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This mock test of JEE Main 2011 Paper - 1 with Solutions for JEE helps you for every JEE entrance exam.
This contains 69 Multiple Choice Questions for JEE JEE Main 2011 Paper - 1 with Solutions (mcq) to study with solutions a complete question bank.
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QUESTION: 1

**SECTION – I (Total Marks : 21)**

**(Single Correct Answer Type)**

This section contains 7 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of

which ONLY ONE is correct.

**Q.** A police car with a siren of frequency 8 kHz is moving with uniform velocity 36 km/hr towards a tall

building which reflects the sound waves. The speed of sound in air is 320 m/s. The frequency of the siren

heard by the car driver is

Solution:

QUESTION: 2

The wavelength of the first spectral line in the Balmer series of hydrogen atom is 6561 Å. The wavelength

of the second spectral line in the Balmer series of singly-ionized helium atom is

Solution:

QUESTION: 3

Consider an electric field where E_{0} is a constant. The flux through the shaded area (as shown in the figure) due to this field is

Solution:

(E_{0}) (Projected area ) = E_{0}a^{2}

QUESTION: 4

5.6 liter of helium gas at STP is adiabatically compressed to 0.7 liter. Taking the initial temperature to be

T_{1}, the work done in the process is

Solution:

QUESTION: 5

A 2 μF capacitor is charged as shown in the figure. The percentage of its stored energy dissipated after the switch S is turned to position 2 is

Solution:

QUESTION: 6

A meter bridge is set-up as shown, to determine an unknown resistance ‘X’ using a standard 10 ohm resistor.

The galvanometer shows null point when tapping-key is at 52 cm mark. The end-corrections are 1 cm and 2 cm respectively for the ends A and B. The determined value of ‘X’ is

Solution:
Applying the condition of balanced Wheatstone bridge, we get
x/10ohm =(52+1) cm/(48+2) cm =53/50
x=10ohm ×53/50
x=10.6ohm
option 'b' is correct.

QUESTION: 7

A ball of mass (m) 0.5 kg is attached to the end of a string having length (L) 0.5 m. The ball is rotated on a horizontal circular path about vertical axis. The maximum tension that the string can bear is 324 N. The maximum possible value of angular velocity of ball (in radian/s) is

Solution:

*Multiple options can be correct

QUESTION: 8

**SECTION – II (Total Marks : 16)**

(Multiple Correct Answers Type)

This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of

which ONE OR MORE may be correct.

**Q.** A metal rod of length ‘L’ and mass ‘m’ is pivoted at one end. A thin disk of mass ‘M’ and radius ‘R’ (<L) is attached at its center to the free end of the rod. Consider two ways the disc is attached: (case A). The disc is not free to rotate about its centre and (case B) the disc is free to rotate about its centre. The rod-disc system

performs SHM in vertical plane after being released from the same displaced position. Which of the following statement(s) is (are) true?

Solution:

*Multiple options can be correct

QUESTION: 9

A spherical metal shell A of radius R_{A} and a solid metal sphere B of radius R_{B} (<R_{A}) are kept far apart and

each is given charge ‘+Q’. Now they are connected by a thin metal wire. Then

Solution:

*Multiple options can be correct

QUESTION: 10

A composite block is made of slabs A, B, C, D and E of different thermal conductivities (given in terms of a

constant K) and sizes (given in terms of length, L) as shown in the figure. All slabs are of same width. Heat

‘Q’ flows only from left to right through the blocks. Then in steady state

Solution:

*Multiple options can be correct

QUESTION: 11

An electron and a proton are moving on straight parallel paths with same velocity. They enter a semiinfinite

region of uniform magnetic field perpendicular to the velocity. Which of the following statement(s) is / are true?

