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JEE Advanced 2011 Paper - 2 with Solutions - Question 1

**SECTION – I (Total Marks : 24)**

(Single Correct Answer Type)

This Section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of

which ONLY ONE is correct.

**Q. **Which of the field patterns given below is valid for electric field as well as for magnetic field?

JEE Advanced 2011 Paper - 2 with Solutions - Question 2

A ball of mass 0.2 kg rests on a vertical post of height 5 m. A bullet of mass 0.01 kg, traveling with a velocity V m/s in a horizontal direction, hits the centre of the ball. After the collision, the ball and bullet travel independently. The ball hits the ground at a distance of 20 m and the bullet at a distance of 100 m from the foot of the post. The velocity V of the bullet is

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 2

v_{ball} = 20 m/s

v_{bullet} = 100 m/s

0.01 V = 0.01 x 100 + 0.2 x 20

v = 100 + 400 = 500 m/s

JEE Advanced 2011 Paper - 2 with Solutions - Question 3

The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with

a screw gauge, whose pitch is 0.5 mm and there are 50 divisions on the circular scale. The reading on the

main scale is 2.5 mm and that on the circular scale is 20 divisions. If the measured mass of the ball has a

relative error of 2 %, the relative percentage error in the density is

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 3

JEE Advanced 2011 Paper - 2 with Solutions - Question 4

A wooden block performs SHM on a frictionless surface with frequency, ν_{0}. The block carries a charge +Q on its surface. If now a uniform electric field is switched-on as shown, then the SHM of the block will be

JEE Advanced 2011 Paper - 2 with Solutions - Question 5

A light ray travelling in glass medium is incident on glass-air interface at an angle of incidence θ. The reflected (R) and transmitted (T) intensities, both as function of θ, are plotted. The correct sketch is

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 5

After total internal reflection, there is no refracted ray.

JEE Advanced 2011 Paper - 2 with Solutions - Question 6

A satellite is moving with a constant speed ‘V’ in a circular orbit about the earth. An object of mass ‘m’ is

ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of its

ejection, the kinetic energy of the object is

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 6

JEE Advanced 2011 Paper - 2 with Solutions - Question 7

A long insulated copper wire is closely wound as a spiral of ‘N’ turns. The spiral has inner radius ‘a’ and outer radius ‘b’. The spiral lies in the XY plane and a steady current ‘I’ flows through the wire. The Z-component of the magnetic field at the centre of the spiral is

JEE Advanced 2011 Paper - 2 with Solutions - Question 8

A point mass is subjected to two simultaneous sinusoidal displacements in x-direction, x_{1}(t) = A sinωt and

Adding a third sinusoidal displacement x_{3}(t) = B sin (ωt + φ) brings the mass to a complete rest. The values of B and φ are

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 8

*Multiple options can be correct

JEE Advanced 2011 Paper - 2 with Solutions - Question 9

**SECTION – II (Total Marks : 16)**

(Multiple Correct Answer(s) 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.** Two solid spheres A and B of equal volumes but of different densities d_{A} and d_{B} are connected by a string. They are fully immersed in a fluid of density d_{F}. They get arranged into an equilibrium state as shown in the figure with a tension in the string. The arrangement is possible only if

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 9

*Multiple options can be correct

JEE Advanced 2011 Paper - 2 with Solutions - Question 10

A thin ring of mass 2 kg and radius 0.5 m is rolling without on a horizontal plane with velocity 1 m/s. A small ball of mass 0.1 kg, moving with velocity 20 m/s in the opposite direction hits the ring at a height of 0.75 m and goes vertically up with velocity 10 m/s. Immediately after the collision

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 10

During collision friction is impulsive and immediately after collision the ring will have a clockwise angular

velocity hence friction will be towards left.

*Multiple options can be correct

JEE Advanced 2011 Paper - 2 with Solutions - Question 11

Which of the following statement(s) is/are correct?

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 11

(D) is correct if we assume it is work done against electrostatic force

*Multiple options can be correct

JEE Advanced 2011 Paper - 2 with Solutions - Question 12

A series R-C circuit is connected to AC voltage source. Consider two cases; (A) when C is without a dielectric medium and (B) when C is filled with dielectric of constant 4. The current I_{R} through the resistor and voltage V_{C} across the capacitor are compared in the two cases. Which of the following is/are true?

