GENERAL INSTRUCTIONS
1. There are 20 Subjective questions in this paper. Attempt ALL questions.
2. Use only Arabic number (0, 1, 2, 9) in answering the questions irrespective of the language in which you
answer.
3. Question numbers 1 - 10 carry 2 marks each and 11 to 20 carry 4 marks each.
1. In the circuit shown A and B are two cells of same emf E but different internal resistances r1 and r2(r1 > r2) respectively. Find the value of R such that the potential difference across the terminals of cell A is zero a long time afte the key K is closed.
2. Consider a horizontally oriented syringe containing water located at a height of 1.25 m above the ground. The diameter of the plunger is 8 mm and diameter of nozel is 2mm. The plunger is pushed with a constant speed of 0.25 m/s. Find the horizontal range of water stream on the ground. (Take g = 10 m/s2).
3. A proton and an particle, after being accelerated through same potential difference, enter uniform magnetic field the direction of which is perpendicular to their velocities. Find the ratio of the radii of the circular paths of the two particles.
4. There are two large parallel metallic plates S and S carrying surface charge densities and respectively
1 2 1 2
( > ) placed at a distance d apart in vacuum. Find the work done by the electric field in moving a point
charge q a distance a(a < d) from S1
towards S2
along a line making an angle /4 with the normal to the
plates. (There is no effect on charge distribution on plate due to this charge)
5. A small sphere falls from rest in a viscous liquid. Due to friction, heat is produced. Find the relation between the rate of production of heat and the radius of the sphere at terminal velocity.
6. An object is approaching a thin convex lens of focal length 0.3 with a speed of 0.01 m/s. Find the magnitude of the rates of change of position and the lateral magnification of image when the object is at a distance of 0.4 m from the lens.
7. In a Young’s double slit experiment, two wavelengths of 500 nm and 700 nm are used. What is the minimum distance from the central maximum where their maximas coincide again ? Take D/d = 103. Symbols have their usual meanings.
8. A solid sphere of radius R is floating in a liquid of density with half of its volume submerged. If the sphere is slightly pushed and released, it starts performing simple harmonic motion. Find the frequency of these oscillations.
9. A cube of coefficient of linear expansion is floating in a bath containing a liquid of coefficient of volume expansion . When the temperature is raised by T, the depth upto which the cube is sumberged in the liquid remains the same. Find the relation between and showing all the steps.
10. Draw the circuit for experimental verification of Ohm’s law using a source of variable D.C. voltage, a main resistance of 100 , two galvanometers and two resistances of values 106 and 10–3 respectively. Clearly show the positions of the voltmeter and the ammeter.
11. One end of a rod of length L and cross-sectional area A is kept in a furnace of temperature T1. The other end of the rod is kept at a temperature T2. The thermal conductivity of the material of the rod is K and emissivity of the rod is e. It is given that T = T + T, where T < rC > rP
v > v
> vP
Therefore, the correct option is (A).
8. From conservation of angular momentum ( = constant), angular velocity will become half. As,
1
K = 2 2
The rotational kinetic energy will become half. Hence, the correct option is (B).
9. The frequency is a characteristic of source. It is independent of the medium. Hence, the correct option is
10. fc = f0 (both first overtone)
vc
v0
4 v0 1
or 3
= 2 2L
L =
L = L
as v .
4L
0
3 vc
11. Temperature of liquid oxygen will first increase in the same phase. Then, phase change (liquid to gas) will take place. During which temperature will remain constant. After that temperature of oxygen in gaseous state will further increase. Hence, the correct option is (C).
12. Slope of adiabatic process at a given state (P,V,T) is more than the slope of isothermal process. The corresponding P–V graph for the two process is as shown in figure.
In the graph, AB is isothermal and BC is adiabatic.
WAB = positive (as volume is increasing)
V
and WBC = negative (as volume is decreasing) plus,
|WBC| > |WAB|, as area under P–V graph gives the work done. Hence, WAB + WBC = W < 0
From the graph itself, it is clear that P3 > P1. Hence, the correct option is (C).
