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JEE Main 2011 Paper - 1 with Solutions


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69 Questions MCQ Test | JEE Main 2011 Paper - 1 with Solutions

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JEE Main 2011 Paper - 1 with Solutions - 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

Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 1

JEE Main 2011 Paper - 1 with Solutions - 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

Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 2

JEE Main 2011 Paper - 1 with Solutions - Question 3

Consider an electric field   where E0 is a constant. The flux through the shaded area (as shown in the figure) due to this field is

Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 3

(E0) (Projected area ) = E0a2

JEE Main 2011 Paper - 1 with Solutions - Question 4

5.6 liter of helium gas at STP is adiabatically compressed to 0.7 liter. Taking the initial temperature to be
T1, the work done in the process is

Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 4

JEE Main 2011 Paper - 1 with Solutions - 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

Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 5

JEE Main 2011 Paper - 1 with Solutions - 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

Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 6 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.
JEE Main 2011 Paper - 1 with Solutions - 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

Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 7

*Multiple options can be correct
JEE Main 2011 Paper - 1 with Solutions - 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?

Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 8

*Multiple options can be correct
JEE Main 2011 Paper - 1 with Solutions - Question 9

A spherical metal shell A of radius RA and a solid metal sphere B of radius RB (<RA) are kept far apart and
each is given charge ‘+Q’. Now they are connected by a thin metal wire. Then

*Multiple options can be correct
JEE Main 2011 Paper - 1 with Solutions - 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

Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 10

*Multiple options can be correct
JEE Main 2011 Paper - 1 with Solutions - 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?

Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 11

Both will travel in semicircular path
Since, m is different, hence time will be different

JEE Main 2011 Paper - 1 with Solutions - 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 ‘e0’. Use dimensional analysis to determine the
correct expression for ωp.

JEE Main 2011 Paper - 1 with Solutions - 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 ‘ωp’ 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 ωp 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.

Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 13

w = 2πc / λ

JEE Main 2011 Paper - 1 with Solutions - 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

JEE Main 2011 Paper - 1 with Solutions - 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 E1 and E2 are the total mechanical energies respectively. Then

Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 15

JEE Main 2011 Paper - 1 with Solutions - 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

*Answer can only contain numeric values
JEE Main 2011 Paper - 1 with Solutions - 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/s2. 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


Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 17

*Answer can only contain numeric values
JEE Main 2011 Paper - 1 with Solutions - 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 1011 N/m2 and radius of the wire is 1 mm. Assume that L diameter of the wire. Then the value of ‘m’ in kg is nearly


Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 18

*Answer can only contain numeric values
JEE Main 2011 Paper - 1 with Solutions - 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


*Answer can only contain numeric values
JEE Main 2011 Paper - 1 with Solutions - 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


Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 20

*Answer can only contain numeric values
JEE Main 2011 Paper - 1 with Solutions - Question 21

The activity of a freshly prepared radioactive sample is 1010 disintegrations per second, whose mean life is
109 s. The mass of an atom of this radioisotope is 10-25 kg. The mass (in mg) of the radioactive sample is


Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 21

*Answer can only contain numeric values
JEE Main 2011 Paper - 1 with Solutions - 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 = I0cos(300 t) where I0 is constant. If the magnetic moment of the loop is Nm0I0sin(300 t), then ‘N’ is


Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 22

*Answer can only contain numeric values
JEE Main 2011 Paper - 1 with Solutions - 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 kgm2,
then N is


Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 23

JEE Main 2011 Paper - 1 with Solutions - 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 N2 can be obtained by heating

Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 24

JEE Main 2011 Paper - 1 with Solutions - 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

JEE Main 2011 Paper - 1 with Solutions - 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,

Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 26

JEE Main 2011 Paper - 1 with Solutions - Question 27

Geometrical shapes of the complexes formed by the reaction of Ni2+ with Cl , CN and H2O, respectively,
are

Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 27

JEE Main 2011 Paper - 1 with Solutions - Question 28

The major product of the following reaction is

JEE Main 2011 Paper - 1 with Solutions - Question 29

Among the following compounds, the most acidic is

Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 29

Due to ortho effect o-hydroxy benzoic acid is strongest acid and correct order of decreasing Ka is

JEE Main 2011 Paper - 1 with Solutions - Question 30

AgNO3(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 AgNO3 is

Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 30

AgNO3 + KCl (aq) → AgCl (s) + KNO (aq)

Initially there is aq. KCl solution now as solution of AgNO3 is added, AgCl(s) is formed. Hence conductivity of solution is almost compensated (or slightly increase) by the formation of KNO3. After end point conductivity increases more rapidly because addition of excess AgNO3 solution.