Solution:

Both will travel in semicircular path

Since, m is different, hence time will be different

QUESTION: 12

**SECTION-III (Total Marls : 15)**

(Paragraph Type)

This section contains 2 paragraphs. Based upon one of paragraphs 2 multiple choice questions and based on the other paragraph 3 multiple choice questions have to be answered. Each of these questions has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

**Paragraph for Question Nos. 12 and 13**

A dense collection of equal number of electrons and positive ions is called neutral plasma. Certain solids containing fixed positive ions surrounded by free electrons can be treated as neutral plasma. Let ‘N’ be the number density of free electrons, each of mass ‘m’. When the electrons are subjected to an electric field, they are displaced relatively away from the heavy positive ions. If the electric field becomes zero, the electrons begin to oscillate about the positive ions with a natural angular frequency ‘wp’ which is called the plasma frequency. To sustain the oscillations, a time varying electric field needs to be applied that has an angular frequency w, where a part of the energy is absorbed and a part of it is reflected. As w approaches wp all the free electrons are set to resonance together and all the energy is reflected. This is the explanation of high reflectivity of metals.

**Q. **Taking the electronic charge as ‘e’ and the permittivity as ‘e_{0}’. Use dimensional analysis to determine the

correct expression for ω_{p}.

Solution:

QUESTION: 13

**Paragraph for Question Nos. 12 and 13**

A dense collection of equal number of electrons and positive ions is called neutral plasma. Certain solids containing fixed positive ions surrounded by free electrons can be treated as neutral plasma. Let ‘N’ be the number density of free electrons, each of mass ‘m’. When the electrons are subjected to an electric field, they are displaced relatively away from the heavy positive ions. If the electric field becomes zero, the electrons begin to oscillate about the positive ions with a natural angular frequency ‘ω_{p}’ which is called the plasma frequency. To sustain the oscillations, a time varying electric field needs to be applied that has an angular frequency ω, where a part of the energy is absorbed and a part of it is reflected. As ω approaches ω_{p} all the free electrons are set to resonance together and all the energy is reflected. This is the explanation of high reflectivity of metals.

**Q.** Estimate the wavelength at which plasma reflection will occur for a metal having the density of electrons

where these quantities are in proper SI units.

Solution:

w = 2πc / λ

QUESTION: 14

**Paragraph for Question Nos. 14 to 16**

Phase space diagrams are useful tools in analyzing all kinds of dynamical problems. They are especially useful in studying the changes in motion as initial position and momenum are changed. Here we consider some simple dynamical systems in onedimension. For such systems, phase space is a plane in which position is plotted along horizontal axis and momentum is plotted along vertical axis. The phase space diagram is x(t) vs. p(t) curve in this plane. The arrow on the curve indicates the time flow. For example, the phase space diagram for a particle moving with constant velocity is a straight line as shown in the figure. We use the sign convention in which positon or momentum upwards (or to right) is positive and downwards (or to left) is negative.

**Q. **The phase space diagram for a ball thrown vertically up from ground is

Solution:

QUESTION: 15

The phase space diagram for simple harmonic motion is a circle centered at the origin. In the figure, the two circles represent the same oscillator but for different initial conditions, and E_{1} and E_{2} are the total mechanical energies respectively. Then

Solution:

QUESTION: 16

Consider the spring-mass system, with the mass submerged in water, as shown in the figure. The phase space diagram for one cycle of this system is

Solution:

*Answer can only contain numeric values

QUESTION: 17

**SECTION-IV (Total Marks : 28)**

**(Integer Answer Type)**

This section contains 7 questions. The answer to each of the questions is a single digit integer, ranging from 0 to 9.

**Enter only the numerical value in the space provided below.**

Q. A boy is pushing a ring of mass 2 kg and radius 0.5 m with a stick as shown in the figure. The stick applies a force of 2N on the ring and rolls it without slipping with an acceleration of 0.3 m/s^{2}. The coefficient of

friction between the ground and the ring is large enough that rolling always occurs and the coefficeint of friction between the stick and the ring is (P/10). The value of P is

Solution:

*Answer can only contain numeric values

QUESTION: 18

Steel wire of lenght ‘L' at 40°C is suspended from the ceiling and then a mass ‘m’ is hung from its free end. The wire is cooled down from 40°C to 30°C to regain its original length ‘L’. The coefficient of linear thermal expansion of the steel is 10^{-5}/°C, Young’s modulus of steel is 10^{11} N/m^{2} and radius of the wire is 1 mm. Assume that L diameter of the wire. Then the value of ‘m’ in kg is nearly

Solution:

*Answer can only contain numeric values

QUESTION: 19

Four point charges, each of +q, are rigidly fixed at the four corners of a square planar soap film of side ‘a’.

