JEE MAINS MOCK TEST DATE: 28/03/2018 FULL TEST – 4 · Mathematics having 30 questions in each...

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7

PHYSICS, CHEMISTRY & MATHEMATICS

JEE MAINS MOCK TEST DATE: 28/03/2018

FULL TEST – 4

Time Allotted: 3 Hours

Maximum Marks: 360

Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.

You are not allowed to leave the Examination Hall before the end of the test.

INSTRUCTIONS

1. Immediately fill in the particulars on this page of the Test Booklet with Blue / Black Ball Point Pen. Use of pencil is strictly prohibited.

2. The Answer Sheet is kept inside this Test Booklet. When you are directed to open the Test

Booklet, take out the Answer Sheet and fill in the particulars carefully. 3. The test is of 3 hours duration. 4. The Test Booklet consists of 90 questions. The maximum marks are 360. 5. There are three parts in the question paper A, B, C consisting of Physics, Chemistry and

Mathematics having 30 questions in each part of equal weightage. Each question is allotted 4 (four) marks for correct response.

6. Candidates will be awarded marks as stated above in instruction No.5 for correct response of

each question. ¼ (one fourth) marks will be deducted for indicating incorrect response of each question. No deduction from the total score will be made if no response is indicated for an item in the answer sheet.

7. There is only one correct response for each question. Filling up more than one response in any

question will be treated as wrong response and marks for wrong response will be deducted accordingly as per instruction 6 above.

8. Use Blue / Black Ball Point Pen only for writing particulars / marking responses on Side-1

and Side-2 of the Answer Sheet. Use of pencil is strictly prohibited. 9. 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.

10. 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.

11. Do not fold or make any stray marks on the Answer Sheet.

Name of the Candidate :____________________________________________

Batch :____________________ Date of Examination :___________________

Enrolment Number :_______________________________________________

BA

TCH

ES

– 1

618

(MA

IN)

FIITJEE

http://www.fiitjee.com

JEE MAINS MOCK TEST-12_FT-4_2


PPPAAARRRTTT ––– AAA ::: PPPHHHYYYSSSIIICCCSSS 1. The particle A is projected from point P with velocity u along

the plane and simultaneously another article B with velocity v at an angle '' with vertical. The particles collide at point Q on the plane. Then :

(A) v sin = u cos (B) v cos ( – ) = u (C) v = u (D) v tan ( – ) = u

2. A particle moves on a rough horizontal ground with some initial velocity say v0. If 3/4th of its

kinetic energy is lost in friction in time t0. Then coefficient of friction between the particle and the ground is

(A) 0

0

v2gt

(B) 0

0

v4gt

(C) 0

0

3v4gt

(D) 0

0

vgt

3. For the arrangement shown in figure the coefficient of friction

between the two blocks is . If both the block are identical, then the acceleration of each block is

(A) F 2 g2m

(B) F2m

(C) F g2m

(D) zero

4. A particle moving in a straight line has velocity and displacement equation as v 4 1 s, where v is in m/s and s is in m. The initial velocity of the particle is : (A) 4 m/s (B) 16 m/s (C) 2 m/s (D) zero 5. Two equal positive point charges q are held at a fixed distance a apart. A point test charge is

located in a plane that is normal to the line joining these charges and midway between them. What is the radius r of the circle in this plane for which the force on the test particle has maximum value ?

(A) a2

(B) a 22

(C) a2

(D) 2a

Rough work




6. Some equipotential plane parallel surface are shown in the figure. The plane are inclined to x-axis

by 45º and distance from one plane to another plane along x-axis is 20 cm. The electric field is –

(A) 177 V at 135º with x-axis (B) 125 V at 45º with x-axis (C) 177 V at 45º with x-axis (D) 125 V at 135º with x-axis 7. The visibility of fringes for intensity ratio 3 in YDSE is -

(A) 45

(B) 54

(C) 23

(D) 32

8. A conducting bar is moving along two parallel conducting bars, connected across a resistor R.

The velocity of the conducting bar is constant in magnetic field B. The conducting bar oscillates between positions B and C, starting from position A due to some external forces. Plot the magnitude of induced current (I) against time (t):

