20
8/12/2019 Aiot Advanced Xi Paper 1 20 Jan 13 Eng http://slidepdf.com/reader/full/aiot-advanced-xi-paper-1-20-jan-13-eng 1/20 Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.  Date : 20-01-2013 Duration : 3 Hours Max. Marks : 219 PAPER 1 CODE 0 ALL INDIA OPEN TEST (AIOT) JEE ADVANCE INSTRUCTIONS A. General : 1. This Question Paper contains 63 questions. 2. The question paper CODE is printed on the right hand top corner on this sheet of this booklet. 3. No additional sheets will be provided for rough work. 4. Blank paper, clipboard, log tables, slide rules, calculators, cellular phones, pagers and electronic gadgets in any form are not allowed. 5. The answer sheet, a machine-gradable Objective Response Sheet (ORS), is provided separately. 6. Do not Tamper / mutilate the ORS or this booklet. 7. Do not break the seals of the question-paper booklet before instructed to do so by the invigilators. 8. Write your Name, Roll No. and  Sign in the space provide on the back page of this booklet. B. Filling the bottom-half of the ORS : Use only Black ball point pen only for filling the ORS. Do not use Gel / Ink / Felt pen as it might smudge the ORS. 9. Write your Roll no. in the boxes given at the top left corner of your ORS with black ball point pen. Also, darken the corresponding bubbles with Black ball point pen only. Also fill your roll no on the back side of your ORS in the space provided (if the ORS is both side printed). 10. Fill your Paper Code as mentioned on the Test Paper and darken the corresponding bubble with Black ball point pen. 11. If student does not fill his/her roll no. and paper code correctly and properly, then his/her marks will not be displayed and 5 marks will be deducted (paper wise) from the total. 12. Since it is not possible to erase and correct pen filled bubble, you are advised to be extremely careful while darken the bubble corresponding to your answer. 13. Neither try to erase / rub / scratch the option nor make the Cross (X) mark on the option once filled. Do not scribble, smudge, cut, tear, or wrinkle the ORS. Do not put any stray marks or whitener anywhere on the ORS. 14. If there is any discrepancy between the written data and the bubbled data in your ORS, the bubbled data will be taken as final. C. Question paper format and Marking scheme : 15. The question paper consists of 3 parts (Physics,Chemistry & Mathematics). Each part consists of FOUR Sections. 16. For each question in Section  –I, you will be awarded 3 marks if you darken the bubble corresponding to the correct answer and zero marks if no bubble is darkened. There is no negative marking for incorrect answer in this section. 17. For each question in Section  –II, you will be awarded 4 marks if you darken the bubble corresponding to the correct answer and zero marks if no bubble is darkened. There is no negative marking for incorrect answer in this section. 18. For each question in Section  –III, you will be awarded 3 marks if you darken the bubble corresponding to the correct answer and zero marks if no bubble is darkened. There is no negative marking for incorrect answer in this section. 19. For each question in Section  –IV, you will be awarded 4 marks if you darken the bubble corresponding to the correct answer and zero marks if no bubble is darkened. In case of bu bbling of incorrect answer, minus one (  –1) mark will be awarded.    D    O    N    O    T    B    R    E    A    K    T    H    E    S    E    A    L    S    W    I    T    H    O    U    T    B    E    I    N    G    I    N    S    T    R    U    C    T    E    D    T    O    D    O    S    O    B    Y    T    H    E    I    N    V    I    G    I    L    A    T    O    R CLASS-XI | TARGET : JEE (IITs) 2014 | COURSE : ALL INDIA TEST SERIES (VIKALP) 

Aiot Advanced Xi Paper 1 20 Jan 13 Eng

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

 Date : 20-01-2013 Duration : 3 Hours Max. Marks : 219

PAPER 1

CODE

0

ALL INDIA OPEN TEST (AIOT) JEE ADVANCE

INSTRUCTIONSA. General :

1. This Question Paper contains 63  questions.

2. The question paper CODE is printed on the right hand top corner on this sheet of this booklet.

3. No additional sheets will be provided for rough work.

4. Blank paper, clipboard, log tables, slide rules, calculators, cellular phones, pagers and electronic gadgets

in any form are not allowed.

