JEE Main 2012 Paper -1 with Solutions - JEE MCQ
30 Questions MCQ Test - JEE Main 2012 Paper -1 with Solutions
SECTION I
Q. No. 1 - 10 carry 3 marks each and 1 mark is deducted for every wrong answer.
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Q.
In the determination of Young’s modulus 
by using Searle’s method, a wire of length L = 2m
and diameter d = 0.5 mm is used. For a load M = 2.5 kg, an extension 
= 0.25 mm in the length of the wire
is observed. Quantities d and are measured using a screw gauge and a micrometer, respectively. They
have the same pitch of 0.5 mm. The number of divisions on their circular scale is 100. The contributions to
the maximum probable error of the Y measurement
by using Searle’s method, a wire of length L = 2mand diameter d = 0.5 mm is used. For a load M = 2.5 kg, an extension
= 0.25 mm in the length of the wireis observed. Quantities d and
are measured using a screw gauge and a micrometer, respectively. Theyhave the same pitch of 0.5 mm. The number of divisions on their circular scale is 100. The contributions to
the maximum probable error of the Y measurement
A small mass m is attached to a massless string whose other end is fixed at P as shown in the figure. The
mass is undergoing circular motion in the x-y plane with centre at O and constant angular speed ω. If the
angular momentum of the system, calculated about O and P are denoted by 
respectively, then
mass is undergoing circular motion in the x-y plane with centre at O and constant angular speed ω. If the
angular momentum of the system, calculated about O and P are denoted by
respectively, then
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A bi-convex lens is formed with two thin plano-convex lenses as shown in the figure. Refractive index n of
the first lens is 1.5 and that of the second lens is 1.2. Both the curved surface are of the same radius of
curvature R = 14 cm. For this bi-convex lens, for an object distance of 40 cm, the image distance will be
the first lens is 1.5 and that of the second lens is 1.2. Both the curved surface are of the same radius of
curvature R = 14 cm. For this bi-convex lens, for an object distance of 40 cm, the image distance will be
A thin uniform rod, pivoted at O, is rotating in the horizontal plane with constant angular speed ω, as shown in the figure. At time t = 0, a small insect starts from O and moves with constant speed v, with respect to the
rod towards the other end. It reaches the end of the rod at t = T and stops. The angular speed of the system remains ω throughout. The magnitude of the torque 
about O, as a function of time is best represented by which plot?
A mixture of 2 moles of helium gas (atomic mass = 4 amu) and 1 mole of argon gas (atomic mass = 40
amu) is kept at 300 K in a container. The ratio of the rms speeds 
is
Two large vertical and parallel metal plates having a separation of 1 cm are connected to a DC voltage
source of potential difference X. A proton is released at rest midway between the two plates. It is found to
move at 450 to the vertical JUST after release. Then X is nearly
Three very large plates of same area are kept parallel and close to each other. They are considered as ideal
black surfaces and have very high thermal conductivity. The first and third plates are maintained at
temperatures 2T and 3T respectively. The temperature of the middle (i.e. second) plate under steady state
condition is
A small block is connected to one end of a massless spring of un-stretched length 4.9 m. The other end of
the spring (see the figure) is fixed. The system lies on a horizontal frictionless surface. The block is
stretched by 0.2 m and released from rest at t = 0. It then executes simple harmonic motion with angular
frequency ω = π/3 rad/s. Simultaneously at t = 0, a small pebble is projected with speed v form point P at
an angle of 450 as shown in the figure. Point P is at a horizontal distance of 10 m from O. If the pebble hits
the block at t = 1 s, the value of v is (take g = 10 m/s2)
Young’s double slit experiment is carried out by using green, red and blue light, one color at a time. The
fringe widths recorded are 
respectively. Then
Consider a thin spherical shell of radius R with centre at the origin, carrying uniform positive surface
charge density. The variation of the magnitude of the electric field 
and the electric potential V(r)
with the distance r from the centre, is best represented by which graph?
SECTION II
Q. No. 11 -15 carry 4 mark each
Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct.
Q.
Consider the motion of a positive point charge in a region where there are simultaneous uniform electric
and magnetic fields 
At time t = 0, this charge has velocity 
in the x-y plane, making an angle q with the x-axis. Which of the following option(s) is (are) correct for time t > 0?
A cubical region of side a has its centre at the origin. It encloses three fixed point charges, -q at
(0, -a/4, 0), +3q at (0, 0, 0) and -q at (0, +a/4, 0). Choose the correct options(s)
are same due to symmetryA person blows into open-end of a long pipe. As a result, a high pressure pulse of air travels down the pipe.
When this pulse reaches the other end of the pipe,
A small block of mass of 0.1 kg lies on a fixed inclined plane PQ which makes an angle θ with the
horizontal. A horizontal force of 1 N acts on the block through its centre of mass as shown in the figure.
The block remains stationary if (take g = 10 m/s2)
For the resistance network shown in the figure, choose the correct option(s)
SECTION III
Q. No. 16 - 20 carry 4 marks each
The answer to each question is single digit integer, ranging from 0 to 9 (both inclusive).
A circular wire loop of radius R is placed in the x-y plane centered at the origin O. A square loop of side a(a<<R) having two turns is placed with its centre at z = along the axis of the circular wire loop, as shown in figure. The plane of the square loop makes an angle of 45° with respect to the z-axis. If the mutual inductance between the loops is given by
then the value of p is
An infinitely long solid cylinder of radius R has a uniform volume charge density r. It has a spherical
cavity of radius R/2 with its centre on the axis of the cylinder, as shown in the figure. The magnitude of the
electric field at the point P, which is at a distance 2R from the axis of the cylinder, is given by the
expression 
The value of k is
A proton is fired from very far away towards a nucleus with charge Q = 120 e, where e is the electronic
charge. It makes a closest approach of 10 fm to the nucleus. The de Broglie wavelength (in units of fm) of
the proton at its start is: (take the proton mass, mp = (5/3) x 10-27 kg; h/e = 4.2 x 10-15 J.s / C;
A lamina is made by removing a small disc of diameter 2R from a bigger disc of uniform mass density and
radius 2R, as shown in the figure. The moment of inertia of this lamina about axes passing though O and P
is IO and IP respectively. Both these axes are perpendicular to the plane of the lamina. The ratio IP / IO to
the nearest integer is
A cylindrical cavity of diameter a exists inside a cylinder of diameter 2a as shown in the figure. Both the
cylinder and the cavity are infinity long. A uniform current density J flows along the length. If the
magnitude of the magnetic field at the point P is given by 
then the value of N is
SECTION – I
Q. No. 21- 30 caeey 3 marks each and 1 mark is deducted for every wrong answer
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Q.
A compound MpXq has cubic close packing (ccp) arrangement of X. Its unit cell structure is shown below.
The empirical formula of the compound is
The carboxyl functional group (–COOH) is present in
As per IUPAC nomenclature, the name of the complex [Co(H2O)4(NH3)2]Cl3 is
In allene (C3H4), the type(s) of hybridization of the carbon atoms is (are)
The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is [a0 is Bohr radius]
Which ordering of compounds is according to the decreasing order of the oxidation state of nitrogen?
For one mole of a van der Waals gas when b = 0 and T = 300 K, the PV vs. 1/V plot is shown below. The
value of the van der Waals constant a (atm.litre2mol–2) is
The number of aldol reaction(s) that occurs in the given transformation is
The colour of light absorbed by an aqueous solution of CuSO4 is
The number of optically active products obtained from the complete ozonolysis of the given compound is
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