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question_answer1) Two particles are performing simple harmonic motion in a straight line about the same equilibrium point. The amplitude and time period for both particles are same and equal to A and T, respectively. At time t = 0 one particle has displacement A while the other one has displacement \[\frac{-A}{2}\]and they are moving towards each other If they cross each at time t, then t is :
JEE Main Online Paper (Held On 09 April 2016)
A)
\[\frac{T}{4}\]
done
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B)
\[\frac{5T}{6}\]
done
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C)
\[\frac{T}{3}\]
done
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D)
\[\frac{T}{6}\]
done
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question_answer2)
To find the focal length of a convex mirror, a student records the following data :
| Object pin |
Convex Lens |
Convex Mirror |
Image Pin |
| 22.2 cm |
32.2 cm |
45.8 cm |
71.2 cm |
The focal length of the convex lens is\[{{f}_{1}}\] and that of mirror is \[{{f}_{2}}.\]Then taking index correction to be negligibly small, \[{{f}_{1}}\]and \[{{f}_{2}}.\] are close to :
JEE Main Online Paper (Held On 09 April 2016)
A)
\[{{f}_{1}}=15.6cm\] \[{{f}_{2}}=25.4cm\]
done
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B)
\[{{f}_{1}}=7.8cm\] \[{{f}_{2}}=12.7cm\]
done
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C)
\[{{f}_{1}}=7.8cm\] \[{{f}_{2}}=25.4cm\]
done
clear
D)
\[{{f}_{1}}=12.7cm\] \[{{f}_{2}}=7.8cm\]
done
clear
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question_answer3)
Figure shows elliptical path abcd of a planet around the sun S such that the area of triangle csa is\[\frac{1}{4}\]the area of the ellipse . (See figure) With db as the semi major axis, and ca as the semi minor axis. If \[{{t}_{1}}\]is the time taken for planet to go over path abc and \[{{t}_{2}}\]for path taken over cda then : 
JEE Main Online Paper (Held On 09 April 2016)
A)
\[{{t}_{1}}=3{{t}_{2}}\]
done
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B)
\[{{t}_{1}}={{t}_{2}}\]
done
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C)
\[{{t}_{1}}=2{{t}_{2}}\]
done
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D)
\[{{t}_{1}}=4{{t}_{2}}\]
done
clear
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question_answer4) A simple pendulum made of a bob of mass m and a metallic wire of negligible mass has time period 2s at T = 0°C. If the temperature of the wire is increased and the corresponding charge in its time period is plotted against its temperature, the resulting graph is a line of slop S. If the coefficient of linear expansion of metal is a then the value of S is :
JEE Main Online Paper (Held On 09 April 2016)
A)
\[\frac{1}{\alpha }\]
done
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B)
\[2\alpha \]
done
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C)
\[\frac{\alpha }{2}\]
done
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D)
\[\alpha \]
done
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question_answer5) The ratio of work done by an ideal monatomic gas to the heat supplied to it in an isobaric process is :
JEE Main Online Paper (Held On 09 April 2016)
A)
\[\frac{3}{2}\]
done
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B)
\[\frac{2}{3}\]
done
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C)
\[\frac{3}{5}\]
done
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D)
\[\frac{2}{5}\]
done
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question_answer6) An unknown transistor needs to be identified as npn or pnp type .A multi meter, with +ve and .ve terminals, is used to measure resistance between different terminals transistor. If terminal 2 is the base of the transistor then which of the following is correct for a pnp transistor?
