2015 Mock Jee Advanced 4 Paper 1 Aceg

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VMC/JEE-2015/Paper-1 1 MOCK JEE ADVANCED - 4/ACEG

Read the following Instructions very carefully before you proceed.1. The question paper consists of 3 parts (Part I : Chemistry, Part II : Physics, Part III : Mathematics).

Each Part has 2 sections (Section I & Section II).2. For answering a question, an ANSWER SHEET (OMR SHEET) is provided separately. Please fill your

Test Code, Roll No. and Group properly in the space given in the ANSWER SHEET.3. Section I contains 2 types of questions [Type 1 & Type 2].

Type 1 contains 10 Single Correct Answer Type Questions. Each question has 4 choices (A), (B), (C) and(D), out of which ONLY ONE Choice is Correct.

Marking scheme [3Marks for Correct answer & 1 NEGATIVE MARKING for wrong] Type 2 contains 5 Multiple Correct Answer Type Questions. Each question has 4 choices (A), (B), (C)

and (D), out of which ONE OR MORE CHOICES may be correct.Marking scheme [5Marks for Correct answer & NO NEGATIVE MARKING for wrong]

4. Section II contains 5 Single Integer Value Type Questions. The answer to each of the questions is asingle-digit integer, ranging from 0 to 9 (both inclusive)

Marking scheme [4Marks for Correct answer & 1 NEGATIVE MARKING for wrong]5. No candidate is allowed to carry any textual material, printed or written, bits of papers, pager, mobile

phone, any electronic device, etc., except the Admit Card inside the examination hall/room.6. On completion of the test, the candidate must hand over the Answer Sheet to the Invigilator on duty in the

Room/Hall. However, the candidates are allowed to take away this Test Booklet with them.7. No one is permitted to leave the test room before the end of the test, i.e. 12.00 NOON

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PART - I (CHEMISTRY) 75 MARKSSECTION - I [Type 1]

SINGLE CORRECT ANSWER TYPEThis section contains 10 Single Choice Questions. Each Question has 4 choices A, B, C & D, out of whichONLY ONE Choice is Correct.

1.

The product (C) in the above sequence of reactions is :

(A) (B) (C) (D)

2. A mixture of 2g each of the sulphates of two metals whose equivalent weights are 12 and32 respectively was dissolved in water. To this solution, an excess of BaCl2 was added, the weight ofBaSO4 precipitated is : (atomic weight of O = 16, S = 32, Ba = 137)(A) 4 g (B) 26.7 g (C) 3.4 g (D) 6.8 g

3. On heating 60 cc of a mixture of equal volume of Cl2 and an oxide of chlorine and cooling to roomtemperature and pressure, the resulting gas measured 75 cc. Treatment of this gas with caustic sodasolution resulted in a contraction to 15 cc. Assuming that all measurements were done at the sametemperature and pressure, 300 cc of the oxide of chlorine diffuses in 40 sec and 400 cc of a gas,

X diffuses in 23

rd of a minute. The gas X could be :

(A) NO2 (B) CH2N2 (C) C4H10 (D) O34. A silvery metal reacts with excess of hot and concentrated HNO3 to form a solution of metal ion (X)

and a paramagnetic gas. To this solution, potassium tetrathiocyanatocobaltate(II) is added, when a deepblue precipitate is formed. The metal ion (X) will be :(A) Ag+ (B) Al3+ (C) Hg2+ (D) Pb2+

SPACE FOR ROUGH WORK

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5. The major product in the reaction given below is :

PhC CMePh

HNO2 (X)OH NH2

H

(A) PhC CMePh

H H

H(B) PhCCHMe

Ph

O

(C) PhC CMeOH

Ph H

H(D) PhCCMe

Ph

O Me

6. PCl5 is highly unstable and in solid state it exists as into [PCl4]+ and [PCl6] ions. The geometry of[PCl6] is :(A) octahedral (B) tetrahedral (C) square pyramidal (D) square planar

7. Pure water is saturated with pure solid AgCl, a silver electrode is placed in the solution and thepotential is measured against normal calomel electrode at 25C. The experiment is then repeated with asaturated solution of AgI. If the difference in potential of the two cases is 0.177 V , what is the ratio ofsolubilities of AgCl and AgI at the temperature of the experiment?