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9. A chain of mass M is placed on a smooth table with 1/n of its length L hanging over the edge. The

work done in pulling the hanging portion of the chain back to the surface of the table is - (A) MgL/n (B) MgL/2n (C) MgL/n2 (D) MgL/2n2 10. The figure shows two NAND gates followed by a NOR gate. The system is equivalent to the

following logic gate –

(A) OR (B) AND (C) NAND (D) None of these 11. A ray of light incident at an angle on a refracting face of a prism emerges from the other face

normally. If the angle of the prism is 5º and the prism is made of a material of refractive index 1.5, the angle of incidence is :

(A) 7.5º (B) 5º (C) 15º (D) 2.5º 12. A potentiometer wire of length 1 m has a resistance of 10 ohm. It is connected in series with a

resistance R and a cell of emf 3V and negligible internal resistance. A source of emf 10 mV is balanced a length of 60 cm of the potentiometer wire. Find the value of R

(A) 10 (B) 1790 (C) 100 (D) 1970 13. For a transistor a change of 8mA in the emitter current results in a change of 7.9 mA in the

collector current then the change in base current will be : (A) 1μA (B) 10μA (C) 100μA (D) 1000μA

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14. A particle having charge that of an electron and mass 1.6 × 10–30 kg is projected with an initial

speed u at an angle 45° to the horizontal from the lower plate of a parallel plate capacitor as shown in figure. The plates are sufficiently long and have separation 2 cm. The maximum value of velocity of particle for it not to hit the upper plate. (Electric field between plates = 103V/m directed upward) (g = 0)

(A) 62 10 m/s (B) 62 2 10 m/s

(C) 62 10 m/s (D) 61 102 m/s

15. In figure, a coil of single turn is wound on a sphere of radius r and mass m. The plane of the coil

is parallel to the inclined plane and lies in the equatorial plane of the sphere. If the sphere is in rotational equilibrium, the value of B is :

(A) mgir

(B) mgsini

(C) mgsinir

(D) none of these 16. The observer 'O' sees the distance AB as infinitely large. If refractive

index of liquid is μ1 and that of glass is μ2, then 1

2

is:

(A) 2 (B) 1/2 (C) 4 (D) None of these

17. A charged particle of mass ‘m’ and charge ‘q’ initially at rest is released in an electric field of

magnitude E. Its kinetic energy after time ‘t’ will be

(A) 2 22E t

mq (B)

2 2 2E q t2m

(C) 2

2

Eq m2t

(D) Eqmt

Rough work




18. A constant horizontal force of 5N magnitude is applied

tangentially to the top most of a ring of mass 10 kg & radius 10 cm kept on a rough horizontal surface with coefficient of the friction between surface and ring being 0.2. The friction force on the ring would be (g = 10 m/s2) (A) 5N directed opposite to the applied force (B) 10 N directed opposite to the applied force

(C) 10 N in the direction of applied force (D) none of these

F(5N)

R

19. Two identical plates of metal are welded

end to end as shown in figure (A), 20 cal of heat flows through it in 4 minutes. If the plates are welded as shown in figure (B) the same amount of heat will flow through the plates in:

A B

(A) 1 minute (B) 2 minute (C) 4 minute (D) 16 minute 20. A simple pendulum of mass m length is kept in a lift moving upwards with an acceleration g.

The time period of oscillation is

(A) T = 22g

(B) T =

2g

(C) T = 2g

(B) T =

g

21. A cyclic process ABCA is shown in V-T diagram. The same process in p-V graph can be represented as

(A) (B)

(C) (D)

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22. Water flows out of a big tank along a big tube bent at right angles, the inner radius of tube is r.

The length of horizontal section of the tube is equal to L. The water flow rate is Q Ls–1. Moment of reaction forces due to water flow acting on tube’s wall w.r.t. point O, where is the density of water.