JEE Main Online Paper (Held On 09 April 2016)
A)
+ve terminal 3, .ve terminal 2, resistance high
done
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B)
+ve terminal 2, .ve terminal 3, resistance low
done
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C)
+ve terminal 1, .ve terminal 2, resistance high
done
clear
D)
+ve terminal 2, .ve terminal 1, resistance high
done
clear
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question_answer7) A uniformly tapering conical wire is made from a material of Young's modulus Y and has a normal, un extended length L. The radii, at the upper and lower ends of this conical wire , have values R and 3R, respectively, The upper end of the wire is fixed to a rigid support and a mass M is suspended from its lower and . The equilibrium extended length, of this wire, would equal
JEE Main Online Paper (Held On 09 April 2016)
A)
\[L\left( 1+\frac{1}{3}\frac{Mg}{\pi Y{{R}^{2}}} \right)\]
done
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B)
\[L\left( 1+\frac{2}{3}\frac{Mg}{\pi Y{{R}^{2}}} \right)\]
done
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C)
\[L\left( 1+\frac{1}{9}\frac{Mg}{\pi Y{{R}^{2}}} \right)\]
done
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D)
\[L\left( 1+\frac{2}{9}\frac{Mg}{\pi Y{{R}^{2}}} \right)\]
done
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question_answer8)
A cubical block of side 30cm is moving with velocity \[2m{{s}^{-1}}\]on a smooth horizontal surface. The surface has a bump ata point O as shown in figure. The angular velocity (in rad/s) of the block immediately after it hits the bump, is : 
JEE Main Online Paper (Held On 09 April 2016)
A)
9.4
done
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B)
6.7
done
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C)
5.0
done
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D)
13.3
done
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question_answer9) In Young's double slit experiment, the distance between slits and the screen is 1.0 m and monochromatic light of 600 nm is being used. A person standing near the slits is looking at the fringe pattern . When the separation between the slits is varied, the interference pattern disappears for a particular distance \[{{d}_{0}}\] between the slits. If the angular resolution of the eye is\[\frac{{{1}^{o}}}{60}\]the value of \[{{d}_{0}}\] is close to
JEE Main Online Paper (Held On 09 April 2016)
A)
2 mm
done
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B)
1 mm
done
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C)
3 mm
done
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D)
4 mm
done
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question_answer10) Which of the following option correctly describes the variation of the speed v and acceleration 'a' of a point mass falling vertically in a viscous medium that applies a force F = -kv, where 'k' is constant , on the body ? (Graphs are schematic and not drawn to scale)
JEE Main Online Paper (Held On 09 April 2016)
A)
done
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B)
done
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C)
done
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D)
done
clear
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question_answer11) A series LR circuit is connected to a voltage source with \[V(t)={{V}_{0}}\sin \Omega t.\]After very large time current I (t) behaves as \[\left( {{t}_{0}}>>\frac{L}{r} \right):\]
JEE Main Online Paper (Held On 09 April 2016)
A)
I (t)
B)
l (t)
C)
I (t)
D)
l (t)
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question_answer12) A car of weight W is on an inclined road that rises by 100 m over a distance of 1km and applies a constant frictional force \[\frac{W}{20}\] on the car. While moving uphill on the road at a speed of \[10m{{s}^{-1}},\]the car needs power \[\frac{P}{2}\]If it needs power while moving downhill at speed v then value of v is :
JEE Main Online Paper (Held On 09 April 2016)
A)
\[5\,m{{s}^{-1}}\]
done
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B)
\[20\,m{{s}^{-1}}\]
done
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C)
\[10\,m{{s}^{-1}}\]
done
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D)
\[15\,m{{s}^{-1}}\]
done
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question_answer13) A rocket is fired vertically from the earth with an acceleration of 2g, where g is the gravitational acceleration. On an inclined plane inside the rocket, making an angle \[\theta \]. With the horizontal , a point object of mass m is kept. The minimum coefficient of friction \[{{\mu }_{\min }}\] between the mass and the inclined surface such that he mass does not move is :
JEE Main Online Paper (Held On 09 April 2016)
A)
\[\tan \theta \]
done
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B)
\[\tan 2\theta \]
done
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C)
\[3\tan \theta \]
done
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D)
\[2\tan \theta \]
done
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question_answer14) Two engines pass each other moving in opposite directions with uniform speed of 30m/s. One of them is blowing a whistle of frequency 540 Hz. Calculate the frequency heard by driver of second engine before pass each other. Speed sound is 330 m/sec.
JEE Main Online Paper (Held On 09 April 2016)
A)
540 Hz
done
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B)
648 Hz
done
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C)
270 Hz
done
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D)
450 Hz
done
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question_answer15) The potential (in volts) of a charge distribution is given by \[V(z)=30-5{{z}^{2}}\]for\[|z|\le 1m\] \[V(z)=35-10|z|\]for\[|z|\ge 1m.\] V(z) does not depend on x and y . If this potential is generated by a constant charge per unit volume \[{{\rho }_{0}},\](in units of \[{{\varepsilon }_{0}}\]) which is spread over certain region ,then choose the correct statement.