(A) 102 (B) 106 (C) 103 (D) 104

8. The final product (B) in the following sequence of reaction,(i) O3(ii) H2O (A)

dilute KOH (B)

would be :

(A)

O

(B) O (C)

O

(D)

O9. During adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute

temperature. The ratio of p vC / C (i.e., ) for the gas is :(A) 3/2 (B) 7/2 (C) 5/3 (D) 9/7

10. Microbial growth in a culture follows first order kinetics. The rate constant for thisgrowth is 0.0462 min1. How many microbes will be in culture after 3 hrs if initially there are4 106 microbes? ( Use: log 4 103 = 3.6 )(A) 1.6 1010 (B) 4.38 109 (C) 1.0 108 (D) 4 108


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SECTION - I [Type 2]MULTIPLE CORRECT ANSWERS TYPE

This section contains 5 Multiple Choice Questions. Each Question has 4 choices A, B, C & D, out of whichONE or MORE Choices may be Correct:11. 5 moles of NO2 and 10 moles of N2O4 are taken in a vessel having total pressure of

2 atm. Which of the following statement is correct about the reaction, 2NO2(g) N2O4(g) [Given:o

fG (N2O4) = 97.3 kJ/mole and ofG (NO2) = 51.5 kJ/mole]?(A) The reaction moves in forward direction (B) The reaction moves in reverse direction(C) KP of the equilibrium reaction is 10 (D) QP of the reaction is 6

12. Which of the following statement is(are) correct for compounds of iron?(A) 4FeSO on heating gives sulphurous anhydride and sulphuric anhydride along with reddish

brown residue of 2 3Fe O .(B) 3 2FeCl .6H O(s) on hating form anhydrous ferrous chloride(C) Brown ring complex on heating releases a paramagnetic gas(D) Sodium fusion extract of thiourea produces blood red colouration with 3FeCl solution

13. Which of the following acid is dibasic and has an identical non-metal non-metal bond?(A) H2S2O8 (B) H2S2O4 (C) H4P2O6 (D) H2N2O2

14. Which of the following is correct about P4O6 and P4O10 ?(A) There are two types of PO bond lengths in P4O10 but only one type in P4O6(B) The PO single bond in P4O6 is longer than in P4O10(C) The PO single bond in P4O10 is longer than in P4O6(D) P4O6 can show Lewis base character but P4O10 cannot

15. Which of the following aqueous solutions produce the same osmotic pressure?(A) 0.1 M NaCl solution(B) 0.1 M Glucose solution(C) 0.6 g Urea in 100 ml solution(D) 1.0 g non-electrolyte solute (X) in 50 ml solution (molecular mass of X = 200)


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SECTION - IISINGLE INTEGER VALUE CORRECT TYPE

This section contains 5 single Integer Value Correct type Questions. Each question has an integer answerbetween 0 and 9. Fill the answer bubbles in the OMR Sheet APPROPRIATELY and CAREFULLY.1. Consider the given sequence of reaction,

CH3CO CO O

O1. LiAlH42. H2O

(P) + (Q) + (R)

(P) 4HIO (S) (T). The total number of stereoisomers involved in (P), (Q), (R), (S) and (T) will be _______ .

2. The unit cell of hydrated TlAl(SO4)2 is face centered with unit cell length a = 1.19 nm.If the density of the salt is 2.32 g/cc, then the approximate number of water of hydration units perTlAl(SO4)2 unit will be (Molar mass of TlAl(SO4)2 is 423.5).

3. Find out the ratio of optically active isomers to meso-isomers for the following reaction:

CH3CH = CHCH3 24

Br

in CCl products .

4. In the reaction given below both complex [X] and complex [Y] obey effective atomic number rule.If effective atomic number of Fe in complex [Y] is 36 then the co-ordination number of Fe in thiscomplex is________

5 2 2[Fe(CO) ] 2NO [Fe(CO) (NO) ] 3CO[Y][X]

5. 736 g of K4[Fe(CN)6] reacts with 40 L of 0.2 M H2SO4 to undergo non-redox reaction to liberate COgas. The number of moles of CO released is ________.


