paper all india integrated test paper

8/12/2019 Paper All India integrated test paper

1/22

FIITJEE L t d . , F I I T JEE Hou se, 2 9 -A , Ka l u Sa r a i , Sa r va p r i y a V i h a r , New De l h i -1 1 00 16 , Ph 461 06000 , 2 656949 3 , Fa x 2651394 2websi t e : w ww . f i i t j e e .c om

HALF COURSE TEST VIII

Time Allotted: 3 Hours Maximum Marks: 360

Please read the instruct ions carefu l ly . You are al lot t ed 5 minutesspecif ical ly for th is purpose.

You are not a l lowed to leave the Examinat ion Hal l before the end ofthe test.

INSTRUCTIONS

A. General Inst ruct ions

1. Attempt ALL the questions. Answers have to be marked on the OMR sheets.

2. This question paper contains Three Parts.

3. Part-Iis Physics, Part-IIis Chemistry and Part-III is Mathematics.

4. Each part has only one section: Section-A.

5. Rough spaces are provided for rough work inside the question paper. No additional sheets will beprovided for rough work.

6. Blank Papers, clip boards, log tables, slide rule, calculator, cellular phones, pagers and electronicdevices, in any form, are not allowed.

B. Filling of OMR Sheet

1. Ensure matching of OMR sheet with the Question paper before you start marking your answerson OMR sheet.

2. On the OMR sheet, darken the appropriate bubble with black pen for each character of yourEnrolment No. and write your Name, Test Centre and other details at the designated places.

3. OMR sheet contains alphabets, numerals & special characters for marking answers.

C. Marking Scheme For Al l Three Parts .

(i) Section-A (01 to 30) contains 30 multiple choice questions which have only one correct answer.Each question carries +4 marks for correct answer and 1 mar k for wrong answer.

Name of the Candidate

Enrolment No.

ALL

IND

IAI

NTEG

RATEDT

EST

SERIES

FIITJEE JEE (Main), 2014

FromC

lassroom/

IntegratedSchoolPrograms7inTop20,23inTop100,54inTop300

,106inTop500AllIndiaRank

s&

2314Students

fromC

lassroom/

Integrated

SchoolPrograms&

3723Stu

dentsfromA

llProgramshave

beenAwardedaRankinJEE

(Advanced),2013


2/22


3/22

AIITS-HCT-VIII-PCM-JEE(Main)/14


3

PPhhyyssiiccss PART I

SECTION A

Single Correct Choice Type

This section contains 30 multiple choice questions. Each question has four choices (A), (B), (C) and (D)out of which ONLY ONE is correct .

1. A simple pendulum having length 1m has a time period as that of a spring mass system withspring constant 0.1N/m. What mass is attached to the spring?(A) 10gm (B) 5gm(C) 100gm (D) 50gm

2. A particle of mass m is released from a point on the axis of a thinuniform heavy ring of mass M as shown. The speed with which itcrosses the plane of the ring is

(A)R

GM (B)

R

GM2

A

3R m

(C)R2

G (D)

R

GM

5

2

3. When a mass is freely suspended from two light springs separately the period of vertical smalloscillations are T1 and T2. When the same mass is suspended form the above two springsconnected in series, the period of oscillations will be

(A) T1+ T2 (B)2

2

2

1

21

TT

TT

(C) 222

1 TT (D) 21 TT

Space for Rough work


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4

4. Unit vector giving direction of a ray incident on a plane mirror with reflecting surface lying in x-y

plane is given as knjmi . The unit vector describing the reflected ray would be

(A) knjmi (B) knjmi

(C) knjmi (D) knjmi

5. One mole of a monoatomic ideal gas undergoes the processA B in the given P-V diagram. The specific heat for thisprocess is

(A) 3R/2 (B) 13 R/6

(C) 5R/2 (D) 2R

P

6P0

3P0

V0 5V0

A

B

6. A uniform rod of length l, hinged at the lower end is free to rotate in a vertical plane. If the rod is

held vertically in the beginning and then released the angular acceleration of the rod when itmakes an angle of 450with the horizontal is

(A) 3g/22l (B) 6g/2l(C) 2g /l (D) 2g /l

7. Suddenly opening an organ pipe it is found that the difference of frequencies for 2nd

overtone ofclosed pipe and first overtone of open pipe is 200 vib/sec. The fundamental frequency of closedpipe is(A) 100 vib/sec. (B) 200 vib/sec.(C) 250 vib/sec. (D) 300 vib/sec.