5. The answer sheet, a machine-gradable Objective Response Sheet (ORS), is provided separately.

6. Do not Tamper / mutilate the ORS or this booklet.

7. Do not break the seals of the question-paper booklet before instructed to do so by the invigilators.

8. Write your Name, Roll No. and  Sign in the space provide on the back page of this booklet.

B. Filling the bottom-half of the ORS :

Use only Black ball point pen only for filling the ORS. Do not use Gel / Ink / Felt pen as it might smudge the ORS.

9. Write your Roll no. in the boxes given at the top left corner of your ORS with black ball point pen. Also, darken

the corresponding bubbles with Black ball point pen only. Also fill your roll no on the back side of your ORS

in the space provided (if the ORS is both side printed).

10. Fill your Paper Code as mentioned on the Test Paper and darken the corresponding bubble with Black ball

point pen.

11. If student does not fill his/her roll no. and paper code correctly and properly, then his/her marks will not be

displayed and 5 marks will be deducted (paper wise) from the total.

12. Since it is not possible to erase and correct pen filled bubble, you are advised to be extremely careful while

darken the bubble corresponding to your answer.

13. Neither try to erase / rub / scratch the option nor make the Cross (X) mark on the option once filled. Do not

scribble, smudge, cut, tear, or wrinkle the ORS. Do not put any stray marks or whitener anywhere on the

ORS.

14. If there is any discrepancy between the written data and the bubbled data in your ORS, the bubbled data will

be taken as final.C. Question paper format and Marking scheme :

15. The question paper consists of 3 parts (Physics,Chemistry & Mathematics). Each part consists of FOUR Sections.

16. For each question in Section –I, you will be awarded 3 marks if you darken the bubble corresponding to the

correct answer and zero marks if no bubble is darkened. There is no negative marking for incorrect

answer in this section.

17. For each question in Section –II, you will be awarded 4 marks if you darken the bubble corresponding to the

correct answer and zero marks if no bubble is darkened. There is no negative marking for incorrect

answer in this section.

18. For each question in Section –III, you will be awarded 3 marks if you darken the bubble corresponding to

the correct answer and zero marks if no bubble is darkened. There is no negative marking for incorrectanswer in this section.

19. For each question in Section –IV, you will be awarded 4 marks if you darken the bubble corresponding to

the correct answer and zero marks if no bubble is darkened. In case of bubbling of incorrect answer, minus

one ( –1) mark will be awarded.

   D   O   N   O   T   B   R   E   A   K   T   H   E   S   E   A

   L   S   W   I   T   H   O   U   T   B   E   I   N   G

   I   N   S   T   R   U   C   T   E   D   T   O   D   O   S   O   B

   Y   T   H   E   I   N   V   I   G   I   L   A   T   O   R

CLASS-XI | TARGET : JEE (IITs) 2014 | COURSE : ALL INDIA TEST SERIES (VIKALP) 

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PHYSICS

Space for Rough Work 

P1AIOTXI200113C0-1

PART I : PHYSICS

SECTION - I

Straight Objective Type 

This section contains 7 questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of

which ONLY ONE is correct.

1. Initially car A is 10.5 m ahead of car B. Both start moving at time t = 0 in the same direction along a

straight line. The velocity time graph of two cars is shown in figure. The time when the car B will catch

the car A, will be

(A) t = 21 sec (B) t = 52 sec (C) 20 sec. (D) None of these

2. The velocity displacement graph of a particle moving along a straight line is shown in figure.

Then the acceleration displacement graph is.