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 12

*Answer can only contain numeric values

JEE Advanced 2011 Paper - 2 with Solutions - Question 13

**SECTION-III (Total Marks : 24)**

(Integer Answer Type)

This section contains 6 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 series R-C combination is connected to an AC voltage of angular frequency ω = 500 radian/s. If the

impedance of the R-C circuit is the time constant (in millisecond) of the circuit is

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 13

*Answer can only contain numeric values

JEE Advanced 2011 Paper - 2 with Solutions - Question 14

A silver sphere of radius 1 cm and work function 4.7 eV is suspended from an insulating thread in freespace.

It is under continuous illumination of 200 nm wavelength light. As photoelectrons are emitted, the

sphere gets charged and acquires a potential. The maximum number of photoelectrons emitted from the

sphere is A x 10^{z }(where 1 < A < 10). The value of ‘Z’ is

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 14

*Answer can only contain numeric values

JEE Advanced 2011 Paper - 2 with Solutions - Question 15

A train is moving along a straight line with a constant acceleration ‘a’. A boy standing in the train throws a

ball forward with a speed of 10 m/s, at an angle of 60° to the horizontal. The boy has to move forward by

1.15 m inside the train to catch the ball back at the initial height. The acceleration of the train, in m/s^{2}, is

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 15

*Answer can only contain numeric values

JEE Advanced 2011 Paper - 2 with Solutions - Question 16

A block of mass 0.18 kg is attached to a spring of force-constant 2 N/m. The coefficient of friction between the block and the floor is 0.1. Initially the block is at rest and the spring is unstretched. An impulse is given to the block as shown in the figure. The block slides a distance of 0.06 m and comes to rest for the first time. The initial velocity of the block m/s is V = N/10. Then N is:

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 16

Let ν be the speed of the block just after impulse. At B, the block comes to rest.

Therefore: Loss in K.E. of the block = Gain in P.E. of the spring + Work done against friction

*Answer can only contain numeric values

JEE Advanced 2011 Paper - 2 with Solutions - Question 17

Two batteries of different emfs and different internal resistances are connected as shown. The voltage across AB in volts is

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 17

*Answer can only contain numeric values

JEE Advanced 2011 Paper - 2 with Solutions - Question 18

Water (with refractive index = 4/3 in a tank is 18 cm deep. Oil of refractive index 7/4 lies on water making a convex surface of radius of curvature ‘R = 6 cm’ as shown. Consider oil to act as a thin lens. An object ‘S’ is placed 24 cm above water surface. The location of its image is at ‘x’ cm above the bottom of the tank. Then ‘x’ is

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 18

V_{2} = 16 cm

x = 18 - 16 = 2 cm

JEE Advanced 2011 Paper - 2 with Solutions - Question 19

**(Matrix-Match Type)**

This section contains 2 questions. Each question has four statements (A, B, C and D) given in Column I and five statements (p, q, r, s and t) in Column II. Any given statement in Column I can have correct matching with ONE or MORE statement(s) given in Column II.

**Q.** One mole of a monatomic gas is taken through a cycle ABCDA as shown in the P-V diagram. Column II give the characteristics involved in the cycle. Match them with each of the processes given in Column I.

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 19

Process A → B → Isobaric compression

Process B → C → Isochoric process

Process C → D → Isobaric expansion

Process D → A → Polytropic with TA = TD

JEE Advanced 2011 Paper - 2 with Solutions - Question 20

Column I shows four systems, each of the same length L, for producing standing waves. The lowest

possible natural frequency of a system is called its fundamental frequency, whose wavelength is denoted as

λ_{f}. Match each system with statements given in Column II describing the nature and wavelength of the

standing waves.

JEE Advanced 2011 Paper - 2 with Solutions - Question 21

**SECTION – I (Total Marks : 24)**

(Single Correct Answer Type)

This Section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of

which ONLY ONE is correct.

**Q.** The freezing point (in ^{o}C) of a solution containing 0.1 g of K_{3}[Fe(CN)_{6} (Mol. Wt. 329) in 100 g of water

(K_{f} = 1.86 K kg mol^{-1}) is

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 21

JEE Advanced 2011 Paper - 2 with Solutions - Question 22

Amongst the compounds given, the one that would form a brilliant colored dye on treatment with NaNO_{2} in

dil. HCl followed by addition to an alkaline solution of β-naphthol is

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 22

JEE Advanced 2011 Paper - 2 with Solutions - Question 23

The major product of the following reaction is

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 23

JEE Advanced 2011 Paper - 2 with Solutions - Question 25

Oxidation states of the metal in the minerals haematite and magnetite, respectively, are