8. A small ball of mass m is connected to a block of mass 2m by a lightextensible string of length r. The block and the ball are kept on the

ground. There is sufficient friction to prevent the block from slipping.The ball is projected vertically up with a velocity u. The velocity u forwhich the centre of mass of the block and the ball moves in a circlesatisfies the condition(A) 3gr u22gr (B) u25gr(C) 2gr u25gr (D) none of these m 2m

u



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9. Monoatomic, diatomic and triatomic gases whose initial volume and pressure are same, each iscompressed till their pressure becomes twice the initial pressure then.(A) If the compression is isothermal then their final volumes will be different(B) If the compression is adiabatic, then their final volume will be same(C) If the compression is adiabatic, then triatomic gas will have maximum final volume(D) If the compression is adiabatic then monoatomic gas will have maximum final volume

10. A black metallic foil is heated by means of a point source placed at a distance r from it. It isobserved that the foil absorbs power P. If the temperature and distance of the source from foilboth are doubled the power absorbed by the foil becomes(A) P (B) 2P(C) 3P (D) 4P

11. In a standing wave, between two consecutive nodes the total energy of the particles of themedium(A) uniformly increases and then decreases to zero.(B) uniformly increases.(C) remains uniform throughout.(D) uniformly decreases and then increases.

12. In a given process du = 0 and dQ < 0. Then for the process(A) There may be a change in temperature. (B) work is done by the gas.(C) work is done on the gas. (D) work is not done at all.

13. One mole of a diatomic gas is carried along an adiabatic process from position A (pressure P0 ,volume V0) to position B (Temperature T0). Find the volume at B

(A) 0

2/5

0

00 VRT

VP

(B) 0

5/2

00

0 VVP

RT

(C) 0

5/2

0

00 V

RT

VP

(D) none of these



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14. A block of mass 4 kg is kept over a rough horizontal surface. The coefficient of static friction

between the block and the surface is 0.1. At t = 0, 3 i m/s, velocity is imparted to the block and

simultaneously 2 i N force starts acting on it. Its displacement in first 5 second is(g = 10 m/s

2)

(A) 8 i (B) i8

(C) i3 (D) 3 i

15. A swimmer crosses a river of width d flowing at velocity v. While swimming, he keeps himselfalways at an angle of 120with the river flow and on reaching the other end he finds a drift of d/2in the direction of flow of river. The speed of the swimmer with respect to the river is

(A) (2 3 ) v (B) 2 (2 3 ) v

(C) 4 (2 3 ) v (D) (2 + 3 ) v

16. When the object is at distances u1and u2from the optic centre of a lens, real and virtual imagesare formed respectively with the same magnification. The focal length of the lens is

(A) (u1+ u2)/2 (B)21

21

uu

uu2

(C)21

uu (D)21

21

uu

uu

17. A bead of mass 2m can slide on a smooth straight horizontal wire. A particle of mass m isattached to the bead by a light string of length l. The particle is held in contact with the wire withthe string taut, & is then released. When the string makes an angle with the wire, the beadwould have slipped a distance(A) l(1 cos ) (B) (l/2) (1 cos )(C) l/3 (1 cos) (D) (l/6) (1 cos )

18. A string of mass m length is suspended through ceiling and a block of mass m is hanging

through the string. If a transverse wave is produced in string what is velocity of the wave at themiddle of string

(A) g2 (B)2

g

(C) g (D) g2

3



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19. If a body is subjected to two mutually perpendicular SHM's given by equation x = a1cos tand y = a2sin (t + ) which of the following is true(A) For = /2, locus of body is circle (B) for = /2 locus of body is ellipse(C) for = or = 0 locus is ellipse (D) for = 0 locus is straight l ine.