(A) 2

2Q L clockwiser

(B) 2

2Q L anti clockwiser

(C) 2

2Q L clockwise2 r

(D) 2

2Q L anti clockwise2 r

23. Two waves represented by ty 2000sin101 ,

2

2000sin202 ty are superimposed at

any point at a particular instant. The amplitude of the resultant wave is (A) 200 (B) 30 (C) 510 (D) 310 24. In a certain region of space, the potential field depends on x and y coordinates as V=(x2–y2) . The

corresponding electric field lines in x–y plane are correctly represented by:

25. A copper rod of length 20 cm and cross-sectional area 2 mm2 is joined with a similar aluminium

rod as shown in the figure. What will be the value of resistance of the combination between the ends? Given, Cu = 1.7 108 –m and Al = 2.6 108 –m.

(A) 1.0 m (B) 3.0 m (C) 5.0 m (D) 10.0 m

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26. A paramagnetic sample shows a net magnetization of 8 Am–1 when placed in an external

magnetic field of 0.6T at a temperature of 4K. When the same sample is placed in an external magnetic field of 0.2T at a temperature of 16K, the magnetization will be

(A) 323

Am–1 (B) 23

Am–1 (C) 6Am–1 (D) 2.4Am–1.

27. A mass m is moving at speed v perpendicular to a rod of length d

and mass M = 6m which pivots around a frictionless axle running through its centre. It strikes and sticks to the end of the rod. The

moment of inertia of the rod about its centre is 2Md .

12 Then the

angular speed of the system just after the collision is

(A) 2v3d

(B) 2vd

(C) vd

(D) 3v2d

28. Maximum height reached by a rocket fired perpendicular to the surface of the earth with a speed equal to 50% of the escape velocity from earth surface is

(A) R2

(B) 16R2

(C) R3

(D) R8

29. In Young’s double slit experiment, one of the slit is wider than other, so that amplitude of the light from one slit double of that from, other slit. If Im be the maximum intensity, the resultant intensity I. When they interfere at phase difference is given by

(A) mI 4 5cos9

(B) 2mI 1 2cos3 2

(C) 2mI 1 4cos5 2

(D) 2mI 1 8cos9 2

30. Two masses m1 and m2 are suspended together by a massless spring of constant K. When the masses are in equilibrium, m1 is removed without disturbing the system, the amplitude of vibration is

(A) 1m gk

(B) 2m gk

(C) 1 2(m m )gk (D) 2 1(m m )g

k

Rough work

M

d

v m

K

m1 m2




PPPAAARRRTTT ––– BBB ::: CCCHHHEEEMMMIIISSSTTTRRRYYY 1. The correct order of dipole moment of the following spicier are

O

(I)

N

(II)

S

(III) (A) I > II > III (B) III > II > I (C) II > III > I (D) I > III > II 2. Strongest acid among the following under the anhydrous condition HF, HCL, HBr, HI (A) HI (B) HF (C) HCl (D) HBr 3. pH of the solution containing 0.1 M, 100 mL acetic acid and 0.1 M, 100 mL benzoic acid having

acid dissociation content (Ka) 510 and 610 respectively. (A) 2.87 (B) 3.65 (C) 3.05 (D) 4.5 4. Correct order of bond angle in the following species it

P

Cl

ClCl

P

Cl

ClCl

O

2D

3D

1D

(A) 1 2 3D D D (B) 3 2 1D D D (C) 1 3 2D D D (D) 2 1 3D D D 5. 2 2 3

2 7Cr O Fe Cr rate of formation of 3Fe is 2 12.0 10 Ms rate of consumption of 2

2 7Cr O is (A) 33.33 (B) 34.6 (C) 35.00 (D) 36.2 6. On decreasing the pressure of the water its melting point (A) Increases (B) Decreases (C) Same (D) Cannot be predicted

Rough work




7. Activation energy for the overall reaction it (A) 40 kJ mol–1 (B) 148 kJ mol–1 (C) 100 kJ mol–1 (D) 50 kJ mol–1 8. 2Cu shows a coordination number of (A) 2 only (B) 2 or 4 (C) 4 only (D) 4 or 6 9. The possible geometric isomers of the complex 3 2 2 6 5 2Pt NH NH OH NO C H N NO (A) 2 (B) 3 (C) 4 (D) 6 10. When excess of KI is added to aqueous 4CuSO , the solution acquires dark brown colouration.

