questions & solutions of aipmt 2009

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Q U E S TIO N S & SOLUTIONS OF AIPMT 2009
CBSE PM/PD 2009
PHYSICS
In the nuclear decay given below:
1.
A A A B 4 ∗ A B 4
X !" Y !" B !" B, the particles emitted in the sequence
Z Z A 1 Z B 1 Z B 1
are:
#, $, % $, #, %
(1) (2)
%, $, # $, %, #
(3) (4)
A A A A B 4 ∗ A B 4 ∗ A B 4
X !" Y : $, Y !" B : %, B !" B : #
Sol: Z Z A 1 Z A 1 Z B 1 Z B 1 Z B 1
( $, %, #)
&
Correct choice : (4)
A thin circular ring of mass M and radius R is rotating in a horizontal plane about
2.
an axis vertical to itsplane with a constant angular velocity'. If two objects each
of mass m be attached gently to the opposite ends of a diameter of the ring, the
ring will then rotate with an angular velocity:
'M ' M A 2m

(1) M A 2m (2) M
'M ' M B 2m

(3) M A m (4) M A 2m
2 2 2
I ' = I ' , I = MR , I = MR + 2 mR
Sol: 1 1 2 2 1 2
I
1 M
& ' = ' = '.
2 I M A 2m
2
&
Correct choice : (1)
In thermodynamic processes which of the following statements is true?
3. not
In an isochoric process pressure remains constant
(1)
In an isothermal process the temperature remains constant
(2)
#
In an adiabatic process PV = constant
(3)
In an adiabatic process the system is insulated from the surroundings
(4)
Pressure constant: ! isobaric, not isochoric
Sol:
&
Correct choice : (1)

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The number of photo electrons emitted for light of a frequency ( (higher than the
4.
threshold frequency ( ) is proportional to:
0
Threshold frequency (( ) Intensity of light
(1) 0 (2)
Frequency of light (() ( ) (
(3) (4) 0
Saturation current * intensity
Sol:
&
Correct choice : (2)
A simple pendulum performs simple harmonic motion about x = 0 with an
5.
a
amplitude a and time period T. The speed of the pendulum at x = will be:
2
2
+a 3+ a

(1) T (2) T
+a 3 +a 3

(3) T (4) 2T
2 2 a
Speed v = ' a B x , x =
Sol: 2
2 2
2 a 3a
& v = ' a B = '
4 4
2+ a 3 +a 3
= =
T 2 T
&
Correct choice : (3)
See the electric circuit shown in this . Which of the following equations is
6. Figure
a correct equation for it?
, B i r B , B i r = 0 B , B i A i R A i r = 0
(1) 2 2 2 1 1 1 (2) 2 1 2 2 2
, B i A i R A i r = 0 , B i A i R B i r = 0
(3) 1 1 2 1 1 (4) 1 1 2 1 1

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Sol:
, ) (i + i )R ) i r = 0.
1 1 2 1 1
&
Correct choice : (4)
A body, under the action of a force F = 6 i B 8 j A 10k, acquires an
7.
2
acceleration of 1 m/s . The mass of this body must be:
10 kg 20 kg 10 2 kg 2 10 kg
(1) (2) (3) (4)
F = 6i B 8 j A 10k
Sol: ,
F = 36 A 64 A 100 = 10 2 N
)2
a = 1 ms
10 2
& m = = 10 2 kg
1
&
Correct choice : (3)
The symbolic representation of four logic gates are given below:
8.
The logic symbols for OR, NOT and NAND gates are respectively:
(iv), (i), (iii) (iv), (ii), (i) (i), (iii), (iv) (iii), (iv), (ii)
(1) (2) (3) (4)
&
Correct choice : (2)