20. A source of sound of frequency f is moving over an elliptical path. Adetector is placed at one of the focii of ellipse. [Time lag in emittedand detected wave is neglected] which of the following is true.(A) There are four positions of source on ellipse for which frequency

observed is equal to frequency of source.(B) Only for point A and B, frequency observed is f.(C) For all positions of source frequency observed is f.(D) none of these.

B

S

AO

21. Two particles A and B are vibrating about a point O along common line such that equation of A isx1= a sin t equation of B is x2= b sin (t + )then motion of A with respect to B is

(A) SHM with period

(B) SHM with amplitude (a +b)

(C) non SHM, periodic (D) SHM with amplitude (a - b)

22. From source S1at point (2, 0) a simple harmonic progressive wave propagate towards +vex axis and from source S2at point (4, 0) similar wave propagate towards -ve x-axis.Velocity of wave = vEquation of motion of source S1, y = a1sin 2 ftEquation of motion of source S2, y = a2sin 2ftThen which of the following is true(A) motion of particle at (3, 0) is SHM with amplitude (a1+ a2) and frequency f.(B) motion of particle at (3, 0) is SHM with amplitude (a1 a2) and frequency f.(C) particle at (0, 0) is always at rest(D) particle at (0, 0) is doing SHM with amplitude a and frequency f.



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23. A block of mass m moves towards a wedgeof mass M free to move with a velocity u asshown. The minimum value of u for which theblock can reach the top of the wedge (allsurfaces are smooth) m

uh

(A) gh2 (B) gh2

m

M

(C)

M

m1gh2 (D)

M

m1gh2

24. A wheel A starts rolling up a rough inclined plane and another identical wheel B starts rolling up asmooth plane having same inclination with the horizontal. If initial velocity of both the wheels issame then(A) A stops earlier than B.(B) Kinetic energy of B never becomes zero.(C) Maximum height ascended by A is less than that by B.

(D) Friction acting on A is twice as it goes up than as it comes down.

25. The centre of mass of a solid cone lies at a height4

1h from the base of

the cone. The moment of inertia of the cone about one of the diameters ofthe base is I. Then moment of inertia of the cone about an axis passing

through a height2

hfrom parallel to the base of the cone is

(mass of the cone is M)

h/2

(A)16

1I (B) I

(C) I165 (D)

1617 I



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26. A simple pendulum of length L is suspended from a point O, distance

below O, a nail is fixed (< L) find time period of oscillation of pendulum

for small displacement.

(A) 2 g

L (B)

g

L

g

L

(C) 2g

L (D) 2

g

L

g

L

N

L

27. The temprature of ice is 100C (specific heat = 0.5 K cal /Kg 0C) and that of water 600C. Theyare mixed in equal amounts. What part of the ice will be melted ? (Latent heat of fusion of ice =80 Kcal/Kg)(A) 5/6 th (B) 11/16 th(C) whole of it will be melted (D) 5/11 th

28. In the given figure the wedge is fixed, pulley is light andfrictionless and string is light. Surface AB is frictionlesswhereas AC is rough. If the block of mass 3 m slides downwith constant velocity, then the coefficient of frictionbetween surface AC and the block is(A) 1/3 (B) 2/3(C) 1/2 (D) 4/3

B C

3mm

= 0 = ?

45

45

A

29. A boy is running over a circular track with uniform speed of 10 m/s.Find the average velocity for movement of boy from A to B.

(A)

20m/s (B)

40m/s

(C) 10 m/s (D) Cannot find

B

20m

A

30. A solid uniform sphere rotating about its axis with kinetic energy E0is gently placed on a roughhorizontal plane. After some time the sphere begins pure rolling with total kinetic energy equal toE. Then(A) E = 5E0/7 (B) E = 2E0/5(C) E = 2E0/7 (D) E = 7/2 E0



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CChheemmiissttrryy PART II

SECTION ASingle Correct Choice Type


1. Number of waves produced by an electron in one complete revolution in nthorbital is(A) n (B) n

2

(C) (n+1) (D) (2n+1)

2. H atom is exposed to electromagnetic radiation of = 1025.6 A

& the excited atom gives outinduced radiations. What is the minimum wavelength of these induced radiation?(A) 102.6 nm (B) 12.09 nm(C) 121.6 nm (D) 810.8 nm