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 25

Haematite : Fe_{2}O_{3} : 2x + 3 × (-2) = 0

x =3

Magnetite : Fe_{3}O_{4} [an equimolar mixture of FeO and Fe_{2}O_{3}]

FeO : x – 2 = 0 ⇒ x = 2

Fe_{2}O_{3} : x = 3

JEE Advanced 2011 Paper - 2 with Solutions - Question 26

Among the following complexes (K-P)

K_{3}[Fe(CN)_{6}] (K), [Co(NH_{3})_{6}]Cl_{3} (L), Na_{3}[Co(oxalate)_{3}] (M), [Ni(H_{2}O)_{6}]Cl_{2} (N), K_{2}[Pt(CN)_{4}] (O) and

[Zn(H_{2}O)_{6}](NO_{3})_{2} (P)

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 26

JEE Advanced 2011 Paper - 2 with Solutions - Question 27

Passing H_{2}S gas into a mixture of Mn^{2+}, Ni^{2+}, Cu^{2+} and Hg^{2+} ions in an acidified aqueous solution precipitates

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 27

H_{2}S in presence of aqueous acidified solution precipitates as sulphide of Cu and Hg apart from Pb^{+2}, Bi^{+3}, Cd^{+2}, As^{+3}, Sb^{+3} and Sn^{+2}.

JEE Advanced 2011 Paper - 2 with Solutions - Question 28

Consider the following cell reaction:

At [Fe^{2+}] = 10^{-3} M, P(O_{2}) = 0.1 atm and pH = 3, the cell potential at 25^{o}C is

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 28

*Multiple options can be correct

JEE Advanced 2011 Paper - 2 with Solutions - Question 29

**SECTION – II (Total Marks : 16)**

(Multiple Correct Answer(s) 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. **Reduction of the metal centre in aqueous permanganate ion involves

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 29

In acidic medium

In neutral medium

Hence, number of electron loose in acidic and neutral medium 5 and 3 electrons respectively.

*Multiple options can be correct

JEE Advanced 2011 Paper - 2 with Solutions - Question 30

The correct functional group X and the reagent/reaction conditions Y in the following scheme are

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 30

Condensation polymers are formed by condensation of a diols or diamine with dicarboxylic acids.

*Multiple options can be correct

JEE Advanced 2011 Paper - 2 with Solutions - Question 31

For the first order reaction

2N_{2}O_{5}(g) → 4NO_{2}(g) + O_{2}(g)

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 31

For first order reaction

[A] = [A]_{0}e^{–kt}

Hence concentration of [NO_{2}] decreases exponentially.

Also, t_{1/2} =. Which is independent of concentration and t_{1/2} decreases with the increase of

temperature.

*Multiple options can be correct

JEE Advanced 2011 Paper - 2 with Solutions - Question 32

The equilibrium

in aqueous medium at 25^{o}C shifts towards the left in the presence of

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 32

Cu^{2+} ions will react with CN^{-} and SCN^{-} forming [Cu(CN)^{4}]^{3-} and [Cu(SCN)^{4}]^{3-} leading the reaction in the backward direction.

Cu^{2+} also combines with CuCl_{2} which reacts with Cu to produce CuCl pushing the reaction in the backward direction.

*Answer can only contain numeric values

JEE Advanced 2011 Paper - 2 with Solutions - Question 33

**SECTION-III (Total Marks : 24)**

**(Integer Answer Type)**

This section contains 6 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. The maximum number of isomers (including stereoisomers) that are possible on monochlorination of the

following compound is

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 33

Total = 2 + 4 + 1 + 1 = 8

*Answer can only contain numeric values

JEE Advanced 2011 Paper - 2 with Solutions - Question 34

The total number of contributing structure showing hyperconjugation (involving C-H bonds) for the

following carbocation is

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 34

6 x H-atoms are there

*Answer can only contain numeric values

JEE Advanced 2011 Paper - 2 with Solutions - Question 35

Among the following, the number of compounds than can react with PCl_{5} to give POCl_{3} is O_{2}, CO_{2}, SO_{2}, H_{2}O, H_{2}SO_{4}, P_{4}O_{10}

