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JEE Main 2012 Paper -1 with Solutions


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JEE Main 2012 Paper -1 with Solutions - Question 1

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

Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 1

JEE Main 2012 Paper -1 with Solutions - Question 2

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

Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 2

JEE Main 2012 Paper -1 with Solutions - Question 3

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

Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 3

JEE Main 2012 Paper -1 with Solutions - Question 4

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?

Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 4

JEE Main 2012 Paper -1 with Solutions - Question 5

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

Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 5

JEE Main 2012 Paper -1 with Solutions - Question 6

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

Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 6

JEE Main 2012 Paper -1 with Solutions - Question 7

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

Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 7

JEE Main 2012 Paper -1 with Solutions - Question 8

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)

Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 8

JEE Main 2012 Paper -1 with Solutions - Question 9

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

Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 9

JEE Main 2012 Paper -1 with Solutions - Question 10

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?

*Multiple options can be correct
JEE Main 2012 Paper -1 with Solutions - Question 11

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?

 

Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 11

If θ = 90°, 

If  θ = 0° 10° ;the charge particle moves in helix with increasing pitch due to 

*Multiple options can be correct
JEE Main 2012 Paper -1 with Solutions - Question 12

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)

Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 12

Net flux through the cubical region  

The flux passing through the faces   are same due to symmetry

*Multiple options can be correct
JEE Main 2012 Paper -1 with Solutions - Question 13

A 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,

Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 13

At the open end, the phase of a pressure wave changes by π radian due to reflection. At the closed end, there is no change in the phase of a pressure wave due to reflection.

*Multiple options can be correct
JEE Main 2012 Paper -1 with Solutions - Question 14

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)

Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 14

At θ = 45° , mg sin q = 1xcosθ
At θ > 45° , mg sin q > 1xcosθ (friction acts upward)
At θ < 45° , mg sin q < 1xcosθ (friction acts downward)

*Multiple options can be correct
JEE Main 2012 Paper -1 with Solutions - Question 15

For the resistance network shown in the figure, choose the correct option(s)

Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 15

Nodes P and Q are equipotential and nodes S
and T are equipotential from wheatstone bridge, no current passes through PQ and ST.

*Answer can only contain numeric values
JEE Main 2012 Paper -1 with Solutions - Question 16

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


Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 16

JEE Main 2012 Paper -1 with Solutions - Question 17

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

Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 17

*Answer can only contain numeric values
JEE Main 2012 Paper -1 with Solutions - Question 18

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;


Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 18

*Answer can only contain numeric values
JEE Main 2012 Paper -1 with Solutions - Question 19

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


Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 19

*Answer can only contain numeric values
JEE Main 2012 Paper -1 with Solutions - Question 20

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


Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 20

JEE Main 2012 Paper -1 with Solutions - Question 21

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

Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 21

So, unit cell formula of the compound is M2X4 and the empirical formula of the compound is MX2.

JEE Main 2012 Paper -1 with Solutions - Question 22

The carboxyl functional group (–COOH) is present in

Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 22

JEE Main 2012 Paper -1 with Solutions - Question 23

As per IUPAC nomenclature, the name of the complex [Co(H2O)4(NH3)2]Cl3 is

Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 23

[Co(H2O)4(NH3)2]Cl3
Diamminetetraaquacobalt (III) chloride

JEE Main 2012 Paper -1 with Solutions - Question 24

In allene (C3H4), the type(s) of hybridization of the carbon atoms is (are)

Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 24

JEE Main 2012 Paper -1 with Solutions - Question 25

The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is [a0 is Bohr radius]

Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 25

JEE Main 2012 Paper -1 with Solutions - Question 26

Which ordering of compounds is according to the decreasing order of the oxidation state of nitrogen?

Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 26

JEE Main 2012 Paper -1 with Solutions - Question 27

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

Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 27

 

JEE Main 2012 Paper -1 with Solutions - Question 28

The number of aldol reaction(s) that occurs in the given transformation is

Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 28

JEE Main 2012 Paper -1 with Solutions - Question 29

The colour of light absorbed by an aqueous solution of CuSO4 is

Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 29

Aqueous solution of copper sulphate absorbs orange red light and appears blue (complementary colour).

JEE Main 2012 Paper -1 with Solutions - Question 30

The number of optically active products obtained from the complete ozonolysis of the given compound is

Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 30

*Multiple options can be correct
JEE Main 2012 Paper -1 with Solutions - Question 31

SECTION II

Q. No. 31 -35 carry 4 marks each

Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct.