Note : At point B, slope of adiabatic (process BC) is greater than the slope of isothermal (process AB).
dQ L dm
Temperaure difference L dm
13. dt = dt
or Thermal resistance dt
dm 1 1
or dt
Thermal resistance q
R
Let the thermal resistance of each rod is R
In the first case rods are in parallel and thermal resistance is R while in second case rods are in series
2
and thermal resistance is 2R.
q1
2R 4
q2 =
R / 2 = 1
Hence, the correct option is (C).
14. Q AT4 and × T = constant. Hence,
Q A (m )4
or Q
r 2
(m )4
QA : QB : QC =
(2)2
(3)4 :
(4)2
(4)4 :
(6)2
(5)4
4 1
= 81 : 16 :
36
625
= 0.05 : 0.0625 : 0.0576
i.e. QB is maximum. Hence, the correct option is (B).
15. Critical angle
1
= sin–1
C
Wavelength increases in the sequence of VIBGYOR. According to Cauchy’s formula refractive index () decreases as the wavelength increases. Hence the refractive index will increase in the sequence of ROYGBIV. The critical angle will thus increase in the same order VIBGYOR. For green light the incidence angle is just equal to the critical angle and for yellow, orange, red critical angle will be greater than the incidence angle. So, these colours will emerge from the glass air interface.
Hence, the correct option is (A).
16. During minimum deviation the ray inside the prism is parallel to the base of the prism in case of an isosceles prism.
Hence, the correct option is (A).
17. When the object is placed at the centre of the glass sphere, the rays from the object fall normally on the surface of the sphere and emerge undeviated.
Hence, the correct option is (C).
18. Let nth minima of 400 nm coincides with m th minima of 560 nm, then
400
560
2n 1
7 14
(2n – 1) 2 = (2m – 1) 2 or
= 5 = 10
=.........
2m 1
i.e. 4th minima of 400 nm coincides with 3rd minima of 560 nm. Location of this minima is,
(2 4 1)(1000)(400 106 )
Y1 =
2 0.1
= 14 mm
Next 11th minima of 400 nm will coincide with 8th minima of 560 nm. Location of this minima is,
(2 11 1)(1000)(400 106 )
+Y2 =
2 0.1
= 42 mm
Required distance = Y – Y = 28 mm Hence, the correct option is (D).
19. R
= 5 r, R
= 4 r and R
= 3 r
PQ 11
QR 11
PR 11
R is maximum. Therefore, the correct option is (A).
20. BC,CD and BA are known resistance.
The unknown resistance is connected between A and D. Hence, the correct option is (C).
E 1
21. Charging current, = e RC
R
Taking log both sides,
log E t
log =
R RC
22. According to optioin (D) the electric field due to P and S and due to Q and T add to zero. While due to U and R will be added up. Hence the correct option is (D).
23. At any point over the spherical Gaussian surface, net electric field is the vector sum of electric fields due to
+q1,–q1 and q2.
Don’t confuse with the electric flux which is zero (net) passing over the Guassian surface as the net charge enclosing the surface is zero.
Hence, the correct option is (C).
24. Magnetic force does not change the speed of charged particle. Hence, v = u. Further magnetic force on the electron in the given condition is along negative y–axis in the starting. Or it describes a circular path in clockwise direction. Hence, when it exists from the field, y < 0.
Therefore, the correct option is (D).
25. Polarity of emf will be opposite in the two cases while entering and while leaving the coil. Only in option (B) polarity is changing. Hence, the correct option is (B).
26. Saturation current is proportional to intensity while stopping potential increases with increase in frequency. Hence f = f while therefore, the correct option is (a)
27. Activity reduces from 6000 dps to 3000 dps in 140 days. It implies that half-life of the radioactive sample is 140 days. In 280 days (or two half-lives) activity will remain 1/4th of the initial activity. Hence the initial activity of the sample is - 4 × 6000 dps = 24000 dps
Therefore, the currect option is (D)
h
1 2mE
1 E1/ 2
28.