*Multiple options can be correct
JEE Main 2011 Paper - 1 with Solutions - 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)

Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 31

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
JEE Main 2011 Paper - 1 with Solutions - Question 32

Extraction of metal from the ore cassiterite involves

Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 32

SnO2 + 2C → 2CO + Sn
The ore cassiterite contains the impurity of Fe, Mn, W and traces of Cu.

*Multiple options can be correct
JEE Main 2011 Paper - 1 with Solutions - Question 33

According to kinetic theory of gases

*Multiple options can be correct
JEE Main 2011 Paper - 1 with Solutions - Question 34

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

JEE Main 2011 Paper - 1 with Solutions - 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 C6H10, 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

Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 35

JEE Main 2011 Paper - 1 with Solutions - Question 36

Paragraph for Question Nos. 35 and 36

An acyclic hydrocarbon P, having molecular formula C6H10, 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

JEE Main 2011 Paper - 1 with Solutions - 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 NH3 dissolves O and gives an intense blue solution.

Q. The metal rod M is

Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 37

While Cu partially oxidizes to Cu(NO3)2 and remaining AgNO3 reacts with NaCl.

JEE Main 2011 Paper - 1 with Solutions - 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 NH3 dissolves O and gives an intense blue solution.

Q. The compound N is

JEE Main 2011 Paper - 1 with Solutions - 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 NH3 dissolves O and gives an intense blue solution.

Q. The final solution contains

Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 39

*Answer can only contain numeric values
JEE Main 2011 Paper - 1 with Solutions - 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 Na2S4O6 is


Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 40

S will have oxidation number = +5, 0
Difference in oxidation number = 5

*Answer can only contain numeric values
JEE Main 2011 Paper - 1 with Solutions - 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


Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 41

*Answer can only contain numeric values
JEE Main 2011 Paper - 1 with Solutions - 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


Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 42

*Answer can only contain numeric values
JEE Main 2011 Paper - 1 with Solutions - Question 43

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


Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 43

*Answer can only contain numeric values
JEE Main 2011 Paper - 1 with Solutions - Question 44

Reaction of Br2 with Na2CO3 in aqueous solution gives sodium bromide and sodium bromate with evolution of CO2 gas. The number of sodium bromide molecules involved in the balanced chemical equation is


Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 44

3Br2 + 3Na2CO3 → 5NaBr + NaBrO3 + 3CO2
So, number of NaBr molecules = 5

*Answer can only contain numeric values
JEE Main 2011 Paper - 1 with Solutions - 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 0oC) are introduced. Considering the ideal gas behaviour, the total volume (in litre) of the gases at 0oC is close to


Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 45

*Answer can only contain numeric values
JEE Main 2011 Paper - 1 with Solutions - Question 46

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


Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 46

JEE Main 2011 Paper - 1 with Solutions - 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 (x0, y0) be solution of the following equations

Then x0 is

Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 47

JEE Main 2011 Paper - 1 with Solutions - Question 48

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

Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 48

JEE Main 2011 Paper - 1 with Solutions - Question 49

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

Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 49

JEE Main 2011 Paper - 1 with Solutions - Question 50

The value of 

Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 50

JEE Main 2011 Paper - 1 with Solutions - 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

Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 51

JEE Main 2011 Paper - 1 with Solutions - Question 52

Let α and β be the roots of x2 – 6x – 2 = 0, with a > b. If an = αn – βn for n > 1, then the value of is

Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 52

JEE Main 2011 Paper - 1 with Solutions - 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 R1(0 << b) and R2(b < x < 1) such that R1 - R2 = 1/4. Then b equals

*Multiple options can be correct
JEE Main 2011 Paper - 1 with Solutions - 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

Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 54

*Multiple options can be correct
JEE Main 2011 Paper - 1 with Solutions - Question 55

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

Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 55

*Multiple options can be correct
JEE Main 2011 Paper - 1 with Solutions - Question 56