3. If the Aufbau principle has not been followed, Ca(Z = 20) would have been placed in the(A) s-block (B) p-block(C) d-block (D) f-block

4. How many sp2& sp hybridized C atoms are present respectively in the following compound?

(A) 4,2 (B) 6,0(C) 3, 3 (D) 5, 1

5. The correct order of bond angle is

(A) 2 2 2NO NO NO (B) 2 2 2NO NO NO

(C) 2 2 2NO NO NO

(D) 2 2 2NO NO NO

6. At a definite temperature (T), the distribution ofvelocities is given by the following curve. Velocitiescorresponding to A, B & C respectively are(A) most probable, average & root mean square(B) average, root mean square & most probable(C) root mean square, average & most probable(D) most probable, root mean square & average

A B C

Velocity

Fractionof

molecules



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7. If Pd v/s P (where P denotes pressure in atm & d denotes density in gm/L) is plotted for He gas

(assume ideal) at a particular temperature. If

P 8.21a tm

p5,

P

then the temperature will be

(A) 160 K (B) 320 K(C) 80 K (D) none of these

8. A decomposes as:K1= 210

3min1

K2= 1103min

1

A(g)

2B(g)

C(g)

the rate of appearance of B, taking 2M concentration of A, is equal to(A) 2 103Ms1 (B) 4 103Ms1(C) 8 103Ms1 (D) none of these

9. Select the correct diagram for an endothermic reaction that proceeds through two steps, with thesecond step is rate determining:(A)

P.E.

Reaction coord inate

(B)

P.E.

Reaction coo rdinate

(C)

P.E.


(D)

P.E.




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10. 1 M NaOH solution was slowly added into 1000 ml o 183.75 gm impure H2SO4 solution &following plot was obtained. The percentage purity of H2SO4 sample & slope of the curverespectively are

[H+]

mol/L

Solvent of NaOHadded (L)

2

1

3

1 2 3

(A)1

75%,3

(B)1

80%,2

(C) 80%, 1 (D) none of these

11. Film actress Katrina Kaif uses a pencil for autographs which is made up of graphite lead coveredwith wood. The percentage by mass of graphite in the pencil is 24%. If the mass of pencil is 20gm & if NA/1000 atoms of carbon is used for each autograph than find the total number ofautograph that she can use each pencil for if she throws away the pencil when 20% of pencil isstill left. [atomic mass of Cl = 12](A) 320 (B) 80(C) 1333 (D) none of these

12. A pressure cooker reduces cooking time for food because(A) higher pressure inside the cooker crushes the food material(B) cooking involves chemical changes which is helped by rise in temperature(C) boiling point of water involved in cooking is increased(D) heat is more evenly distributed in the cooking space

13. pH of an aqueous solution of NaCl solution at 50C should be(A) 7 (B) >7(C)


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15. A triatomic linear (neglect vibrational degree of freedom) gas of which two moles is taken througha reversible process starting from A as shown in the figure. The volume ratioVB/VA= 4. If the temperature at A is 73C, then total enthalpy charge in both the steps is

Volum

e

(L)

Temperature

(K)

A

B

C

(A) 3000 R (B) 4200 R(C) 2100 R (D) 0

16. When two mole of an monoatomic ideal gas is heated from 300 K to 600 K at constant pressure.The change in entropy of the gas is

(A) 3Rln22

(B) 3R ln22

(C) 5R ln2 (D)5

R ln22

17. Consider following reactions:

2 2C s O g CO g x kJ

2 21

CO g O g CO g y kJ2

The heat of formation of CO(g) is(A) (x + y) kJ/mol (B) (x y) kJ/mol

(C) (y x) kJ/mol (D) none of these

18. Double bond equivalent or degree of unsaturation inCO2H

(A) 12 (B) 13(C) 14 (D) 15



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19. Order of stability of enol content:

CH3 C

O

CH3(a)

CH3 C

O

CH2 C

O

CH3(b)

CH3 C

O

CH2 C

O

OH

(c) (A) a > b > c (B) b > a > c

(C) b > c > a (D) a > c > b

20. Rank the following in decreasing order of heat of hydrogenation:

(i) (ii) (iii)