2 hc
E
or 2
Therefore, the correct option is (B)
MAIN EXAMINATION
1. After a long time, resistance across an inductor becomes zero while resistance across capacitor becomes infinite. Hence, net external resistance,
Rnet
R R 3R
= 2 =
2 4
Currents through the batteries,
2E
i = 3R r r
4 1 2
Given that potential across the terminals of cell A is zero.
2E
E – ir = 0 or
E
3R / 4 r r
r1 0
4
Solving this equaiton, we get, R = 3 (r1 – r2).
2. From equation of continuity (Av = constant)
1 2
(8)2 (0.25) =
4
(2)2 (v)
4
Here, v is the velocity of water with which water comes out of the syringe (Horizontally).
Solving eq. (i), we get
v = 4m/s
The path of water after leaving the syringe will be parabola. Substituting proper values in equation of trajec- tory.
y = x tan –
gx2
2u2 cos2
(10)(R)2
we have, –1.25 = R tan0º – (2)(4)2 cos2 0º
(R = horizontal range)
Solving this equation, we get R = 2m.
2qvm
3. r = Bq
or r
rp
r =
= = .
4. Electric field near a large metallic plate is given by E = / . In between the plates the two fields will be in opposite direction. Hence,
1 2
Enet = 0
= E0(say)
Now, W = (q) (potential difference)
1 2 a
= q(E a cos45º) = (q)
0 0
=
2
5. Terminal velocity v
2r 2g
=
( – )
T 9 s L
and viscous force F = 6rv
Rate of production of heat (power), as viscous force is the only dissipative force. Hence,
dQ
= Fv = (6rv ) (v ) = 6rv 2
dt T
2 r 2g
T T T
2
8g2 dQ
= 6r9
(s L )
= 27 (
– )2 r5 =
r 5 .
dt
6. Differentiating the lens formula 1 1 = 1 with respect to time, we get
v u
1 . dv 1 . du 0
f
(as f = constant)
v2 dt u2 dt
dv
v 2 du
= 2
............(i)
dt dt
Further, substituting proper values in lens formula,
we have,
1 1
v 0.4
1
0.3
(u = –0.4 m, f = 0.3 m) or v = 1.2 m
Putting the values in Eq. (i)
Magnitude of rate of change of position of image = 0.09 m/s
v
Lateral magnification, m = u
dm
dt
u dv v. du
= dt dt u2
(0.4)(0.09) (1.2)(0.01)
= (0.4)2
= –0.3 /s.
7. Let n bright fringe corresponding to wavelength = 500 nm coincides with n
bright fringe corresponding to
1 1 2
wavelength = 700 nm.
n 1D = n 2D
n1 2 7
or = =
1 d 2 d
n2 1 5
This implies that 7th maxima of
coincides with 5th maxima of . Similarly 14th maxima of
will coincide
with 10th maxima of
1 2 1
and so on.
n11D
Minimum distance = d
= 7 × 5 × 10–7 × 103 = 3.5 × 10–3 m = 3.5 mm.
8. Half of the volume of sphere is submerged. For equilibrium of sphere,
weight = upthrust V ,g =
V ( ) (g) = L
2 L s 2
When slightly pushed downwards by x, weight will remain as it, while upthrust will increase. The increased upthrust will become the net restoring force (upwards).
F = – (extra upthrust)
= (extra volume immersed) ( ) (g)
or ma = –(R2) x g (a = acceleration)
4 L 3g
R3 a = – (R2 g) x a = x
3 2 L 2R
as a – x motion is simple harmonic Frequency of oscillation,
f = = .
9. When the temperature is increased, volume of the cube will increase while density of liquid will decrease. The depth upto which the cube is submerged in the liquid remains the same, hence the upthrust will not change.
F = F’
V g = V’ ’ g (V = volume immersed)
i L i L
i
L
(Ah ) ( ) (g) = (1 + 2 T) (Ah ) 1 T g
1 L s
i 1
Solving this equation, we get = 2 .