The surface tension of the soap film is γ. The system of charges and planar film are in equilibrium, and

where ‘k’ is a constant. Then N is

Solution:

*Answer can only contain numeric values

QUESTION: 20

A block is moving on an inclined plane making an angle 45° with the horizontal and the coefficient of friction is m. The force required to just push it up the inclined plane is 3 times the force required to just prevent it from sliding down. If we define N = 10 μ, then N is

Solution:

*Answer can only contain numeric values

QUESTION: 21

The activity of a freshly prepared radioactive sample is 10^{10 }disintegrations per second, whose mean life is

10^{9} s. The mass of an atom of this radioisotope is 10^{-25} kg. The mass (in mg) of the radioactive sample is

Solution:

*Answer can only contain numeric values

QUESTION: 22

A long circular tube of length 10 m and radius 0.3 m carries a current I along its curved surface as shown. A wire-loop of resistance 0.005 ohm and of radius 0.1 m is placed inside the tube with its axis coinciding with the axis of the tube. The current varies as I = I_{0}cos(300 t) where I_{0} is constant. If the magnetic moment of the loop is Nm_{0}I_{0}sin(300 t), then ‘N’ is

Solution:

*Answer can only contain numeric values

QUESTION: 23

Four solid spheres each of diameter cm and mass 0.5 kg are placed with their centers at the corners of

a square of side 4 cm. The moment of inertia of the system about the diagonal of the square is N x 10^{-4} kgm^{2},

then N is

Solution:

QUESTION: 24

**SECTION – I (Total Marks : 21)**

(Single Correct Answer Type)

This section contains 7 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of

which ONLY ONE is correct.

**Q.** Extra pure N_{2} can be obtained by heating

Solution:

QUESTION: 25

Dissolving 120 g of urea (mol. wt. 60) in 1000 g of water gave a solution of density 1.15 g/mL. The molarity of the solution is

Solution:

QUESTION: 26

Bombardment of aluminium by a-particle leads to its artificial disintegration in two ways, (i) and (ii) as shown. Products X, Y and Z respectively are,

Solution:

QUESTION: 27

Geometrical shapes of the complexes formed by the reaction of Ni^{2+} with Cl^{–} , CN^{–} and H_{2}O, respectively,

are

Solution:

QUESTION: 28

The major product of the following reaction is

Solution:

QUESTION: 29

Among the following compounds, the most acidic is

Solution:

Due to ortho effect o-hydroxy benzoic acid is strongest acid and correct order of decreasing K_{a} is

QUESTION: 30

AgNO_{3}(aq.) was added to an aqueous KCl solution gradually and the conductivity of the solution was

measured. The plot of conductance (L) versus the volume of AgNO_{3} is

Solution:

AgNO_{3} + KCl (aq) → AgCl (s) + KNO (aq)

Initially there is aq. KCl solution now as solution of AgNO_{3} is added, AgCl(s) is formed. Hence conductivity of solution is almost compensated (or slightly increase) by the formation of KNO_{3}. After end point conductivity increases more rapidly because addition of excess AgNO_{3} solution.

*Multiple options can be correct

QUESTION: 31

**SECTION – II (Total Marks : 16)**

(Multiple Correct Answers Type)

This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of

which ONE OR MORE may be correct.

Q. Amongst the given options, the compound(s) in which all the atoms are in one plane in all the possible

conformations (if any), is (are)

Solution:

Along C-C single bond conformations are possible in butadiene in which all the atoms may not lie in the same plane.