Q.

Which of the following hydrogen halides react(s) with AgNO3(aq) to give a precipitate that dissolves in Na- 2S2O3(aq)?

Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 31

*Multiple options can be correct
JEE Main 2012 Paper -1 with Solutions - Question 32

Identify the binary mixture(s) that can be separated into individual compounds, by differential extraction, as
shown in the given scheme

Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 32

(A) Both are soluble in NaOH, hence inseparable.
(B) Only benzoic acid (C6H5COOH) is soluble in NaOH and NaHCO3, while benzyl alcohol (C6H5CH2OH)
is not. Hence, separable.
(C) Although NaOH can enable separation between benzyl alcohol (C6H5CH2OH) and phenol (C6H5OH) as
only the later is soluble in NaOH. However, in NaHCO3, both are insoluble. Hence, inseparable.
(D) a-phenyl acetic acid (C6H5CH2OH) is soluble in NaOH and NaHCO3. While benzyl alcohol
(C6H5CH2OH) is not. Hence, separable.

*Multiple options can be correct
JEE Main 2012 Paper -1 with Solutions - Question 33

For an ideal gas, consider only P-V work in going from an initial state X to the final state Z. The final state
Z can be reached by either of the two paths shown in the figure. Which of the following choice(s) is(are)
correct? [Take DS as change in entropy and w as work done]

Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 33

*Multiple options can be correct
JEE Main 2012 Paper -1 with Solutions - Question 34

Which of the following molecules, in pure form, is (are) unstable at room temperature?

Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 34

Compound  being antiaromatic are unstable at room temperature

*Multiple options can be correct
JEE Main 2012 Paper -1 with Solutions - Question 35

Choose the correct reason(s) for the stability of the lyophobic colloidal particles.

Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 35

Lyophobic colloids are stable due to preferential adsorption of ions on their surface from solution and potential difference between the fixed layer and the diffused layer of opposite charges around the colloidal
particles that makes lyophobic sol stable

*Answer can only contain numeric values
JEE Main 2012 Paper -1 with Solutions - Question 36

SECTION III

Q. No. 36 - 40 carry 4 marks each

The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive).

Q.

29.2 % (w/w) HCl stock solution has density of 1.25 g mL-1. The molecular weight of HCl is 36.5 g mol-1.
The volume (mL) of stock solution required to prepare a 200 mL solution of 0.4 M HCl is


Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 36

*Answer can only contain numeric values
JEE Main 2012 Paper -1 with Solutions - Question 37

The substituents R1 and R2 for nine peptides are listed in the table given below. How many of these
peptides are positively charged at pH = 7.0?


Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 37

Peptides with isoelectric point (pI) > 7, would exist as cation in neutral solution (pH = 7).
IV, VI, VIII and IX

*Answer can only contain numeric values
JEE Main 2012 Paper -1 with Solutions - Question 38

An organic compound undergoes first-order decomposition. The time taken for its decomposition to 1/8 and
1/10 of its initial concentration are t1/8 and t1/10 respectively. What is the value of

0.3


Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 38

*Answer can only contain numeric values
JEE Main 2012 Paper -1 with Solutions - Question 39

When the following aldohexose exists in its D-configuration, the total number of stereoisomers in its
pyranose form is


Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 39

Hence total number of stereoisomers in pyranose form of D-configuration = 23 = 8

*Answer can only contain numeric values
JEE Main 2012 Paper -1 with Solutions - Question 40

The periodic table consists of 18 groups. An isotope of copper, on bombardment with protons, undergoes a
nuclear reaction yielding element X as shown below. To which group, element X belongs in the periodic
table?


Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 40

JEE Main 2012 Paper -1 with Solutions - Question 41

SECTION I

Q. No 42- 50 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.

if  , then

Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 41

JEE Main 2012 Paper -1 with Solutions - Question 42

Let P = [aij] be a 3 × 3 matrix and let  If the determinant of P is 2, then the determinant of the matrix Q is

Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 42

JEE Main 2012 Paper -1 with Solutions - Question 43

The locus of the mid–point of the chord of contact of tangents drawn from points lying on the straight line
4x – 5y = 20 to the circle x2 + y2 = 9 is

Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 43

JEE Main 2012 Paper -1 with Solutions - Question 44

The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that
each person gets at least one ball is

Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 44

JEE Main 2012 Paper -1 with Solutions - Question 45

The integral   equals (for some arbitrary constant K)

Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 45

JEE Main 2012 Paper -1 with Solutions - Question 46

The point P is the intersection of the straight line joining the points Q(2, 3, 5) and R(1, –1, 4) with the plane
5x – 4y – z = 1. If S is the foot of the perpendicular drawn from the point T(2, 1, 4) to QR, then the length
of the line segment PS is

Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 46

JEE Main 2012 Paper -1 with Solutions - Question 47

Let 

Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 47

JEE Main 2012 Paper -1 with Solutions - Question 48

Let z be a complex number such that the imaginary part of z is nonzero and a = z2 + z + 1 is real. Then a
cannot take the value

Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 48

Given equation is z2 + z + 1 - a = 0
Clearly this equation do not have real roots if
D < 0
 1 - 4(1 - a) < 0
  4a < 3

a<3/4

JEE Main 2012 Paper -1 with Solutions - Question 49

The ellipse  is inscribed in a rectangle R whose sides are parallel to the coordinate axes.
Another ellipse E2 passing through the point (0, 4) circumscribes the rectangle R. The eccentricity of the
ellipse E2 is

Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 49

Alternate
Let the ellipse be  as it is passing through (0, 4) and (3, 2).

JEE Main 2012 Paper -1 with Solutions - Question 50

The function f : [0, 3] → [1, 29], defined by f(x) = 2x3 – 15x2 + 36x + 1, is

Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 50

*Multiple options can be correct
JEE Main 2012 Paper -1 with Solutions - Question 51

SECTION II

Q. No. 51 -55 carry 4 marks each.

Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct.

Q.

Tangents are drawn to the hyperbola   parallel to the straight line 2x - y = 1. The points of contact of the tangents on the hyperbola are

Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 51

Slope of tangent = 2

*Multiple options can be correct
JEE Main 2012 Paper -1 with Solutions - Question 52

Let  be such that   and   Then φ cannot satisfy

Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 52

*Multiple options can be correct
JEE Main 2012 Paper -1 with Solutions - Question 53

If y(x) satisfies the differential equation  y' - ytanx = 2x secx and y(0) = 0, then

Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 53

*Multiple options can be correct
JEE Main 2012 Paper -1 with Solutions - Question 54

A ship is fitted with three engines E1, E2 and E3. The engines function independently of each other with
respective probabilities 1/2, 1/4,  and 1/4 For the ship to be operational at least two of its engines must
function. Let X denote the event that the ship is operational and let X1, X2 and X3 denote respectively the
events that the engines E1, E2 and E3 are functioning. Which of the following is(are) true ?

Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 54

(B) P [exactly two engines of the ship are functioning  

*Multiple options can be correct
JEE Main 2012 Paper -1 with Solutions - Question 55

Let S be the area of the region enclosed by 

Then

Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 55

*Answer can only contain numeric values
JEE Main 2012 Paper -1 with Solutions - Question 56

SECTION III

Q. No. 56 - 60 carry 4 marks each

The answer to each question is single digit integer, ranging from 0 to 9 (both inclusive).

Q.

if  are unit vectors satisfying   is


Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 56

*Answer can only contain numeric values
JEE Main 2012 Paper -1 with Solutions - Question 57

Let f : IR → IR be defined as   The total number of points at which f attains either a local
maximum or a local minimum is


Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 57

so, total number of points of local maximum or minimum is 5.

*Answer can only contain numeric values
JEE Main 2012 Paper -1 with Solutions - Question 58

Let S be the focus of the parabola y2 = 8x and let PQ be the common chord of the circle x2 + y2 - 2x - 4y =
0 and the given parabola. The area of the triangle PQS is


Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 58

The parabola is x = 2t2, y = 4t
Solving it with the circle we get :

so, the points P and Q are (0, 0) and (2, 4) which are also diametrically opposite points on the circle. The
focus is S º (2, 0).

*Answer can only contain numeric values
JEE Main 2012 Paper -1 with Solutions - Question 59

Let p(x) be a real polynomial of least degree which has a local maximum at x = 1 and a local minimum at x
= 3. If p(1) = 6 and p(3) = 2, then p'(0) is


Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 59

*Answer can only contain numeric values
JEE Main 2012 Paper -1 with Solutions - Question 60

The value of  


Detailed Solution for JEE Main 2012 Paper -1 with Solutions - Question 60

 

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