10.
11. Rate of heat conduction through rod = rate of the heat lost from right end of the rod.
KA(T1 T2 ) = eA(T 4 – T 4) (i)
L 2 s
Given that T = T + T
T 4
T 4 = (T
+ T)4 = T4 1
T
s
Using binomial expansion, we have
4 T
T 4 = Ts 1 4 T
(as T << T )
2 s s
T 4 – T 4 = 4(T)(T 3)
2 s s
Substituting in eq. (i), we have
K(T1 Ts ) T = 4eT 3 .T
L s
T = K(T1 Ts )
s
K
Comparing with the given relation, proportionality constant = 4eLT3 K
12. Free body diagram of the wire is as shown in figure. Considering the equilibrium of wire in vertical direction,
we have, a
T T
2T𝑙 cos = 𝑙g (i)
y
For y << a, cos y
a
Substituting the values in eq. (i), we get
ag
W=/g
T = surface tension
T = 2y
13. Applying Snell’s law on face AB,
(1) sin 45º = (
)sin r sin r =
1 or r = 30º
2
i.e. ray becomes parallel to AD inside the block. Now applying,
2 1 = 2 1
on face CD,
v u R
1.514
OE
1.514 2
= 0.4
Solving this equation, we get OE = 6.06 m.
14. Inductive reactance
X = L = (50) (2) (35 × 10–3) 11
Impedence Z = =
Given vrms = 220 V Hence, amplitude of voltage
= 11 2
v0 =
vrms
= 220
V Amplitude of current i =
v 0 =
Z
or i0
= 20 A
X
Phase difference = tan–1 R
11
= tan–1 11 =
4
In L–R circuit voltage leads the currents, Hence, instantaneous current in the circuit is, i = (20A) sin(t – /4)
Corresponding i–t graph in shown in figure.
t
10
15. At constant pressure, V T
V2 T2
Ah2 T2
T2
400 4
or V = T
or Ah = T
h = h1
= (1.0) 300 m = m
1 1 1 1
1
3
The process is adiabatic when gas is compressed without exchange of heat
T1
V 1
4 0.4
= 2
T = 400
= 448.8 K.
T2 V1
1 3
16. Acceleration of A down the plane,
a = g sin45º – g cos45º
1 1
= (10)
– (0.2) (10)
2 2
= 4 m/s2
Similarly, acceleration of B down the plane,
1
(3.0)
a = g sin45º –
g cos45º = (10) –
2
0.3
(10)
= 3.5
2 m/s2
The front face of A and B will come in a line when,
1 1
s = s +
or 2 a t2 = 2 a t2 +
1 a t2 =
2
1 × 3.5
2
× t2 +
Solving this equation, we get
t = 2s
1 1
Further, sA
= a t2 = ×
2 A 2
× (2)2 = 8 m
Hence, both the blocks will come in a line after A has travelled a distance 8
17. Young’s modulus of elasticity is given by
m down the plane.
stress
Y = strain
F / A
= 𝑙 / L
FL
= 𝑙A
FL
= d2
Substituting the values, we get
50 11 4
𝑙
4
Y = (1.25 103 ) (5.0 104 )2
= 2.24 × 1011 N/m2
Y L 𝑙 d
0.1 0.001
0.001
Now,
= 2
= 110 0.125
2
0.05
= 0.0489
Y L 𝑙 d
Y = (0.0489)Y = (0.0489) × (2.24 × 1011) N/m2 = 1.09 × 1010 N/m2 .