JEE Main Online Paper (Held On 09 April 2016)
A)
\[{{\rho }_{0}}=40{{\varepsilon }_{0}}\]in the entire region
done
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B)
\[{{\rho }_{0}}=20{{\varepsilon }_{0}}\] in the entire region
done
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C)
\[{{\rho }_{0}}=20{{\varepsilon }_{0}}\] for \[|z|\]in\[\le 1m\]and \[{{\rho }_{0}}=0\]else where
done
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D)
\[{{\rho }_{0}}=10{{\varepsilon }_{0}}\]for \[|z|\]in \[\le 1m\]and\[{{\rho }_{0}}=0\] else where
done
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question_answer16) An audio signal consists of two distinct sound : one a human speech signal in the frequency band of 200 Hz to 2700 Hz, while the other is a high frequency music signal in the frequency band of 10200 Hz to 15200 Hz. The ratio of the AM signal band width required to send both the signals together to the AM signal band width required to send just the human speech is :
JEE Main Online Paper (Held On 09 April 2016)
A)
6
done
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B)
5
done
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C)
3
done
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D)
2
done
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question_answer17)
A convex lens, of focal length 30cm, a concave lens of focal length 120 cm, and a plane mirror are arranged as shown. For an object kept at a distance of 60 cm from the convex lens, the final image, formed by the combination, is a real image, at a distance of : 
Focal length| |Focal length| = 30 cm =120 cm 
JEE Main Online Paper (Held On 09 April 2016)
A)
70 cm from the concave lens
done
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B)
60 cm from the convex lens
done
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C)
60 cm from the concave lens
done
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D)
70 cm from the convex lens
done
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question_answer18) Three capacitors each of \[4\mu F\]are to be connected in such a way that the effective capacitance is \[6\mu F.\] This can be done by connecting them :
JEE Main Online Paper (Held On 09 April 2016)
A)
all in series
done
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B)
two in parallel and one in series
done
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C)
two in series and one in parallel
done
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D)
all in parallel
done
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question_answer19) To know the resistance G of a galvanometer by half deflection method, a battery of emf \[{{V}_{E}}\] and resistance R is used to deflect the galvanometer by angle\[\theta .\]If a shunt of resistance S is needed to gat half deflection then G, R and S are related by the equation :
JEE Main Online Paper (Held On 09 April 2016)
A)
2S = G
done
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B)
2G = S
done
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C)
S(R+G) = RG
done
clear
D)
2S(R+G) = RG
done
clear
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question_answer20)
In the circuit shown, the resistance r is a variable resistance. If for r = fR, the heat generation in r is maximum then the value of f is : 
JEE Main Online Paper (Held On 09 April 2016)
A)
1
done
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B)
\[\frac{3}{4}\]
done
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C)
\[\frac{1}{4}\]
done
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D)
\[\frac{1}{2}\]
done
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question_answer21) A hydrogen atom makes a transition from n = 2 to n=1 and emits a photon. This photon strikes a doubly ionized lithium atom (z = 3) in excited state and completely removes the orbiting electron. The least quantum number for the excited stated of the ion for the process is :
JEE Main Online Paper (Held On 09 April 2016)
A)
4
done
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B)
5
done
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C)
2
done
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D)
3
done
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question_answer22) 200 g water is heated from \[40{}^\circ C\] to \[60{}^\circ C\]. Ignoring the slight expansion of water, the change in its internal energy is closed to (Given specific heat of water = 4184 J/kg/K) :
JEE Main Online Paper (Held On 09 April 2016)
A)
16.7 kJ
done
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B)
167.4kJ
done
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C)
4.2 kJ
done
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D)
8.4 kJ
done
clear
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question_answer23) An experiment is performed to determine the I - V characteristics of a Zener diode, which has a protective resistance of \[R=100\Omega ,\]and maximum power of dissipation rating of 1W. The minimum voltage range of the DC source in the circuit is :
JEE Main Online Paper (Held On 09 April 2016)
A)
\[0.12V\]
done
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B)
\[0.5V\]
done
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C)
\[0.24\]
done
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D)
\[0 . 8V\]
done
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question_answer24) Microwave oven acts on the principle of :
JEE Main Online Paper (Held On 09 April 2016)
A)
giving rotational energy to water molecules
done
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B)
giving vibrational energy to water molecules
done
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C)
giving translational energy to water molecules
done
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D)
transferring electrons from lower to higher energy levels in water molecule
done
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question_answer25) A magnetic dipole is acted upon by two magnetic fields which are inclined to each other a tan angle of \[75{}^\circ \]. One of the fields has magnitude of 15mT. The dipole attains stable equilibrium at an angle \[30{}^\circ \] with this field. The magnitude of the other field (in mT) is close to :
JEE Main Online Paper (Held On 09 April 2016)
A)
11
done
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B)
1060
done
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C)
36
done
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D)
1
done
clear
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question_answer26) \[A50\Omega \]resistance is connected to a battery of 5V. A galvanometer of resistance \[100\Omega \]is to be used as ammeter to measure current through the resistance, for this a resistance \[{{r}_{s}}\] is connected to the galvanometer. Which of the following connections should be employed if the measured current is within 1% of the current without the ammeter in the circuit ?