*Answer can only contain numeric values

JEE Advanced 2011 Paper - 2 with Solutions - Question 36

The volume (in mL) of 0.1 M AgNO_{3} required for complete precipitation of chloride ions present in 30 mL

of 0.01 M solution of [Cr(H_{2}O)_{5}Cl]Cl_{2}, as silver chloride is close to

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 36

Number of ionisable Cl^{-} in [Cr(H_{2}O)_{5}Cl]Cl_{2} is 2

Millimoles of Cl^{-} = 30 x 0.01 ´ 2 = 0.6

Millimoles of Ag^{+} required = 0.6

0.6 = 0.1 V

V = 6 ml

*Answer can only contain numeric values

JEE Advanced 2011 Paper - 2 with Solutions - Question 37

In 1 L saturated solution of AgCl [K_{sp}(AgCl) = 1.6 x 10^{-10}], 0.1 mol of CuCl [K_{sp}(CuCl) = 1.0 x 10^{-6}] is

added. The resultant concentration of Ag+ in the solution is 1.6 x 10^{-x}. The value of “x” is

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 37

*Answer can only contain numeric values

JEE Advanced 2011 Paper - 2 with Solutions - Question 38

The number of hexagonal faces that are present in a truncated octahedron is

JEE Advanced 2011 Paper - 2 with Solutions - Question 39

**SECTION-IV (Total Marks : 16)**

**(Matrix-Match Type)**

This section contains 2 questions. Each question has four statements (A, B, C and D) given in Column I and five statements (p, q, r, s and t) in Column II. Any given statement in Column I can have correct matching with ONE or MORE statement(s) given in Column II.

**Q. **Match the transformations in column I with appropriate options in column II

JEE Advanced 2011 Paper - 2 with Solutions - Question 40

Match the reactions in column I with appropriate types of steps/reactive intermediate involved in these

reactions as given in column II

JEE Advanced 2011 Paper - 2 with Solutions - Question 41

**SECTION – I (Total Marks : 24)**

(Single Correct Answer Type)

This Section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of

which ONLY ONE is correct.

**Q.** If

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 41

JEE Advanced 2011 Paper - 2 with Solutions - Question 42

Let f : [-1, 2] → [0, ∞) be a continuous function such that f(x) = f(1 - x) for all x ε[-1, 2]. Let and R_{2} be the area of the region bounded by y = f(x), x = -1, x = 2, and the x-axis. Then

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 42

JEE Advanced 2011 Paper - 2 with Solutions - Question 43

Let f(x) = x^{2} and g(x) = sinx for all x ε R. Then the set of all x satisfying (f o g o g o f) (x) = (g o g o f) (x),

where (f o g) (x) = f(g(x)), is

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 43

(fogogof) (x) = sin^{2} (sin x^{2})

(gogof) (x) = sin (sin x^{2})

sin^{2} (sin x^{2}) = sin (sin x^{2})

⇒ sin (sin x^{2}) [sin (sin x^{2}) - 1] = 0

⇒ sin (sin x^{2}) = 0 or 1

⇒ sin x^{2} = nπ or 2mπ + π/2, where m, n ε I

⇒ sin x^{2} = 0

⇒ x^{2} = np x = ± np , n Î {0, 1, 2, …}.

JEE Advanced 2011 Paper - 2 with Solutions - Question 44

Let (x, y) be any point on the parabola y^{2} = 4x. Let P be the point that divides the line segment from (0, 0)

to (x, y) in the ratio 1 : 3. Then the locus of P is

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 44

y^{2} = 4x and Q will lie on it

(4k)^{2} = 4 ´ 4h

k^{2} = h

y^{2} = x (replacing h by x and k by y)

JEE Advanced 2011 Paper - 2 with Solutions - Question 45

Let P(6, 3) be a point on the hyperbola If the normal at the point P intersects the x-axis at (9,

0), then the eccentricity of the hyperbola is

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 45

JEE Advanced 2011 Paper - 2 with Solutions - Question 46

A value of b for which the equations

x^{2} + bx - 1 = 0

x^{2} + x + b = 0,

have one root in common is

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 46

x^{2} + bx - 1 = 0

x^{2} + x + b = 0 … (1)

Common root is

(b - 1) x - 1 - b = 0

JEE Advanced 2011 Paper - 2 with Solutions - Question 47

Let ω =1 be a cube root of unity and S be the set of all non-singular matrices of the form where each of a, b, and c is either ω or ω^{2}. Then the number of distinct matrices in the set S is

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 47

JEE Advanced 2011 Paper - 2 with Solutions - Question 48

The circle passing through the point (-1, 0) and touching the y-axis at (0, 2) also passes through the point

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 48

Circle touching y-axis at (0, 2) is (x - 0)^{2} + (y - 2)^{2} + λx = 0 passes through (- 1, 0)

1 + 4 - λ = 0 ⇒ λ = 5

x^{2} + y^{2} + 5x - 4y + 4 = 0

Put y = 0 ⇒ x = - 1, - 4

Circle passes through (- 4, 0)

*Multiple options can be correct

JEE Advanced 2011 Paper - 2 with Solutions - Question 49

**SECTION – II (Total Marks : 16)**

**(Multiple Correct Answer(s) 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. **

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 49

Clearly, f (x) is not differentiable at x = 0 as f´(0^{-}) = 0 and f´(0^{+}) = 1.

f (x) is differentiable at x = 1 as f' (1^{–}) = f'(1^{+}) = 1.