1mm
18. Least count of screw gauge = 100 = 0.01 mm
Diameter of wire = (1 + 47 × 0.01)mm = 1.47 mm
d
curved surface area (in cm2) = (2) 2 (L) or S = dL = () (1.47 × 10–1) (5.6)cm2
= 2.5848 cm2
19. Let N be the initial number of nuclei of 238U.
1 n
After time t, N = N
U 0 2
Here n = number of half-lives =
t t1/ 2
1.5 109 1
= 4.5 109 = 3
1
1 1 3
1 3
1–
N 2
N = N
1 3
1–
Pb
U 0 2
and NPb = N0 – NU = N0
2
NU =
1 = 0.259
1 3
2
20. Wavelengths corresponding to minimum wavelength (min) or maximum energy will emit photoelectrons having maximum kinetic energy.
min
) belonging to Balmer series and lying in the given range (450 nm to 750 nm) corresponds to transition
from (n = 4 to n = 2). Here,
13.6
13.6
E4 =
(4)2
= – 0.85 eV and E2 = –
(2)2
= – 3.4 eV
E = E4 – E2 = 2.55 eV
Kmax = Energy of photon – work function
= 2.55 – 2.0 = 0.55 eV
STAGE
3
Time : 1.00 Hr
SIMILAR TEST PAPERS (PHYSICS)
SCREENING EXAMINATION
Max. Marks : 84
GENERAL INSTRUCTIONS
1. This question paper has 28 objective type questions. Each question has four choices (A), (B), (C) and (D) out of which only one is correct.
2. For each question you will be awarded 3 Marks if you give the correct answer and zero Mark if no answer is
given. In all other cases, minus one (–1) Mark will be awarded.
1. In the relation,
K = ..𝑙n
K is coefficient of thermal conductivity, is coefficient of viscosity and is the temperature. The dimension of will be :
(A) [M–1 LT –1] (B) [ML–2 T –2]
(C) [Mº L2 T–2 –2] (D) [M–1 L2 T–2 –2]
2. A cylinder has radius (6+0.003) cm and length [8 + 0.004] m and density [2 + 0.004] kg/m3 . Then maximum percentage error in the calculation of mass is -
(A) 3.5 (B) 0.35
(C) 0.5 (D) 4
3. A particle starts from rest, its acceleration (a) versus time (t) is shown in figure, the maximum speed of particle will be :
(A) 100 m/s (B) 24 m/s
(C) 160 m/s (D) 80 m/s
4. A small block moves on smooth horizontal surface starts from rest with constant acceleration 2 m/s2 . Let S
be the distance travelled from t = n–1 to t = n second. Then S(n+2) . S(n–1) :
(A)
2n 1
2n 3
(B)
2n 3
2n 3
(C) 2(4n2 – 9) (D) (4n2 – 9)
5. A block of mass '2m' is placed on a horizontal frictionless plane. A second block of mass 'm' is placed on it. Both blocks are connected to springs of spring constant 'K'. The two blocks are pulled by distance A. Block Q oscil late without slipping. What is the maximum value of frictional force between the two blocks ?
(A) kA (B) kA/3
(C) 2k A/3 (D) µs mg
6. A particle is placed at the origin a force, F = – K is acting on it where K is a positive constant if U(x) = 0, the graph of U(x) versus 'x' wll be (where U is the potential energy function)
(A) (B)
(C) (D)
7. A disc is rolling (without slipping) on a horizontal surface. C is its centre and Q & P are two points equalent from C. Let VP , VQ & VC be the magnitude of velocities of points P, Q & C respectively then
(A) VQ > VC > VP (B) VQ < VC < VP
(C) VP
= VQ
, VC
= 1/2 VP
(D) VC V
= VP
8. A disc of mass 2m, radius r along with two insects of masses m on periphery on opposite side, is rotating about centre with angular velocity . Now two insects crawl towards each other on the disc and come nearer upto r distance by moving equal distance then new kinetic energy of the system is -
(A) Halved (B) Doubled
(C) Quadrupled (D) become one fourth
9. A source of sound of frequency 600 Hz is placed inside water. The speed of sound in water is 1500 m/s, in air it is 300 m/s. The wavelength of sound recorded by an obsever who is standing in air is .