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PART - II (PHYSICS) 75 MARKSSECTION - I [Type 1]

SINGLE CORRECT ANSWER TYPEThis section contains 10 Single Choice Questions. Each Question has 4 choices A, B, C & D, out of whichONLY ONE Choice is Correct.1. Three long thin wires, each carrying current I in the same direction are in the x-y plane of a gravity

free-space, mass per unit length of the central wire is . The central wire is along y-axis while theother two are along .x d If the central wire is displaced along the z-direction by a small amount andreleased keeping the other two wires fixed, the frequency of oscillation is :

(A) 0Id

(B) 0I d (C) 02 d (D)

0

2Id

2. A lift ascends with constant acceleration a, then with constant velocity and finally stops under constantretardation a. If the total distance ascended is h and total time taken is t, the time during which the lift isascended with constant velocity is :

(A) 2 4hta

(B) 2 8hta

(C) 2 43

ht

a (D) 2 8

3h

ta

3. A sinusoidal wave pulse of amplitude A and wavelength , ispropagating in a string towards right with speed c. At t = 0, it startsreflecting from the fixed end as shown. Find the velocity of the pointwhich is at a distance of /6 left from fixed end in its mean positionat instant .

6t

c

(A) 3 22

cA down (B)

3 22

cA up (C)

1 22

cA down (D)

1 22

cA up


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4. Light from a discharge tube containing hydrogen atoms falls on the surface of a piece of sodium.The K.E. of the fastest photoelectrons emitted from sodium is 0.73 eV. The work function of sodium is1.82 eV then,(A) the energy of the photons causing the photoelectric emission is 2.55 eV(B) the quantum number of the two levels involved in the emission of these photons are 1 and 4

(C) the change in the angular momentum of the electron in the hydrogen atom is2h (in the above

transition)(D) assuming it to be at rest before transition, the recoil speed of the emitting hydrogen atom of

mass 1.6 1027 kg is 8.5 m/s

5. A particle of mass m is allowed to oscillate near the minimum of a frictionlessvertical parabolic path having the equation 2 4 .x ay The angular frequency ofsmall oscillation is given by :

(A) ga

(B) 2gh

(C)2ga

(D) 2 gha

6. A particle is thrown horizontally with relative velocity 10 m/sfrom a big inclined plane, which is also moving withacceleration 10 m/s2 vertically upward. The time after which itlands on the plane (Take g = 10 m/s2)(A) 1 sec (B) 2 sec(C) 1

2sec (D) 1

3sec

7. A uniform chain of length L has one of its end attached to the wall at

point A, while 34L

of the length of the chain is lying on table as

shown in figure. The minimum coefficient of friction between tableand chain so that chain remains in equilibrium is :(A) 1/3 (B) 1/4 (C) 3/4 (D) 1/5


a = 10 m/s2v = 10 m/s

30

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8. A ball is released from a point, it goes vertically downwards and collides with a fixed smooth inclinedplane of angle of inclination of 30 from the ground, then ball goes horizontally just after collision.Find the coefficient of restitution between the ball and the inclined plane.

(A) 12

(B) 13

(C) 1 (D) 15

9. Two small rings each of mass m are connected to the block of same mass m through inextensiblemassless strings of length l each. Rings are constrained to move over smooth rod AB. Initially systemis held at rest as shown in the figure. Let u be the velocity of ring when string makes an angle 60 withthe vertical then :

(A)5

glu (B) 85gl

u (C) 3u gl (D) 35

glu

10. A disc, having plane parallel to the horizontal is moving suchthat velocity of point P with respect to ground on its periphery is2m/s j as shown in the figure. If radius of disc is R = 1m andangular speed of disc about vertical axis passing through disc is = 2 rad/s, the velocity of centre of disc in m/s is :(A) 2 j (B) 2 2i j(C) 2 2 i j (D) 2 2i j


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This section contains 5 Multiple Choice Questions. Each Question has 4 choices A, B, C & D, out of whichONE or MORE Choices may be Correct:11. For any general body, under the framework of Newtonian mechanics,