JEE Main Online Paper (Held On 09 April 2016)
A)
\[{{r}_{s}}=0.5\Omega n\]parallel with the galvanometer
done
clear
B)
\[{{r}_{s}}=0.5\Omega \]in series with the galvanometer
done
clear
C)
\[{{r}_{s}}=1\Omega \] in series with galvanometer
done
clear
D)
\[{{r}_{s}}=1\Omega \] in parallel with galvanometer
done
clear
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question_answer27) When photons of wavelength \[{{\lambda }_{1}}\], are incident on an isolated sphere, the corresponding stopping potential is found to be V. When photons of wavelength \[{{\lambda }_{2}}\]are used , the corresponding stopping potential was thrice that of the above value. If light of wavelength \[{{\lambda }_{3}}.\]is used then find the stopping potential for this case
JEE Main Online Paper (Held On 09 April 2016)
A)
\[\frac{hc}{e}\left[ \frac{1}{{{\lambda }_{3}}}+\frac{1}{2{{\lambda }_{2}}}-\frac{3}{2{{\lambda }_{1}}} \right]\]
done
clear
B)
\[\frac{hc}{e}\left[ \frac{1}{{{\lambda }_{3}}}+\frac{1}{{{\lambda }_{2}}}-\frac{3}{{{\lambda }_{1}}} \right]\]
done
clear
C)
\[\frac{hc}{e}\left[ \frac{1}{{{\lambda }_{3}}}+\frac{1}{2{{\lambda }_{2}}}-\frac{1}{{{\lambda }_{1}}} \right]\]
done
clear
D)
\[\frac{hc}{e}\left[ \frac{1}{{{\lambda }_{3}}}-\frac{1}{{{\lambda }_{2}}}-\frac{1}{{{\lambda }_{1}}} \right]\]
done
clear
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question_answer28) In the following 'I' refers to current and other symbols have their usual meaning choose the option that corresponds to the dimensions of electrical conductivity :
JEE Main Online Paper (Held On 09 April 2016)
A)
\[{{M}^{-1}}{{L}^{-3}}{{T}^{3}}{{I}^{2}}\]
done
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B)
\[{{M}^{-1}}{{L}^{3}}{{T}^{3}}I\]
done
clear
C)
\[M{{L}^{-3}}{{T}^{-3}}{{I}^{2}}\]
done
clear
D)
\[{{M}^{-1}}{{L}^{-3}}{{T}^{3}}I\]
done
clear
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question_answer29)
Consider a water jar of radius R that has water filled up to height H and is kept on a stand of height h (see figure). Through a hole of radius r (r<<R) at its bottom, the water leaks out and the stream of water coming down towards the ground has a shape like a funnel as shown in the figure. If the radius of the cross-section of water stream when it hits the ground is x. Then : 
JEE Main Online Paper (Held On 09 April 2016)
A)
\[x=r{{\left( \frac{H}{H+h} \right)}^{2}}\]
done
clear
B)
\[x=r\left( \frac{H}{H+h} \right)\]
done
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C)
\[x=r{{\left( \frac{H}{H+h} \right)}^{\frac{1}{4}}}\]
done
clear
D)
\[x=r{{\left( \frac{H}{H+h} \right)}^{\frac{1}{2}}}\]
done
clear
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question_answer30)
The truth table given in fig. represents :
| A |
B |
Y |
| 0 |
0 |
0 |
| 0 |
1 |
1 |
| 1 |
0 |
1 |
| 1 |
1 |
1 |
JEE Main Online Paper (Held On 09 April 2016)
A)
AND - Gate
done
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B)
OR - Gate
done
clear
C)
NOR - Gate
done
clear
D)
NAND - Gate
done
clear
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