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If F is the force acting on a particle having position vector r and - be the torque
9.
of this force about the origin, then:
r ⋅- > 0 and F⋅- < 0
(1)
r ⋅- = 0 and F⋅- = 0
(2)
r ⋅- = 0 and F⋅- ≠ 0
(3)
r ⋅- ≠ 0 and F⋅- = 0
(4)
- = r × F . r ⋅- = 0 F⋅- = 0
Sol:
&
Correct choice : (2)
The two ends ofa rod of length L anda uniform cross-sectional area A arekept at
10.
dQ
two temperatures T and T (T > T ). The rate of heat transfer, through the
1 2 1 2
dt
rod in a steady state is given by:
dQ = k T1 B T2 dQ = kLA T B T
(1) dt LA (2) dt 1 2
kA T B T kL T B T
dQ = 1 2 dQ = 1 2
(3) dt L (4) dt A
kA T B T
dQ 1 2
=
Sol: dt L
&
Correct choice : (3)
A p-n photodiode is fabricated from a semiconductor with a band gap of 2.5 eV. It
11.
can detect a signal of wavelength:
4000 nm 6000 nm 4000 Å 6000 Å
(1) (2) (3) (4)
B34 8
hc 6.6 × 10 × 3 × 10
/ = = ≃ 5000 Å
Sol: max E 2.5 × 1.6 × 10B19
/ < / = 4000 Å
max
&
Correct choice : (3)

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a b c
If the dimensions of a physical quantity are given by M L T , then the physical
12.
quantity will be:
Velocity if a = 1, b = 0, c = ) 1
(1)
Acceleration if a = 1, b = 1, c = ) 2
(2)
Force if a = 0, b = ) 1, c = ) 2
(3)
Pressure if a = 1, b = ) 1, c = ) 2
(4)
B2
MLT B1 B2
Pressure = = ML T
Sol: 2
L
. a = 1, b = ) 1, c = ) 2.
&
Correct choice : (4)
A transistor is operated in common-emitter configuration at V = 2 V such that a
13. c
change in the base current from 100 0A to 200 0A produces a change in the
collector current from 5 mA to 10 mA. The current gain is:
100 150 50 75
(1) (2) (3) (4)
1 1 1
Sol: I = I + I
E B C
1I
C
$ =
1I
B
)3
1I = 5 2 10 A
C
)6
1I = 100 2 10 A
B
5
$ = × 1000 = 50
100
&
Correct choice : (3)
The mass of a lift is 2000 kg. When the tension in the supporting cable is 28000 N,
14.
then its acceleration is:
)2 )2
4 ms upwards. 4 ms downwards.
(1) (2)
)2 )2
14 ms upwards. 30 ms downwards.
(3) (4)
2000 a = 28000 ) 20000 = 8000
Sol:
8000 B2
a = = 4 ms 3
2000
&
Correct choice : (1)

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Four identical thin rods each of mass M and length l, form a square frame.
15.
Moment of inertia of this frame about an axis through the centre of the square
and perpendicular to its plane is :
2 2 13 2 1 2 4 2
Ml Ml Ml Ml
(1) 3 (2) 3 (3) 3 (4) 3
2 2 2 2
mL mL 4mL mL
A = =
Sol: 12 4 12 3
2
mL
Total M.I. = 4 2
3
&
Correct choice : (4)
Each of the two strings of length 51.6cm and 49.1 cm are tensioned separately by
16.
20 N force. Mass per unit length of both the strings is same and equal to 1 g/m.
When both the strings vibrate simultaneously the number of beats is:
7 8 3 5
(1) (2) (3) (4)
l B l
f = 1 T, f = 1 T, f ) f = 1 T 1 2
Sol: 1 2l m 2 2l m 2 1 2 m l l
1 2 1 2
T 20 2
= = 2 × 10 = 1.414 × 100 = 141.4
m B3
10
l1 B l2 51.6 B 49.1 × 102 2.5 × 102 1
= = =
l l 51.6 × 49.1 50 × 50 10
1 2
1 1
& f ) f = × 141.4 × = 7 beats
2 1
2 10
&
Correct choice : (1)
The number of beta particles emitted by a radioactive substance is twice the
17.
number of alpha particles emitted by it. The resulting daughter is an:
isomer of parent isotone of parent
(1) (2)
isotope of parent isobar of parent
(3) (4)
&
Correct choice : (3)

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The shows a plot of photo current versus anode potential for a photo
18. Figure
sensitive surface for three different radiations. Which one of the following is a
statement?
correct
curves (a) and (b) represent incident radiations of same frequency but of
(1)
different intensities.
curves (b) and (c) represent incident radiations of different frequencies and
(2)
different intensities.
curves (b) and (c) represent incident radiations of same frequency having
(3)
same intensity.
curves (a) and (b) represent incident radiations of different frequencies and
(4)
different intensities.
&
Correct choice : (1)
The showselliptical orbit ofa planet about thesum S. Theshaded area
19. Figure m
SCD is twice the shaded area SAB. If is the time for the planet of move from C
t
1
to D and is the time to move from A to B then:
t
2
t = 4t t = 2t t = t t > t
(1) 1 2 (2) 1 2 (3) 1 2 (4) 1 2
SCD : A ) t (areal velocity constant)
Sol: 1 1
SAB : A ) t
2 2
A A A
1 = 2, t = t 4 1, A = 2A
1 2 1 2
t t A
1 2 2
& t = 2t
1 2
&
Correct choice : (2)