(A) Center of mass and center of gravity will coincide if the body is placed in uniform gravitationalfield

(B) Center of mass and center of gravity will surely coincide if the body has uniform density(C) Center of mass and centroid will coincide if the body has uniform density but it is placed in

non-uniform gravitational field(D) Center of mass and centroid will coincide if the body has non-uniform density but it is placed in

uniform gravitational field

12. The given arrangement carries a capacitor with capacitance 40mF and two inductors 1 25L H and.1002 HL If the capacitor initially carries a charge of 10 mC, then

C L2L1

k1 k2

''Q +

(A) the maximum current through the inductor 1L when key 1k is closed is 20 mA(B) the maximum current through the inductor 2L when key 2k is closed is 5mA

(C) the maximum current through inductor 2L when both the keys are closed is 5 mA(D) time period of oscillation of charge is minimum when both the keys are closed

13. The rate of heat energy emitted by a body at an instant depends upon(A) Area of the surface(B) Difference of temperature between the surface and its surroundings(C) Nature of the surface(D) None of these


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14. A long plank of mass M = 20 kg can move on horizontal frictionless surface freely. Initially the plank isat rest and an object of mass m = 5kg is given a velocity of 25 m/s and placed on the floor of the plank.Co-efficient of friction between object and floor of the plank is

85

. After having some relative

movement w.r.t. the plank, the object finally starts moving with the plank in one piece. Then :(A) the total work done by friction is 1250 J(B) the minimum length of the plank should be 40 metres(C) final velocity of plank is 10 m/s(D) for time t = 3.2 seconds, the object is having relative motion w.r.t. plank

15. A block B of mass 0.6 kg slides down the smooth face PR of a wedge Aof mass 1.7 kg which can move freely on a smooth horizontal surface.The inclination of the face PR to the horizontal is 45. Then:(A) the acceleration of A is 3g/20(B) the vertical component of the acceleration of B is 23 g/40(C) the horizontal component of the acceleration of B is 17 g/40

(D) relative acceleration of B w.r.t. A is 2340 2

g


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This section contains 5 single Integer Value Correct type Questions. Each question has an integer answerbetween 0 and 9. Fill the answer bubbles in the OMR Sheet APPROPRIATELY and CAREFULLY.1. A conducting ring of circular cross section with inner and outer radii

a and b is made of a material of resistivity . The thickness ofring is h. It is placed coaxially in a vertically cylindrical region oflarge radius of a magnetic field B = krt, where k is a positiveconstant, r is the distance from axis t is the time. If current through

the ring is 3 3/ , I kh b a then find the value of .2. Consider as infinite wire carrying uniform linear charge density , placed along the body diagonal of

an imaginary cubical surface. Edge length of cube is a. Find the flux of electric field (in SI units)through one surface of the cube.

For calculations, take0

3 3 , 4a m SI units.

3. A plano-convex lens of refractive index 1.5 and radius of curvature 30 cm is silvered at the curvedsurface. Now, this lens is used to form the image of an object. A real image of the size of the object isformed when the object is placed at a distance of 100

xcm from the lens. Find x.

4. A radioactive sample decays with a mean life of 20 ms. A capacitor of capacitance 100 F is charged tosome potential and then the plates are connected through a resistance R. If the ratio of the charge on thecapacitor to the activity of the radioactive sample remains constant in time, then find the value of theresistance R. (in terms of 100 )

5. A uniform quarter circular thin rod of weight W and radius r is pivoted atpoint B and rests against a frictionless vertical wall at A. The reaction

force of wall on circular rod is P W . Find P.


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PART - III (MATHEMATICS) 75 MARKSSECTION - I [Type 1]

SINGLE CORRECT ANSWER TYPEThis section contains 10 Single Choice Questions. Each Question has 4 choices A, B, C & D, out of whichONLY ONE Choice is Correct.1. If f x and 21 2g x f x f x are monotonically increasing functions, then ,x R

(A) 1f x (B) 23

f x (C) 13

f x (D) 12

f x

2. Suppose, that f is differentiable for all x and that ' 2f x for all x. If 1 2f and 4 8,f thenf (2) has the value equal to :(A) 3 (B) 4 (C) 6 (D) 8

3. Let sin ,g x f x x where f x is a twice differentiable function on , such that ' 1.f The value of "g equals to :

(A) 1 (B) 2 (C) 2 (D) 04. A box contains 12 pairs of shoes. 4 shoes are taken at random. What is the probability that there is at

least one pair?

