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JEE Main DPYQ Full Syllabus PAPER-9

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Page 1
DPYQ JEE Main FULL Test - 9
for
JEE Main & NEET Aspirants
Topic : Full Syllabus
Time: 75 Min
(Moment of inertia of a spherical shell of mass m and radius R
about its diameter = 2/3mR2) :
[DPYQ From 2013]
Section - A : MCQs with Single Option Correct
1. A boy can throw a stone up to a maximum height of 20 m.
The maximum horizontal distance that the boy can throw the
same stone up to, will be :
[DPYQ From 2012]
(A) 20 2 m
(B) 40 m
(C) 10 2 m
(D) 20 m
the coefficient of friction between the box and the floor is
FA
is :
FB
1
3
,
[DPYQ From 2014]
(A)
3
(B)
(C)
3
2
(D)
O
2.0 m
2. A heavy box is to dragged along a rough horizontal floor.
To do so, person A pushes it at an angle 30º from the horizontal
and requires a minimum force FA, while person B pulls the box at
an angle 60º from the horizontal and needs minimum force FB. If
the ratio
Marking: +4 –1
5
3
2
3
30º
A
0.4 m
(A) 1.87 m
(C) 1.57 m
B
(B) 2.08 m
(D) 1.66 m
6. India's Mangalyan was sent to the Mars by launching it
into a transfer orbit EOM around the sun. It leaves the earth at
E and meets Mars at M. If the semi-major axis of Earth's orbit is
ae = 1.5 × 1011 m, that of Mars orbit am = 2.5 × 1011 m, taken
Kepler's laws give the estimate of time for Mangalyan to reach
Mars from Earth to be close to :
[DPYQ From 2014]
Mars orbit
O
3. A person trying to lose weight by burning fat lifts a mass
of 10 kg upto a height of 1 m 1000 times. Assume that the
potential energy lost each time he lowers the mass is dissipated.
How much fat will he use up considering the work done only
when the weight is lifted up? Fat supplies 3.8 × 107 J of energy
per kg which is converted to mechanical energy with a 40%
efficiency rate. Take g = 9.8 ms–2 :
[DPYQ From 2016]
(A) 2.45 × 10–3 kg
(B) 6.45 × 10–3 kg
(C) 9.89 × 10–3 kg
(D) 12.89 × 10–3 kg
(A) 500 days
(C) 262 days
4. A boy of mass 20 kg is standing on a 80 kg free to move on
a long cart. There is negligible friction between cart and ground.
Initially, the boy is standing 25 m from a wall. If he walks 20 m on
the cart towards the wall, then the final distance of the boy from
the wall will be :
[DPYQ From 2013]
(A) 15 m
(B) 12.5 m
(C) 9 m
(D) 17 m
7. A tank with a small hole at the bottom has been filled with
water and kerosene (specific gravity 0.8). The height of water is
4 m and that of kerosene 2 m. When the hole is opened the
velocity of fluid coming out from it is nearly : (take g = 10 ms–2
and density of water = 103 kg m–3) :
[DPYQ From 2014]
(A) 10.5 ms–1
(B) 9.6 ms–1
(C) 8.5 ms–1
(D) 7.6 ms–1
5. A tennis ball (treated as hollow spherical shell) starting
from O rolls down a hill. At point A the ball becomes air borne
leaving at an angle of 30º with the horizontal. The ball strikes
the ground at B. What is the value of the distance AB ?
8. This question has Statement-1 and Statement-2. Of the
four choices given after the Statements, choose the one that
best describes the two Statements.
[DPYQ From 2013]
M
am
ae
Sun
E
Earth's orbit
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(B) 320 days
(D) 220 days
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Statement-1 : A capillary is dipped in a liquid and liquid rises
to a height h in it. As the temperature of the liquid is raised, the
height h increases (if the density of the liquid and the angle of
contact remain the same).
Statement-2 : Surface tension of a liquid increases with the
rise in its temperature.
(A) Statement-1 is true, Statement-2 is true; Statement-2 is not
the correct explanation for Statement-1
(B) Statement-1 is false, Statement-2 is true
(C) Statement-1 is false, Statement-2 is false
(D) Statement-1 is true, Statement-2 is true; Statement-2 is the
correct explanation for Statement-1
9. Three rods of Copper, Brass and Steel are welded together
to form a Y-shaped structure. Area of cross-section of each rod
= 5 cm2. End of copper rod is maintained at 100°C where as ends
of brass and steel are kept at 0°C. Lengths of the copper, brass
and steel rods are 46, 13 and 12 cms respectively. The rods are
thermally insulated from surroundings except at ends. Thermal
conductivities of copper, brass and steel are 0.92, 0.26 and
0.12 CGS units respectively. Rate of heat flow through copper
rod is :
[DPYQ From 2014]
(A) 1.2 cal/s
(B) 2.4 cal/s
(C) 4.8 cal/s
(D) 6.0 cal/s
Page 2
potential.