*Multiple options can be correct

QUESTION: 32

Extraction of metal from the ore cassiterite involves

Solution:

SnO_{2} + 2C → 2CO + Sn

The ore cassiterite contains the impurity of Fe, Mn, W and traces of Cu.

*Multiple options can be correct

QUESTION: 33

According to kinetic theory of gases

Solution:

*Multiple options can be correct

QUESTION: 34

The correct statement(s) pertaining to the adsorption of a gas on a solid surface is (are)

Solution:

QUESTION: 35

**SECTION-III (Total Marls : 15)**

(Paragraph Type)

This section contains 2 paragraphs. Based upon one of paragraphs 2 multiple choice questions and based on the other paragraph 3 multiple choice questions have to be answered. Each of these questions has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

**Paragraph for Question Nos. 35 and 36**

An acyclic hydrocarbon P, having molecular formula C_{6}H_{10}, gave acetone as the only organic product through the following sequence of reaction, in which Q is an intermediate organic compound.

**Q. **The structure of compound P is

Solution:

QUESTION: 36

**Paragraph for Question Nos. 35 and 36**

An acyclic hydrocarbon P, having molecular formula C_{6}H_{10}, gave acetone as the only organic product through the following sequence of reaction, in which Q is an intermediate organic compound.

**Q. **The structure of the compound Q is

Solution:

QUESTION: 37

**Paragraph for Question Nos. 37 to 39**

When a metal rod M is dipped into an aqueous colourless concentrated solution of compound N, the solution turns light blue. Addition of aqueous NaCl to the blue solution gives a white precipitate O. Addition of aqueous NH_{3} dissolves O and gives an intense blue solution.

Q. The metal rod M is

Solution:

While Cu partially oxidizes to Cu(NO_{3})_{2} and remaining AgNO_{3} reacts with NaCl.

QUESTION: 38

**Paragraph for Question Nos. 37 to 39**

When a metal rod M is dipped into an aqueous colourless concentrated solution of compound N, the solution turns light blue. Addition of aqueous NaCl to the blue solution gives a white precipitate O. Addition of aqueous NH_{3} dissolves O and gives an intense blue solution.

**Q.** The compound N is

Solution:

QUESTION: 39

**Paragraph for Question Nos. 37 to 39**

When a metal rod M is dipped into an aqueous colourless concentrated solution of compound N, the solution turns light blue. Addition of aqueous NaCl to the blue solution gives a white precipitate O. Addition of aqueous NH_{3} dissolves O and gives an intense blue solution.

**Q.** The final solution contains

Solution:

*Answer can only contain numeric values

QUESTION: 40

**SECTION-IV (Total Marks : 28)**

(Integer Answer Type)

This section contains 7 questions. The answer to each of the questions is a single digit integer, ranging from 0 to 9.

**Enter the numerical value only in the space provided below.**

**Q.** The difference in the oxidation numbers of the two types of sulphur atoms in Na_{2}S_{4}O_{6} is

Solution:

S will have oxidation number = +5, 0

Difference in oxidation number = 5

*Answer can only contain numeric values

QUESTION: 41

A decapeptide (Mol. Wt. 796) on complete hydrolysis gives glycine (Mol. Wt. 75), alanine and phenylalanine. Glycine contributes 47.0% to the total weight of the hydrolysed products. The number of glycine units present in the decapeptide is

Solution:

*Answer can only contain numeric values

QUESTION: 42

The work function (φ) of some metals is listed below. The number of metals which will show photoelectric effect when light of 300 nm wavelength falls on the metal is

Solution:

*Answer can only contain numeric values

QUESTION: 43

The maximum number of electrons that can have principal quantum number, n = 3, and spin quantum

number, is

Solution:

*Answer can only contain numeric values

QUESTION: 44

Reaction of Br_{2} with Na_{2}CO_{3} in aqueous solution gives sodium bromide and sodium bromate with evolution of CO_{2} gas. The number of sodium bromide molecules involved in the balanced chemical equation is

Solution:

3Br_{2} + 3Na_{2}CO_{3} → 5NaBr + NaBrO_{3} + 3CO_{2}

So, number of NaBr molecules = 5

*Answer can only contain numeric values

QUESTION: 45

To an evacuated vessel with movable piston under external pressure of 1 atm, 0.1 mol of He and 1.0 mol of

an unknown compound (vapour pressure 0.68 atm. at 0^{o}C) are introduced. Considering the ideal gas behaviour, the total volume (in litre) of the gases at 0^{o}C is close to

Solution:

*Answer can only contain numeric values

QUESTION: 46

The total number of alkenes possible by dehydrobromination of 3-bromo-3-cyclopentylhexane using alcoholic KOH is

Solution:

QUESTION: 47

**SECTION – I (Total Marks : 21)**

(Single Correct Answer Type)

This section contains 7 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of

which ONLY ONE is correct.

**Q.** Let (x_{0}, y_{0}) be solution of the following equations

Then x_{0} is

Solution:

QUESTION: 48

Let P = {θ : sinθ - cosθ = cosθ} and Q = {θ : sin θ + cosθ = sin θ} be two sets. Then

Solution:

QUESTION: 49

Let be three vectors. A vector , whose projection on , is given by

Solution:

QUESTION: 50

The value of

Solution:

QUESTION: 51

A straight line L through the point (3, -2) is inclined at an angle 60° to the line . If L also

intersects the x-axis, then the equation of L is

Solution:

QUESTION: 52

Let α and β be the roots of x^{2} – 6x – 2 = 0, with a > b. If a_{n} = α_{n} – β_{n} for n __>__ 1, then the value of is

Solution:

QUESTION: 53

Let the straight line x = b divides the area enclosed by y = (1 - x)^{2}, y = 0 and x = 0 into two parts R_{1}(0 __<__ x __<__ b) and R_{2}(b __<__ x __<__ 1) such that R_{1} - R_{2} = 1/4. Then b equals

Solution:

*Multiple options can be correct

QUESTION: 54

**SECTION – II (Total Marks : 16)**

(Multiple Correct Answers Type)

This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of

which ONE or MORE may be correct.

**Q.** Let f: R → R be a function such that If f(x) is differentiable at x = 0, then

Solution:

*Multiple options can be correct

QUESTION: 55

The vector(s) which is/are coplanar with vectors and perpendicular to the vector is/are

Solution:

*Multiple options can be correct

QUESTION: 56

Let the eccentricity of the hyperbola be reciprocal to that of the ellipse x^{2} + 4y^{2} = 4. If the

hyperbola passes through a focus of the ellipse, then

Solution:

*Multiple options can be correct

QUESTION: 57

Let M and N be two 3 x 3 non-singular skew symmetric matrices such that MN = NM. If P^{T} denotes the

transpose of P, then M^{2}N^{2} (M^{T}N)–1 (MN^{–1})^{T} is equal to

Solution:

MN = NM

QUESTION: 58

**SECTION-III (Total Marls : 15)**

(Paragraph Type)

This section contains 2 paragraphs. Based upon one of paragraphs 2 multiple choice questions and based on the other paragraph 3 multiple choice questions have to be answered. Each of these questions has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

**Paragraph for Question Nos. 58 to 59**

Let U_{1} and U_{2} be two urns such that U1 contains 3 white and 2 red balls, and U_{2} contains only 1 white ball. A fair coin is tossed. If head appears then 1 ball is drawn at random from U_{1} and put into U_{2}. However, if tail appears then 2 balls are drawn at random from U_{1} and put into U_{2}. Now 1 ball is drawn at random from U_{2}.

**Q.** The probability of the drawn ball from U_{2} being white is

Solution:

QUESTION: 59

**Paragraph for Question Nos. 58 to 59**

Let U_{1} and U_{2} be two urns such that U1 contains 3 white and 2 red balls, and U_{2} contains only 1 white ball. A fair coin is tossed. If head appears then 1 ball is drawn at random from U_{1} and put into U_{2}. However, if tail appears then 2 balls are drawn at random from U_{1} and put into U_{2}. Now 1 ball is drawn at random from U_{2}.