This is due to the formation of (A) 2 sCuI (B) 2 2 sCu I (C) 3 aqI (D) 2 sI

11. Which of the following has the highest decomposition temperature? (A) 3BaCO (B) 3SrCO (C) 3CaCO (D) 3MgCO 12. Anomers are those stereoisomers which differ in the configuration at (A) 1C (B) 2C (C) both (D) glycosidic carbon 13. Which of the following structure represent meso-compounds? (A)

H OH

H

H

(B)

CH3

H

(C)

CH3 CH3

HO

(D)

C

C

BrCH3 H

CH3H Br

Rough work

A

B

C

1K

2K

1

4 1 11 aK 4 10 s , E 40 kJmol

2

4 1 12 aK 1 10 s , E 60 kJmol




14. Identify the product in the following reaction

O

O

O

O

2 heatCa

(A)

O

(B)

O

(C) O

(D)

O

O

O

15. Identify (C) and (D) in the following series of reaction

3

excessof AgOH heat3 2 CH ICH NH A B C D

(A) 3 3 23CH COH, CH NH (B) 3 2 3 22

CH C CH ,CH NH

(C) 3 33CH N,CH OH (D) 3 2 32

CH C CH ,CH OH

16. H

6 5 3 6 5 6 5 2 6 5C H CCH OHCC H C H C CH CHC H

O O OH

The above aldol condensation does not involve the formation of (A)

6 5 3C H C CH

OH

(B) 6 5C H C H

OH

(C)

6 5 2C H C CH

O

(D)

Both A and B

Rough work




17. In Cannizzaro reaction, the intermediate that will be best hydride donor (A)

CH

OH

O

(B)

CH

O

O

(C) C

CH3O

H

O

O

(D)

C

O2N

H

O

O

18. The basic character of ethyl amine, diethyl amine and trimethyl amine in chlorobenzene is (A) 2 5 2 2 5 2 52 3

C H NH C H NH C H N (B) 2 5 2 2 5 2 53 2C H NH C H N C H NH

(C) 2 5 2 5 2 5 23 2C H N C H NH C H NH (D) 2 5 2 5 2 2 53 2

C H N C H NH C H NH

19. For a gas-solid adsorbent system, the adsorption isotherm 1 nx kpm

is applicable, where n = 5 in

the specified case. Point out the correct statement:

(A) x Vs.Pm

plot is a linear graph with slope equal to 5

(B) xlog Vs. log Pm

plot is a straight line with slope equal to 5

(C) xlog Vs. log Pm

is a straight line with slope equal to 0.2

(D) none of these 20. Consider the galvanic cell

2 0aq 1 aq 2 cells sPb Pb x M Cu x M Cu E 0.47 V

Which of the following graphs represents the variation of cellE when Pb+ is added to Cu2+ (A)

(B)

(C)

(D)

Rough work

0.47V 0.47V

0.47V 0.47V




21. What current strength would be required to produce hydrogen gas at the rate of 1.12

3 1cm s (STP) by the electrolysis of aqueous NaCl solution with 96.5% current efficiency? (A) 9.65 A (B) 9.31 A (C) 10.00 A (D) 0.10 A 22. Calculate the entropy change when 2.8 g of N2 gas expands isothermally and reversibly from an

initial volume of 1 L to final volume of 10 L at 27ºC (A) 119.15JK (B) 11.915JK (C) 0.83 JK–1 (D) 18.31JK 23. Entropy of mixing of ideal gases in terms of mole fractions iX is given by (A) i n 1nR X X (B) i n iR X X (C) i n iR X (D) i n inRT R X 24. The increasing order of Ag ion concentration in I. Saturated solution of AgCl II. Saturated solution of AgI III. 3 2