(A) 5/2 m (B) 1 m
(C) 2 m (D) 1/2 m
10. A closed organ pipe and open orgen pipe of equal length contain gasses of densities & respectively. The
1 2
compressiblity of gasses are equal in both the pipes. Both the pipes are vibrating in their first overtone with same frequency. The ratio of the densities of gasses is.:
(A) 3/4 (B) 4/3
(C) 16/9 (D) 9/16
11. Ice piece at 50 K is heated to 400 K at constant pressure of 1 atm. The rate of heating is constant which of the following graphs represents the variation of temperature with time ?
(A) (B)
(C) (D)
12. An ideal gas expands isobarically from a volume v1 to v2 and then compressed to original volume v1
adiabatically. Initial pressure P1 and final pressure is P3. The total work done by gas is w then - (A) P3 > P1 , W > 0 (B) P3 > P1 ; W < 0
(C) P3 < P1 : W > 0 (D) P3 = P1 ; W = 0
13. Two identical conducting rods are first connected independently to two vessels, one containing water at 100°C and other containing ice at 0° C. Now if rate of melting has to reduce to 1/8 times of earlier case then how many identical rods should be used and in what manner they should be combined? (Other losses are negligible)
(A) 4, in series (B) 4 in parallel (C) 8 in series (D) 8 in parallel
14. Three discs A, B and C having radii 5 m, 10 m and 15 m respectively are coated with carbon black on their outer surface. The wavelengths corresponding to maximum intensity are 300 nm, 400 nm and 500 nm in their radiation respectively. The power (watt/m2) radiated by them are Q , Q , Q respectively -
(A) QA is maximum (B) QB is maximum
(C) QC is maximum (D) QA = QB = QC
15. White light is incident on the interface of glass and air as shown in the figure. If green light is just totally internally reflected from glass at 37º. Now white light is incident at 85° angle with normal from air then entering ray into glass contains
(A) Yellow, Orange, Red (B) Violet, Indigo, Blue
(C) All colours (D) No color except green
16. A ray of light is incident on an equilateral glass prism placed on a horizon tal table for maximum deviation which of the following is true.
(A) PQ is horizontal
(B) QR is horizontal P S
(C) RS is horizontal
(D) Either PQ or RS is grazing to the surface
17. A point object is placed at 4cm inside from the one surface of a glass sphere of radius 8 cm and refractive index 1.5 The distance of the virtual image observed from the other surface of the sphere is
(A) 12 cm (B) 6 cm
(C) 5.33 cm (D) 6.13 cm
18. In a Y.D.S.E. bichromatic light of wavelength 400 nm and 560 nm are used The distance between the slits is
0.1 mm and the distance between the plane of the slits and the screen is 1m. The order of maxima of both rays coincides again second consecutive ways after central maxima.
(A) 10th and 14th (B) 5th and 7th
(C) 14th and 10th (D) 7th and 10th
19. Ten equal resistances are connected between points P,Q,R,S, as shown in
the figure then the net resistance will be minimum between
(A) only P and S (B) Q and S
(C) P and R (D) any sides (not diagonal)
20. For the post office arrangement to determine the value of unknown resistance, the galvanometer should be connected between
(A) A and B1 (B) A and B
(C) A and D (D) D and C1
B C D
21. A capacitor is charged using an external battery with a resistance x in series. The dashed line shows the variation of 𝑙n I with respect to time if the capacitance of capacitor is double the new graph will be -
(A) P (B) Q
(C) R (D) S
22. Six charges four positive & two negative of equal magnitude are to be placed at the vertices of a regular hexagon such that electric field at '0' is double the electric field when only one positive charge of same magnitude
is placed at R cwhich of the following arrangement of charge is possible for U R
P,Q,R,S,T & U respectively
T S
(A) – + + + – + (B) – + – + + +
(C) + – + – + + (D) – – + + + +
23. Consider the charge configuration and spherical surface as shown in the figure. When calculating the flux of the electric field over the spherical surface. The electric flux on spherical surface will be due to -
(A) q2 (B) only the positive charges
(C) All the charges (D) +q1 & –q1