*Multiple options can be correct

JEE Advanced 2011 Paper - 2 with Solutions - Question 50

where be is a constant such that 0 < b < 1. Then

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 50

*Multiple options can be correct

JEE Advanced 2011 Paper - 2 with Solutions - Question 51

Let L be a normal to the parabola y^{2} = 4x. If L passes through the point (9, 6), then L is given by

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 51

y^{2} = 4x

Equation of normal is y = mx – 2m – m^{3}.

It passes through (9, 6)

⇒ m^{3} – 7m + 6 = 0

⇒ m = 1, 2, – 3

⇒ y – x + 3 = 0, y + 3x – 33 = 0, y – 2x + 12 = 0.

*Multiple options can be correct

JEE Advanced 2011 Paper - 2 with Solutions - Question 52

Let E and F be two independent events. The probability that exactly one of them occurs is and the

probability of none of them occurring is If P(T) denotes the probability of occurrence of the event T,

then

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 52

*Answer can only contain numeric values

JEE Advanced 2011 Paper - 2 with Solutions - Question 53

**SECTION-III (Total Marks : 24)**

(Integer Answer Type)

This section contains 6 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. **Let be three given vectors. If and then the value of is

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 53

*Answer can only contain numeric values

JEE Advanced 2011 Paper - 2 with Solutions - Question 54

The straight line 2x - 3y = 1 divides the circular region x2 + y2 __<__ 6 into two parts. If

then the number of point(s) in S lying inside the smaller part is

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 54

*Answer can only contain numeric values

JEE Advanced 2011 Paper - 2 with Solutions - Question 55

Let ω = e^{iπ/3}, and a, b, c, x, y, z be non-zero complex numbers such that

a + b + c = x

a + bω + cω^{2} = y

a + bω^{2} + cω = z.

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 55

The expression may not attain integral value for all a, b, c

If we consider a = b = c, then

x = 3a

*Answer can only contain numeric values

JEE Advanced 2011 Paper - 2 with Solutions - Question 56

The number of distinct real roots of x^{4} - 4x^{3} + 12x^{2} + x - 1 = 0 is

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 56

Let f (x) = x^{4} - 4x^{3} + 12x^{2} + x - 1 = 0

f'(x) = 4x^{3} - 12x^{2} + 24x + 1= 4 (x^{3} - 3x^{2} + 6x) + 1

f''(x) = 12x^{2} - 24x + 24 = 12 (x^{2} - 2x + 2)

f''(x) has 0 real roots

f (x) has maximum 2 distinct real roots as f (0) = –1.

*Answer can only contain numeric values

JEE Advanced 2011 Paper - 2 with Solutions - Question 57

Let y'(x) + y(x)g'(x) = g(x)g'(x), y(0) = 0, x ε R, where f'(x) denotes and g(x) is a given nonconstant

differentiable function on R with g(0) = g(2) = 0. Then the value of y(2) is

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 57

y'(x) + y(x) g'(x) = g(x) g'(x)

⇒ e^{g(x)} y'(x) + e^{g(x)} g'(x) y(x) = e^{g(x)} g(x) g'(x)

*Answer can only contain numeric values

JEE Advanced 2011 Paper - 2 with Solutions - Question 58

Let M be a 3 x 3 matrix satisfying

Then the sum of the diagonal entries of M is

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 58

JEE Advanced 2011 Paper - 2 with Solutions - Question 59

**SECTION-IV (Total Marks : 16)**

**(Matrix-Match Type)**

This section contains 2 questions. Each question has four statements (A, B, C and D) given in Column I and five statements (p, q, r, s and t) in Column II. Any given statement in Column I can have correct matching with ONE or MORE statement(s) given in Column II.

**Q.** Match the statements given in Column I with the values given in Column II

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 59

JEE Advanced 2011 Paper - 2 with Solutions - Question 60

Match the statements given in Column I with the intervals/union of intervals given in Column II

Detailed Solution for JEE Advanced 2011 Paper - 2 with Solutions - Question 60

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