(A) 15322

(B) 3378

(C) 1223

(D) 41161

5. If the function 1 2 3

24 12 3

xx xf x e x

and 1g x f x then the value of 7'

6g equals

to

(A) 15

(B) 15

(C) 67

(D) 67

6. Let ln ln

0

sin sinlim ,

x h x

h

x h xf xh

then

2f is

(A) equal to 1 (B) equal to 0 (C) ln2 (D) Non-existent


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7. If the algebraic sum of perpendicular distance from the points A(0, 2), B(2, 0) and C(1, 1) on a variablestraight line is zero, then the line always passes through a fixed point P, which w.r.t. the ABC is its(A) centroid (B) incentre (C) orthocentre (D) circumcentre

8. Let 2 2

03

0 0

x x tan x x tan x; xg x ax tan x tan x

; x

If ' 0g exist and is equal to non-zero value of b, then b

a is equal to :

(A) 713

(B) 726

(C) 752

(D) 552

9. The number of ways in which 2n white and 2n black balls can be arranged such that no consecutive nwhite balls are together, (n > 1) are :(A) 2 1 42 2n n nC C (B) 2 1 2 1 3 42 1 2n n n nn nC C C C (C) 2 1 2 1 3 42 1 21 nn n n nn nC C C C (D) 2 1 2 1 32 1 1 nn n n nC C C

10. Let X be a set containing n elements. If two subsets A and B of X are picked at random, the probabilitythat A and B have the same number of elements, is :

(A)2

2

nn

n

C (B)2

1n

nC(C) 1 3 5 2 1

2nn

n!

(D)34

n

n


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This section contains 5 Multiple Choice Questions. Each Question has 4 choices A, B, C & D, out of whichONE or MORE Choices may be Correct:11. If a and b are two distinct non-zero real numbers such that 1 1 ,aa b

b b a then :

(A) a > 0 (B) a < 0 (C) b < 0 (D) b > 0

12. If 1 2 2 2 2 1sin a x b y cos ax by , where 0,ab then :(A) 1 , 1

2ab xy (B) 1 1,

2 2ax by

(C) 1 , 12

ay bx (D) 1a b x y

13. The possible values of a for which 2 2 0x xe a e a holds for atleast one 0, ,x are :(A) 6 (B) 9 (C) 12 (D) 16

14. If 2 x xf x a e be cx satisfies the conditions 0 1, ' log2 31,f f 4

0

392

log f x cx dx , then :(A) 5a (B) 6b (C) c = 2 (D) a = 3

15. Which of the following sets can be the subset of the general solution of the equation1 3 2 2cos x cos x? (A)

3n

(B)6

n (C)

6n

(D) 2n


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This section contains 5 single Integer Value Correct type Questions. Each question has an integer answerbetween 0 and 9. Fill the answer bubbles in the OMR Sheet APPROPRIATELY and CAREFULLY.

1. If A, B, C and D are four points in space, then AB CD BC AD CA BD k (area of ABC),where k is equal to __________.

2. If z is a complex number lying in the first quadrant such that Re Im 3,z z then the maximumvalue of 2Re z Im z , is __________.

3. The distance of the point (2, 1, 3) from the plane 2 3 3 0,x y z measured parallel to the line1

1 2 3x y z is equal to 14

3a

units, where a is equal to __________.

4. From a point on the line ,y x c tangents are drawn to the hyperbola2 2

12 1x y such that chords of

contact pass through a fixed point 1 1, .x y Then, 11

x

y is equal to __________.

5. A circle is inscribed in the ellipse2 2

116 25x y

, where centre is one of the foci. If circle is touching theellipse, then the radius of the circle is __________.


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End of Mock JEE Advanced - 4/PAPER-1/JEE-2015

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2015 Mock Jee Advanced 4 Paper 1 Aceg