1MAg NH in 0.1 M KCN

IV. 21MAg CN in 0.1 M NH3 Given: spK of AgCl = 1.0 10–10, Ksp of 16AgI 1.0 10

dK of 83 2

Ag NH 1.0 10 dK of 212

Ag CN 1.0 10 (A) I < II < III < IV (B) IV < III < II < I (C) IV < II < III < I (D) IV < II < I < III 25. The correct order of increasing solubility of AgCl in (A) water, (B) 0.1 M NaCl, (C) 0.1 M BaCl2

and (D) 0.1 M NH3 is (A) A B C D (B) B C A D (C) C B D A (D) C B A D

Rough work




26. At temperature TK, Kp for the reaction CO2 with excess of hot graphite to form CO is 9 atm.

Calculate the mole % of CO in the equilibrium mixture of gases (A) 20% (B) 25% (C) 60% (D) 75% 27. 10 ml of 2 4KHC O solution requires 10 ml of 0.1M NaOH for complete neutralization. 10 ml of

same 2 4KHC O solution is oxidized by 10 ml of KMnO4 solution in acidic medium. Molarity of KMnO4 solution is

(A) 0.1 M (B) 0.02M (C) 0.04M (D) 0.05M 28. 0.010 M solution an acid HA freezes at –0.0205C. If fk for water is 1.860 K kg mol–1, the

ionization constant of the conjugate base of the acid will be (assume 0.010 M = 0.010 M) (A) 1.110–4 (B) 1.110–3 (C) 9.010–11 (D) 9.010–12

29. Consider a hypothetical gas with no intermolecular forces but contains the molecules which are

not point masses. During free expansion of the gas, the gas will exhibit (A) cooling effect at all temperature (B) heating effect at all temperatures (C) neither cooling nor heating effect at all temperature (D) ideal behavior 30. Which is the correct sequence of decreasing O–O bond length in 2 2 2O , H O and 3O ? (A) 2 2 3 2H O O O (B) 2 3 2 2O O H O (C) 2 2 2 3O H O O (D) 3 2 2 2O H O O

Rough work




PPPAAARRRTTT ––– CCC ::: MMMAAATTTHHHEEEMMMAAATTTIIICCCSSS 1. If n A n B 4 then number of bijections from A to B is (A) 44 (B) 24 (C) 12 (D) 18 2. The function f(x) = |sin 4x | + |cos 2x| is a periodic function with period (A) /2 (B) 2 (C) (D) /4 3. The number of complex numbers z s.t. | z i | | z i | | z 1| is (A) 0 (B) 1 (C) 2 (D)

4. 10

k 1

2k 2ksin icos11 11

is

(A) – i (B) i (C) 1 (D) –1

5. 4If z 2,z

then find the maximum value of z is equal to

(A) 1 (B) 2 2 (C) 3 1 (D) 5 1 6. If kx 0, k 1, 2, 3, 4, 5 and 1 2 3 4 5x x x x x 20 and x1 + x2 + x3 = 5 then the number of

integral solution of (x1, x2, x3, x4, x5) (A) 84 (B) 168 (C) 286 (D) 336 7. The number of different messages by signals with three dots and two dashes is (A) 120 (B) 12 (C) 10 (D) 20 8. The sum of the last eight coefficients in the expansion at (1 + x)16 is equal to (A) 215 (B) 214

(C)

162

16 !28!

(D)

152

16 !22 8!

Rough work




9. The sum of 1 1 11 .....2 3 4

is equal to

(A) 1e (B) 2 1e2e

(C) ln 2 (D) ln (1 – e) 10. If = /7, then cos + cos 3 + cos 5 is

(A) 12

(B) 14

(C) 18

(D) 1 .16

11. The value of 1 1 1tan 1 tan 2 tan 3 is (A) 0 (B) /2 (C) (D) –/2. 12. a b clog b log c log da is equal to (A) b (B) c (C) d (D) b c d 13. The diameter of the circumcircle of a triangle with sides 5, 6, 7 is

(A) 35 612

(B) 2 6

(C) 3848

(D) 92

14. If Pth term of on H.P. is qr and qth term is pr then rth term of the H.P. is

(A) pqr2 (B) pq

(C) qb

(D) pq

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15. If a1, a2, ………an are positive real numbers whose product is fixed number c, then the minimum

value of a1 + a2 + …….+an-1 + 2an is (A) 1/nn. 2c (B) 1/nn 1 c (C) 1/n2nc (D) (n + 1)(2c)1/n. 16. The equation of the base of an equilateral triangle is x + y – 2 = 0 and one vertex is (2, –1). Then

the length of the side of the triangle is

(A) 12

(B) 32

(C) 23

(D) 2

17. The angle between the tangents drawn from origin to the circle 22x 7 y 1 25 is

(A) 3 (B)