**Q.** Given that the drawn ball from U_{2} is white, the probability that head appeared on the coin is

Solution:

QUESTION: 60

**Paragraph for Question Nos. 60 to 62**

Let a, b and c be three real numbers satisfying

**Q.** If the point P(a, b, c), with reference to (E), lies on the plane 2x + y + z = 1, then the value of 7a + b + c is

Solution:

a + 8b + 7c = 0

9a + 2b + 3c = 0

a + b + c = 0

Solving these we get

b = 6a ⇒ c = – 7a

now 2x + y + z = 0

⇒ 2a + 6a + (–7a) = 1 ⇒ a = 1, b = 6, c = – 7.

QUESTION: 61

**Paragraph for Question Nos. 60 to 62**

Let a, b and c be three real numbers satisfying

**Q.** Let w be a solution of x^{3} – 1 = 0 with I_{m}(ω) > 0. If a = 2 with b and c satisfying (E), then the value of

is equal to

Solution:

a = 2, b and c satisfies (E)

b = 12, c = – 14

QUESTION: 62

**Paragraph for Question Nos. 60 to 62**

Let a, b and c be three real numbers satisfying

**Q.** Let b = 6, with a and c satisfying (E). If α and β are the roots of the quadratic equation ax^{2} + bx + c = 0,

then

Solution:

ax^{2} + bx + c = 0 ⇒ x^{2} + 6x – 7 = 0

⇒ α = 1, β = – 7

*Answer can only contain numeric values

QUESTION: 63

**SECTION-IV (Total Marks : 28)**

(Integer Answer Type)

This section contains 7 questions. The answer to each of the questions is a single digit integer, ranging from 0 to 9.

**Enter only the numerical value in space provided below.**

**Q.** Consider the parabola y^{2} = 8x. Let Δ_{1} be the area of the triangle formed by the end points of its latus rectum and the point on the parabola, and Δ_{2} be the area of the triangle formed by drawing tangents at P and at the end points of the latus rectum. Then is

Solution:

y_{2} = 8x = 4.2.x

*Answer can only contain numeric values

QUESTION: 64

Solution:

*Answer can only contain numeric values

QUESTION: 65

Let f: [1, ∞) → [2, ∞) be a differentiable function such that f(1) = 2. If = 3xf(x) - x^{3} for all x __ >__1, then the value of f(2) is

Solution:

3f(x) + 3xf'(x) – 3x^{2}

⇒ 3f(x) = 3xf'(x) – 3x^{2} ⇒ xf'(x) – f(x) = x^{2}

…(i)

Multiplying (i) both sides by 1/x

integrating

= x + c

Put x = 1, y = 2

⇒ 2 = 1 + c ⇒ c = 1 ⇒ y = x^{2} + x

⇒ f(x) = x^{2} + x ⇒ f(2) = 6.

Note: If we put x = 1 in the given equation we get f(1) = 1/3.

*Answer can only contain numeric values

QUESTION: 66

The positive integer value of n > 3 satisfying the equation

Solution:

*Answer can only contain numeric values

QUESTION: 67

Let a_{1}, a_{2}, a_{3}, …, a_{100} be an arithmetic progression with a_{1} = 3 and S_{p} = , 1 __<__ p __< __100. For any integer

n with 1 __<__ n __<__ 20, let m = 5n. If does not depend on n, then a_{2} is

Solution:

a_{1}, a_{2}, a_{3}, … a_{100} is an A.P.

*Answer can only contain numeric values

QUESTION: 68

If z is any complex number satisfying |z – 3 – 2i| __<__ 2, then the minimum value of |2z – 6 + 5i| is

Solution:

*Answer can only contain numeric values

QUESTION: 69

The minimum value of the sum of real numbers a^{–5}, a^{–4}, 3a^{–3}, 1, a^{8} and a^{10} with a > 0 is

Solution:

minimum value = 8

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