24. An alpha particle moving with a speed v along the positive y axis at x = 0 enters a region of uniform magnetic field B = B0i which exists above the x-axis to some distance. The alpha particles exits from the region after some time with the speed v at co-ordinate z then -
(A) v > u , z < 0 (B) v = u , z < 0
(C) v > u , z > 0 (D) v = u , z > 0
25. The variation of induced emf (e) with time (t) in a coil if a short bar magnet is doing S.H.M. between point A and B along axis of coil, is best repre sented as :
(A) (B)
t
(C) (D)
26. The graph is showing the photocurrent with the applied voltage of a photoelectric effect experiment. Let , and be the intensities and f , f and fc be the frequencies for the curves A, B and C respectively, then
(A) fa
= fb
and
(B) fa
= fc
and
(C) fa f
and
(D) fa f
and =
27. A radioactive sample currently decay at the rate of 2000 disintegration/second but 3 years ago it was 16000 disintegration/second then find decay rate after 2 years of current time -
(A) 1000 d/s (B) 500 d/s
(C) 200 d/s (D) 400 d/s
28. The kinetic energy of a proton is four times that of an particle let be the de-Broglie wave length of the proton and be that of particle. The ratio of / is -
(A) 1 (B) 2 2
1
(C) (D) 2
SIMILAR PROBLEM FOR MAIN EXAMINATION
Time : 2.00 Hr Max. Marks : 60
GENERAL INSTRUCTIONS s
1. There are 20 Subjective questions in this paper. Attempt ALL questions.
2. Use only Arabic number (0, 1, 2, 9) in answering the questions irrespective of the language in which you
answer.
3. Question numbers 1 - 10 carry 2 marks each and 11 to 20 carry 4 marks each.
1. In the circuit shown A and B are two cells of e.m.f. E and 2E and internal resistence r1 and r2 (r1 < r2) repectively. Find the value of R such that the potential difference accross the terminal of both cell become equal a long time after the key K is closed.
2. A boy is playing with a toy used in Holi festival for colouring the people. The boy wants to colour the face of his friend standing in the first floor just above him as shown in the diagram then what will be the minimum constant speed of plunger so that he succeds.
3. An particle and oxygen nucleus are given same momentum by accelerating in electric potential difference enter in uniform magnetic field the direction of which is perpendicular to their velocities. Find the ratio of the radii of the circular path of the two particles.
4. There are two large parallel metallic plates S & S carrying surface charge densities & (< ) respec- tively placed at a distance d apart in vacuum. Find the work done by the electric field in moving a point charge q, a distance 'a' < d from S and outside the two plates along a line making an angle /6 with the normal to the plates. (There is no effect on charge distribution on plate due to this charge)
5. A small sphere falls from rest in viscous liquid. Due to friction, heat is produced. Find the relation between the rate of rise of temperature and radius of the sphere at terminal velocity (all heat produced is used to raise the temperature of sphere)
6. An object is approaching a thin concave lens of focal length 0.6 m with speed 0.01 m/s find the magnitude of the rate of change of position and the lateral magnification of image when the object is at a distance of 0.2 m from the lens.
7. In a Young's double slit experiment, two wavelengths of 600 nm & 800 nm are used what is the minimum separation between two consecutive coincinding maxima after central maxima, formed again?
Take D/d = 103 symbols have their usual meaning.
8. A solid cylinder of radius R & length 4R is floating in a liquid of density with three fourth of its volume submerged, If the cylinder is slightly pushed into water till its full length released, it starts performing simple harmonic motion, find frequency of these oscillations.
9. A cube of coefficient of linear expansion is floating half submerged in a bath containing a liquid of coeffi-
cient of volume expansion when the temperature is raised by T, the depth upto which the cube is sub-
merged in the liquid become three fourth of the initial height of cube find the relation between & , showing
all the steps.
10. Draw the circuit for experiment verification of balanced Wheatstone bridge using a source of D.C. voltage, two resistance 100 , 300 respectively, meter bridge having wire 60 and a Galvanometer. Show clear position of balancing point.