(A) Statement-1 is false and Statement-2 is true
(B) Statement-1 and Statement-2 both are true. Statement-2 is
the correct explanation of Statement-1
(C) Statement-1 is true and Statement-2 is false
(D) Statement-1 and Statement-2 both are false.
11. A body is in simple harmonic motion with time period half
second (T = 2 sec.) and amplitude one cm (A = 1 cm). Find the
average velocity in the interval in which it moves form
equilibrium position to half of its amplitude :
[DPYQ From 2014]
(A) 3 cm/s
(B) 6 cm/s
(C) 12 cm/s
(D) 16 cm/s
12. The region between two concentric spheres of radii ‘a’ and
‘b’ respectively (see figure), has volume charge density
2A
=
, where A is a constant and r is the distance from the
r
centre. At the centre of the spheres is a point charge Q. The
value of A such that the electric field in the region between the
spheres will be constant, is :
[DPYQ From 2016]
a
Q
Chamber-I
ideal gas
b
10.
(A)
1
2
(C)
Chamber-II
Q
2 a
(B)
2
2Q
2
2
( a  b )
(D)
Q
2 (b 2  a 2 )
Q
4 a 2
real gas
13. The potential (in volts) of a charge distribution is given by
V(z) = 30 – 10z2 for |z|  1m
3
4
There are two identical chambers, completely thermally insulated
from surroundings. Both chambers have a partition wall dividing
the chambers in two compartments. Compartment 1 is filled
with an ideal gas and Compartment 3 is filled with a real gas.
Compartments 2 and 4 are vacuum. A small hole (orifice) is made
in the partition walls and the gases are allowed to expand in
vacuum.
[DPYQ From 2013]
Statement-1 : No change in temperature of the gas takes place
when ideal gas expands in vacuum. However, the temperature
of real gas goes down (cooling) when it expands in vacuum.
Statement-2 : The internal energy of an ideal gas in only
potential. The internal energy of a real gas is kinetic as well as
V(z) = 35 – 20 |z| for |z|  1m
V(z) does not depend on x and y. If this potential is generated
by a constant charge per unit volume 0 (in units of 0) which is
spread over a certain region, then choose the correct statement:
[DPYQ From 2016]
(A) 0 = 20 0 in the entire region
(B) 0 = 10 0 for | z |  1 m and p0 = 0 elsewhere
(C) 0 = 20 0 for | z |  1 m and p0 = 0 elsewhere
(D) 0 = 40 0 in the entire region
14. The circuit in figure consists of wires at the top and bottom
and identical springs as the left and right sides. The wire at the
bottom has a mass of 10 g and is 5 cm long. The wire is hanging
as shown in the figure. The springs stretch 0.2 cm under the
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weight of the wire and the circuit has a total resistance of 12 .
When the lower wire is subjected to a static magnetic field, the
springs, stretch an additional 0.3 cm. The magnetic field is :
[DPYQ From 2012]
24V
Magnetic
field region
5cm
(A) 0.6 T and directed out of page
(B) 1.2 T and directed into the plane of page
(C) 0.6 T and directed into the plane of page
(D) 1.5 T and directed out of page
15. A fighter plane of length 20 m, wing span (distance from tip
of one wing to the tip of the other wing) of 15 m and height 5 m
is lying towards east over Delhi. Its speed is 200 ms–1. The
earth’s magnetic field over Delhi is 5 × 10–5 T with the declination
angle ~ 0° and dip of  such that sin  = 2/3. If the voltage
developed is VB between the lower and upper side of the plane
of VW between the tips of the wings then VB and VW are close
to:
[DPYQ From 2016]
(A) VB = 37 mV; Vw = 100 mV with left side of pilot at higher
voltage
(B) VB = 45 mV; VW = 120 mV with right side of pilot at higher
voltage
(C) VB = 40 mV; VW = 135 mV with right side of pilot at higher
voltage
(D) VB = 45 mV; VW = 120 mV with left side of pilot at higher
voltage
Page 3
17. A lamp emits monochromatic green light uniformly in all
directions. The lamp is 4% efficient in converting electrical power
to electromagnetic waves and consumes 100 W of power. The
amplitude of the electric field associated with the
electromagnetic radiation at a distance of 5 m from the lamp will
be nearly :
[DPYQ From 2014]
(A) 1.34 V/m
(B) 2.68 V/m
(C) 3.09 V/m
(D) 5.36 V/m
18. An air bubble of radius 0.1 cm is in a liquid having surface
tension 0.06 N/m and density 103 kg/m3. The pressure inside
the bubble is 2080 Nm–2 greater than the atmospheric pressure.
At what depth is the bubble below the surface of the liquid ?