Let the eccentricity of the hyperbola  be reciprocal to that of the ellipse x2 + 4y2 = 4. If the
hyperbola passes through a focus of the ellipse, then

Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 56

*Multiple options can be correct
JEE Main 2011 Paper - 1 with Solutions - Question 57

Let M and N be two 3 x 3 non-singular skew symmetric matrices such that MN = NM. If PT denotes the
transpose of P, then M2N2 (MTN)–1 (MN–1)T is equal to

Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 57

MN = NM

JEE Main 2011 Paper - 1 with Solutions - 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 U1 and U2 be two urns such that U1 contains 3 white and 2 red balls, and U2 contains only 1 white ball. A fair coin is tossed. If head appears then 1 ball is drawn at random from U1 and put into U2. However, if tail appears then 2 balls are drawn at random from U1 and put into U2. Now 1 ball is drawn at random from U2.

Q. The probability of the drawn ball from U2 being white is

Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 58

JEE Main 2011 Paper - 1 with Solutions - Question 59

Paragraph for Question Nos. 58 to 59

Let U1 and U2 be two urns such that U1 contains 3 white and 2 red balls, and U2 contains only 1 white ball. A fair coin is tossed. If head appears then 1 ball is drawn at random from U1 and put into U2. However, if tail appears then 2 balls are drawn at random from U1 and put into U2. Now 1 ball is drawn at random from U2.

Q. Given that the drawn ball from U2 is white, the probability that head appeared on the coin is

Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 59

JEE Main 2011 Paper - 1 with Solutions - 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

Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 60

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.

JEE Main 2011 Paper - 1 with Solutions - 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 x3 – 1 = 0 with Im(ω) > 0. If a = 2 with b and c satisfying (E), then the value of
 is equal to

Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 61

a = 2, b and c satisfies (E)
b = 12, c = – 14

JEE Main 2011 Paper - 1 with Solutions - 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 ax2 + bx + c = 0,
then 

Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 62

ax2 + bx + c = 0 ⇒ x2 + 6x – 7 = 0
⇒ α = 1, β = – 7

*Answer can only contain numeric values
JEE Main 2011 Paper - 1 with Solutions - 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 y2 = 8x. Let Δ1 be the area of the triangle formed by the end points of its latus rectum and the point  on the parabola, and Δ2 be the area of the triangle formed by drawing tangents at P and at the end points of the latus rectum. Then  is


Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 63

y2 = 8x = 4.2.x

 

*Answer can only contain numeric values
JEE Main 2011 Paper - 1 with Solutions - Question 64


Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 64

*Answer can only contain numeric values
JEE Main 2011 Paper - 1 with Solutions - Question 65

Let f: [1, ∞) → [2, ∞) be a differentiable function such that f(1) = 2. If  = 3xf(x) - x3 for all x >1, then the value of f(2) is


Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 65

3f(x) + 3xf'(x) – 3x2

⇒ 3f(x) = 3xf'(x) – 3x2 ⇒ xf'(x) – f(x) = x2
…(i)

Multiplying (i) both sides by 1/x

  integrating

 = x + c

Put x = 1, y = 2

⇒ 2 = 1 + c ⇒ c = 1 ⇒ y = x2 + x

⇒ f(x) = x2 + 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
JEE Main 2011 Paper - 1 with Solutions - Question 66

The positive integer value of n > 3 satisfying the equation 


Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 66

*Answer can only contain numeric values
JEE Main 2011 Paper - 1 with Solutions - Question 67

Let a1, a2, a3, …, a100 be an arithmetic progression with a1 = 3 and Sp, 1 < p 100. For any integer
n with 1 < n < 20, let m = 5n. If  does not depend on n, then a2 is


Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 67

a1, a2, a3, … a100 is an A.P.

*Answer can only contain numeric values
JEE Main 2011 Paper - 1 with Solutions - Question 68

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


Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 68

*Answer can only contain numeric values
JEE Main 2011 Paper - 1 with Solutions - Question 69

The minimum value of the sum of real numbers a–5, a–4, 3a–3, 1, a8 and a10 with a > 0 is


Detailed Solution for JEE Main 2011 Paper - 1 with Solutions - Question 69

minimum value = 8

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