11. One end of a rod of length L and cross–sectional area ‘A’ is kept in a furnace f temperature T1. The other end of the rod is kept at a Temperature
T2 . The other end of the rod is kept at a temperature T2 . The thermal T
conductivity ofthe rod is k and emissivity is e. It is given that T = T + T
& T - T = 2T. Where T << T , T being thetemperature of the surrounding
1 2 S S T2
if T1 & T2 remainconstant with respect of time then find length of rod consider
that heat is lost only by radiation at the end where temperature of the rod is T2 .
12. A container of width 2a is filled with a liquid A thin square plate of side b of weight per unit area is gently placed over the liquid surface in the middle of the surtace as shown in the figure as a result the liquid sur- face is depressed by a disstance y (y << a) Determine the surface
ension of the liquid.
13. Figure shows an irregular block of material of refractive index 2 . A ray of light strikes the face AB as shown inthe figure.] After refraction it is inci- dent on a spherical surface CD of radius of curvature 60 cm and enters a medium of refractive index 1.514 to meet or appear to meet PQ at E. Find the dis tance OE upto two places of decimal.
14. In an L-R series circuit a voltage V= V cos t applied L = 70 H,
R = 22 V
rms
= 220 V f = 50 Hz and = 22/7. Find the amplitude of current
in the steady state and obtain the phase difference between the current for t
one cycle on the given graph.
15. The piston & cylinder arrangement shown contain a diatomic gas at tem- perature 300K. The cross sectional area of the cylinder is 1m2, Initial height of the piston above the base of the cylinder is 1m. The tempera ture is now raised to 400K at constant volume now piston is released find new height
& temperature of gas in equilibrium. Process is without any heat loss and
1m
you can have the answer in fractio
16. Two blocks A and B of equal masses are released from an inclined plane of inclination 45º at t = 0. one block with some initial velocity and other block from rest. The coefficient of kinetic friction between the block A and the inclined plane is 0.2 while it is 0.3 for block B. Initially the block A is
2 m behind the block B. Now both block reaches common lines one by
one with same velocity and B travels 8 2 m distance. Then which block has initialspeed and how much given? Then the final speed at the common line? [Take g = 10 m/s2]
17. In a searle's of experiment the radius of the wire as measured by screw gauge of least count 0.001 cm is 0.04 cm The length, measured by a scale of least count 0.1 cm is 1.60 m when a weight of 80 N is suspended from the wire. The extension is measured to be 0.120 cm by a micrometer of least count 0.001 cm. Find the maximum error in the measurement of Young's modulus of the material of the wire from these data.
18. The pitch of a screw gauge is 1mm and there are 100 divisions on the circular scale. While measuring the two thickness of rectangular cross-sectional wire (along side). The linear scale reads 2mm & 4mm respectively, and 40 division and 60 division on the circular scale coincide with the reference line respectively in two cases. The length of the wire is 8.4 cm then find the total surface area of the wire in approximate number of signficant figures.
19. A rock sample contains 238U and 206Pb in the ratio of 1/5 in the number of atoms. Assume that the only end- product of the decay of 238U is 206Pb and no 206Pb was present at the begining find the age of the rock. (The half life of 238U is 4.5 × 109 years).
20. If photo electron emission from a metal surface of work function 1 e.V. is done by source of light having range 900 Å to 1800 Å wavelength. Then find the maximum possible kinetic energy of photo electron.
A nswers
3 2 1 9
4. (1 2 )
2
5. d r 2
dt
6. 5.62 × 10–3 m/s , 26.24/
s
7. 2.4 mm 8. f =
9. =
6sT 1
4T
10. 11. L =
K
2eT3
12. T =
bg(2a b) 8y
13. at 13.03 cm appears to meet left of O. 14. 10 A , /4
4 5 / 7 3 2 / 7
15. h = , T =
400 K
2 3 2 4
16. B has initial velocity 4 and final velocity 4 17.
2.033 × 1010 N/m2
18. 6.1 cm2 19. 11.631 × 109 years 20. 3.75 e.V..
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