(g = 9.8 ms–2) :
[DPYQ From 2014]
(A) 0.1 m
(B) 0.15 m
(C) 0.20 m
(D) 0.25 m
19. A beam of light has two wavelengths of 4972 Å and 6216 Å
with a total intensity of 3.6 × 10–3 Wm–2 equally distributed
among the two wavelengths. The beam falls normally on an
area of 1 cm2 of a clean metallic surface of work function 2.3 eV.
Assume that there is no loss of light by reflection and that each
capable photon ejects one electron. The number of
photoelectrons liberated in 5s is approximately :
[DPYQ From 2014]
11
11
(A) 6 × 10
(B) 9 × 10
(C) 22.5 × 1011
(D) 15 × 1011
20. Which logic gate with inputs A and B performs the same
operation as that performed by the following circuit ?
[DPYQ From 2012]
A
B
V
Lamp
16. In an LCR circuit shown in the following figure, what will
be the readings of the voltmeter across the resistor and ammeter
if an a.c. source of 200 V and 100 Hz is connected to it as
shown ?
[DPYQ From 2012]
L
V
300V
C
V
300V
~
200 V, 100 Hz
(A) 800 V, 8 A
(B) 110 V, 1.1 A
(C) 200 V, 4 A
(D) 220 V, 2.2 A
\
(B) OR gate
(D) AND gate
Section- B: INTEGER Answer Type Questions
50 
V
VR
(A) NAND gate
(C) NOR gate
A
1. A bullet fired into a fixed target loses half of its velocity
after penetrating 3 cm. How much further it will penetrate before
coming to rest, assuming that it faces constant resistance to
motion ? (in cm)
[DPYQ From 2005]
2.
 The gravitational field in a region is given by
g = 5 N/kg iˆ + 12 N/kg ĵ . The change in the gravitational
potential energy of a particle of mass 1 kg when it is taken from
the origin to a point (7 m, –3 m) is : (in J) [DPYQ From 2014]
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3. A steel wire can sustain 100 kg weight without breaking. If
the wire is cut into four equal parts, each can sustain a weight
of................ (in kg)
[DPYQ From 2012]
between the points A and D will be :
5
2 × 10
A
B
5
D
C
300K
T
[DPYQ From 2015]
D
E
2V
4
2
R
4V
A
9V
B
3V
C
7. If the temperature of the sun were to increase from T to 2T
and its radius from R to 2R, then the ratio of the radiant energy
received on earth to what it was previously, will be :
[DPYQ From 2004]
P(Pa)
1 × 10
2
F
4. Directions : This question is based on the following
paragraph.
Two moles of helium gas are taken over the cycle ABCDA, as
shown in the P-T diagram.
P
Page 4
T
500K
The net work done on the gas in the cycle ABCDA is mR. Find
‘m’.
[DPYQ From 2009]
5. When two waves travel in the same direction in a medium,
the displacements of a particle located at ‘x’ at time ‘t’ is given
by :
y1 = 0.05 cos (0.50x – 100t)
y2 = 0.05 cos (0.45x – 92t)
where y1, y2 and x are in meters and t in seconds. The speed of
sound in the medium is : (in m/s)
[DPYQ From 2013]
6. In the electric network shown, when no current flows
through the 4  resistor in the arm EB, the potential difference
*
* *
8. In an experiment of single slit diffraction pattern, first
minimum for red light coincides with first maximum of some
other wavelength. If wavelength of red light is 6900 Å, then
wavelength of first maximum will be : (in Å)
[DPYQ From 2014]
9. The intensity of gamma radiation from a given source is I.
On passing through 36 mm of lead, it is reduced to I/16. The
thickness of lead, which will reduce the intensity to I/2 will be :
(in mm)
[DPYQ From 2005]
L
.
g
Measured value of L is 20.0 cm know to 1 mm accuracy and time
for 100 oscillations of the pendulum is found to be 90 s using a
wrist watch of 1 s resolution. Find the percentage accuracy in
the determination of g.
[DPYQ From 2015]
10. The period of oscillation of a simple pendulum is T = 2
*
*
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DPYQ JEE Main FULL Test - 9
for
JEE Main & NEET Aspirants
Topic : Full Syllabus
Time: 75 Min
Marking: +4 –1
ANSWER KEY
Section - A : MCQs with Single Option Correct
1. (B)
5. (D)
9. (D)
13. (C)
17. (C)
2. (A)
6. (C)
10. (D)
14. (D)
18. (C)
3. (B)
7. (A)
11. (A)
15. (A)
19. (C)
4. (C)
8. (C)
12. (D)
16. (C)
20. (B)
3. (100)
7. (64 )
4. (276)
8. (4600)
Section- B: INTEGER Answer Type Questions
1. (1)
5. (200)
9. (9)
2. (1)
6. (5)
10. (2.72)
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