6

(C) 2 (D)

8

18. Minimum distance between the curves y2 = x – 1 and x2 = y – 1 is equal to

(A) 5 24

(B) 3 24

(C) 24

(D) 7 24

19. Vertex of the parabola whose parametric equation is x = t + 1 y = t2 + 1 ; t R is (A) (1, 1) (B) (2, 2)

(C) 1 1,2 2

(D) (3, 3)

20. The eccentric angle of a point on the ellipse 2 2x y 1

6 1 in the 1st quadrant whose distance from

the centre of ellipse is 3 is (A) 30º (B) 45º (C) 60º (D) None of these

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21. If P is any pt on the hyperbola 22 y 1x 1 1

9 16

and 1 2S , S are its foci, then 1 2S P S P is

equal to (A) 3 (B) 4 (C) 6 (D) 8 22. The eccentricity of the hyperbola whose length of the conjugate axis is equal to half the distance

between the foci is

(A) 43

(B) 43

(C) 25

(D) 23

23. The vectors ˆ ˆ ˆ ˆ ÂB 3i 4k and AC 5i 2j 4k

are the sides of ABC. The length of the median

through A is (A) 18 (B) 72 (C) 33 (D) 288 . 24. Let a and b be two unit vectors s.t. â b is also a unit vector, then the angle between â and b

is (A) 30º (B) 60º (C) 90º (D) 120º 25. A, B, C

be three vectors resp. given by ˆ ˆ ˆ ˆ ˆ2i k, i j k and ˆ ˆ ˆ4i 3 j 7k, then R

, which satisfies

the relation R B C B

and R.A 0

is

(A) ˆ ˆ ˆ2i 5 j 4k (B) ˆ ˆ î 4 j 2k

(C) ˆ ˆ î 8 j 2k (D) ˆ ˆ î 8 j 2k 26. The equation of the plane containing the line 2x + z – 4 = 0 = 2y z and passing through the

point (2, 1, –1) is (A) x y z 4 (B) x y z 2 (C) x y z 2 0 (D) x y z 2

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27. The volume of the tetrahedron included between the plane 3x + 4y –5z = 60 and the coordinate

planes is (A) 60 (B) 600 (C) 720 (D) 840

28. The value of 100

10

x x dx is

(A) 0 (B) 45 (C) 90 (D) 50

29. h 0

2 3 sin h cos h6 6lim

3h 3 cosh sinh

is equal to

(A) 23

(B) 43

(C) 23

(D) 43

30. The set of points where xf x4 x

is differentiable is

(A) , (B) 0, (C) , 0 0, (D) None of these

Rough work




FIITJEE INTERNAL TEST

JEE MAINS MOCK TEST DATE: 28/03/2018

FULL TEST – 4

ANSWERS KEY

PHYSICS

1. A 2. A 3. C 4. C 5. B 6. C 7. D 8. A 9. D 10. B

11. A 12. B 13. C 14. B 15. A 16. A 17. B 18. D 19. A 20. A

21. D 22. B 23. C 24. D 25. A 26. B 27. A 28. C 29. D 30. A

CHEMISTRY

1. C 2. B 3. A 4. D 5. A 6. A 7. B 8. D 9. B 10. C

11. A 12. D 13. D 14. A 15. C 16. C 17. C 18. A 19. C 20. B

21. C 22. B 23. A 24. C 25. D 26. D 27. C 28. C 29. C 30. A

MATHEMATICS

1. B 2. A 3. B 4. B 5. D 6. D 7. C 8. D 9. C 10. A

11. C 12. C 13. A 14. D 15. A 16. C 17. C 18. B 19. A 20. D

21. C 22. D 23. C 24. D 25. C 26. D 27. B 28. B 29. B 30 A


JEE MAINS MOCK TEST DATE: 28/03/2018 FULL TEST – 4 · Mathematics having 30 questions in each...

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Transcript of JEE MAINS MOCK TEST DATE: 28/03/2018 FULL TEST – 4 · Mathematics having 30 questions in each...