(A) i > ii > iii (B) iii > ii > i(C) ii > I > iii (D) ii > iii > ii

21. Which of the following carbocation is most stable?

(A) CH2

(B) CH2

(C)CH2

(D)CH2

22.Br2CCl4

Product

Product of above reaction is(A) meso (B) racemic(C) diastereomer (D) structural isomer



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23. Which of the following correctly ranks the cycloalkanes in order of increasing ring strain permethylene?Cyclopropane Cyclobutane Cyclohexane Cycloheptane

(i) (ii) (iii) (iv)

Cyclopentane

(v) (A) i < ii < iii < iv (B) iii < v < ii < i(C) v < I < ii < iii (D) i < v < ii < iii

24. How many distinct monochlorinated products, including steroisomers,can result when alkane below is heated in presence of Cl2?(A) 8 (B) 4(C) 5 (D) 6

25. Cumene

can be prepared by(A) Cl

AlCl3

(B)

Cl AlCl3

(C)H

(D) All of these



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17

MMaatthheemmaattiiccss PART III

SECTION A

Single Correct Choice Type


1. Ifp

1P , p

x

;q

1Q , q

x

;r

1R , r

x

where xk0, k = p, q, r N denotes the kth term of a

harmonic progression, then

(A) area (PQR) = 2 2 2

2 2 2p q rp q q r r p

2

(B) PQR is right angled triangle(C) the points P, Q, R are collinear(D) none of these

2. If 5a + 4b + 20c = t, then the value of t for which the line ax + by + c 1 = 0 always passesthrough a fixed point is(A) 0 (B) 20(C) 30 (D) none of these

3. The circle described on the line joining the points (0, 1), (a, b) as diameter cuts the x-axis at

points whose abscissae are roots of the equation

(A) x2+ ax + b = 0 (B) x

2- ax + b = 0

(C) x2+ ax - b = 0 (D) x

2- ax - b = 0

4. If the ellipse2 2

2

x y1

13 5aa 7

is inscribed in a square of side length 2a then a is equal to

(A)6

5 (B) 13, 7 3,

5

(C) 13, 7 , 75

(D) no such a exists



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5. From a point P on ellipse2 2

2 2

x y1

a b , the normals intersects the axis at M. If S and S are foci of

the ellipse thenMS MS '

PS PS '

is equal to

(A) e

2

(B) 21

e

(C) e (D)1

e

6.i j k

i 1 j 1 k 1

1

a

is equal to where |a| > 1

(A) (a 1)3

(B)3

a 1

(C)3

1

a 1 (D) none of these

7. If 6, 8 and 12 be the th, mth, nth term of an AP and f(x) = nx2+ 2lx 2m, then f(x) = 0 has

(A) a root between 0 and 1 (B) both the roots are imaginary(C) both the roots are negative (D) none of these

8. If a2+ b

2+ c

2+ d

2= 1, then the maximum value of ab + bc + cd + da is

(A) 0 (B) 1(C) 2 (D) none of these

9. The complex number z satisfying |z + 2 + i| + |z 2 + i| = 4, 0 arg(z + 2 + 2i) 4

and

3

4

arg(z 2 + 2i) will lie on a line segment of length

(A) 4 (B) 2(C) 2 (D) none of these



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10. If z1, z2, z3are the vertices of an equilateral triangle inscribed in the circle |z| = 1, then the area ofregion common to a given triangle and another triangle having vertices z1, z2, z3, is

(A)3

2 (B)

3

4

(C)7 3

4

(D)5 3

4

11. If

1 t

0

2dt A

t 3

anda t

a 1

a 1

2dt 2 A

t b

, then b is equal to

(A) 3 (B) a + 3(C) 4 a (D) none of these

12. Total number of ways in which n2number of identical balls can be put in n numbered boxes

(1, 2, 3, ..... n) such that ithbox contains atleast i number of balls is

(A)2n

n 1C (B)2n 1

n 1C

(C)

2n n 2

2 n 1C

(D) none of these

13. If a sin x + b cos (C + x) + b cos (C x) = , then the minimum value of |cos C| is

(A)2 2

2

a

b

(B)

2 2

2

a

4b

(C)2 2

2

a

16b

(D) none of these

14. In a ABC, angle B is greater than angle A, B A

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