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A black body at 2275C radiates heat at the rate of 7 Cals/cm2s. At a temperature
20.
of 7275C, the rate of heat radiated in the same units will be:
50 112 80 60
(1) (2) (3) (4)
4
E = 6T ,
Sol:
4
4
E T
2 2 1000
= = = 16
E T 500
1 1
T = 500 K
1
T = 1000 K
2
2
& E = 16 2 7 = 112 cal/cm s.
2
&
Correct choice : (2)
The driver of a car travelling with speed 30 m/sec towards a hill sounds a horn of
21.
frequency 600 Hz. If the velocity of sound in air is 330 m/s, the frequency of
reflected sound as heard by driver is:
555.5 Hz 720 Hz 500 Hz 550 Hz
(1) (2) (3) (4)
Sol:
v v A 30 v A 30 360
f7 = f, f8 = f7 = f = × 600
v B 30 v v B 30 300
= 720 Hz
&
Correct choice : (2)
A wire of resistance 12 ohms per meter is bent to form a complete circle of radius
22.
10 cm. The resistance between its two diametrically opposite points, A and B as
shown in the is:
Figure,
3 9 6 + 9 6 9 0.6 + 9
(1) (2) (3) (4)

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Sol:
2+R !" 12 9
6 × 6
& R = = 3 9
12
&
Correct choice : (1)
A rectangular, a square, a circular and an elliptical loop, all in the (x ) y) plane,
23.
are moving out of a uniform magnetic field with a constant velocity, V =vi. The
magnetic field is directed along the negative z axis direction. The induced ,
emf
during the passage of these loops, out of the field region, will not remain constant
for:
the circular and the elliptical loops.
(1)
only the elliptical loop.
(2)
any of the four loops.
(3)
the rectangular, circular and elliptical loops.
(4)
As the loop leaves the magnetic field, area in magnetic field decreases for all
Sol:
loops, so induced emf does not remain constant. (Any of four loops)
&
Correct choice : (3)
A galvanometerhaving a coilresistance of 609 shows fullscale deflection whena
24.
current of 1.0 amp passes through it. It can be converted into an ammeter to read
currents upto 5.0 amp by:
putting in series a resistance of 15 9
(1)
putting in series a resistance of 240 9
(2)
putting in parallel a resistance of 15 9
(3)
putting in parallel a resistance of 240 9
(4)
G = 60 9, I = 1.0 A, I = 5 A.
Sol: g
I G= (I ) I ) S,
g g
I G
S = g = 1 × 60 = 15 9
I B I 5 B 1
g
putting 15 9 in parallel.
&
Correct choice : (3)

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Power dissipated in an LCR series circuit connected to an a.c source of , is:
25. emf
2 2
,2 R2 A Lw B 1 ,2 R2 A Lw B 1
Cw Cw

(1) R (2) R
2 2
, R , R

(3) 2 (4) 2
R2 A Lw B 1 R2 A Lw B 1
Cw Cw
2 2
, , R
Power dissipated in series LCR: P = I2R = R =
Sol: 2 2
Z
2 1
R A 'L B
'C
&
Correct choice : (4)
Three concentricspherical shells haveradii a, band c (a< b< c) andhave surface
26.
charge densities 6, ) 6 and 6 respectively. If V , V and V denote the potentials
A B C
of the three shells, then for c = a + b, we have:
V = V : V V : V : V
(1) C B A (2) C B A
V = V = V V = V : V
(3) C B A (4) C A B
c = a + b.
Sol:
6Q 6b 6c 6
v = B A = c B b B a
A , , , ,
0 0 0 0
2
B 6b 1 6 × 4+a 6c
V = A ⋅ A
B , 4+, b ,
0 0 0
2 2
6 b B a
= c B
, b
0
6c 1 6 × 4+b2 1 6 × 4+a2 6 b2 B a2
V = B ⋅ A ⋅ = c B
C , 4+, c 4+, c , c
0 0 0 0
6
= c B b B a
,
0
V = V : V
A C B
&
Correct choice : (4)

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