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

Space for Rough Work 

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PHYSICS

Space for Rough Work 

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Space for Rough Work 

3. Figure shows five identical open –top container filled upto the brim with water. In figure(b), toy duck is

floating, in figure(c) a heavy toy duck sinks and touches the bottom, in figure (d) a heavy toy duck is

suspended from a str ing and in figure (e) a light toy duck is tied with a massless string. If all the five

containers are put on weighing machine, the correct order of their reading will be :

 

(A) (a) = (b) = (c) = (d) = (e) (B) (e) < (a) = (b) = (d) < (c)

(C) (e) < (d) < (a) = (b) < (c) (D) (a) = (b) = (d) = (e) < (c)

4. A man can swim certain distance in still water up and down in time t1. If he swims to some distance down

stream the river and returns back to same point he takes time t2. Then :(A) t1 = t2 (B) t1 < t2 (C) t1 < t2 (D) t1 & t2 can't be compared

5. If the fundamental frequency of a pipe closed at one end is 512Hz. The fundamental frequency of a

pipe of the same dimensions but open at both ends will be:

(A) 1024 Hz (B) 512Hz (C) 256 Hz (D) 128Hz

6. For an adiabatic process graph between PV and V for a monoatomic gas is :

(A)

PV

V

(B)

PV

V

(C)

PV

V

(D)

PV

V

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PHYSICS

Space for Rough Work 

P1AIOTXI200113C0-3

7. The length of the wire shown in figure between the pulleys is 1.5 m and its mass is 12.0 g. The frequency

of vibration with which the wire vibrates in three loops forming antinode at the mid point of the wire is -

(Take g = 9.8 m/s2)

9kg 9kg

(A) 210 Hz (B) 140 Hz (C) 70 Hz (D) none of these

SECTION - II

True & False Statement Type This Section Contains 3 questions. Each questions contains 3 or 4 statements S

1, S

2, S

3or S

4. Each

statement is either true (T) or false (F). Each questions has 4 choices (A), (B), (C) and (D) each of

which contains whether S1, S

2, S

3 or S

4are true or false. Exactly one choice contains the correct order

of truthness or falseness of S1, S

2, S

3 or S

4 respectively and is the correct choice.

8. S1 :  Net torque on a system due to all internal forces about any point is zero.

S2 : For a rigid body undergoing fixed axis rotation, the direction of its angular acceleration and angularvelocity are always same.

S3 :  If net torque on a rigid body about its centre of mass is zero, the angular speed of the rigid body is

always zero.

(A) T F T (B) T T F (C) F F F (D) T F F

9. S1 : If the absolute temperature of a gas is doubled, the final rms-velocity of the gas particles becomes

2  times the initial value.S

2  : In isothermal process involving an ideal gas, whole of the heat energy supplied to the gas is

converted into internal energy.

S3 : In a perfectly inelastic collision, all the initial kinetic energy of the colliding bodies is converted to heat

(A) T F F (B) T T F (C) T F T (D) F F T

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PHYSICS

Space for Rough Work 

P1AIOTXI200113C0-4

Space for Rough Work 

10. S1 : Two identical spheres undergo headon collision, then the kinetic energy of each sphere is least

at the same instant of time.

S2 : For a particle undergoing circular motion the angular velocity (considered non-zero) is always

perpendicular to acceleration of the particle.

S3 : The number of nodes and antinodes are equal in a standing sound wave in a pipe, then the pipe

has both ends open.

(A) T T F (B) T F T (C) F F F (D) F T F

SECTION - III

Comprehension Type This section contains 2 paragraphs. Based upon each paragraph, there are 2 questions. Each question

has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

Paragraph for Question Nos. 11 to 12

, A bar of mass m is held as shown between 4 uniform discs, each of mass m! & radius r = 75 mm. The

bar has been released from rest, knowing that the normal forces exerted on the discs by vertical

walls are sufficient to prevent any slipping. Answer the following questions assuming attachments

are massless and fixed to the bar. (Acceleration due to gravity is g)

11. If m = 5 kg and m ! = 2 kg, then acceleration of the bar is

(A) g (B) 13g/7 (C) 13g/17 (D)17

g

12. If the mass m! of the discs is negligible, then acceleration of the bar is

(A) g (B) 2g/3 (C) 13g/17 (D)17

g

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PHYSICS

Space for Rough Work 

P1AIOTXI200113C0-5

Space for Rough Work 

Paragraph for Question Nos. 13 to 14

A sinusoidal wave is propagating in negative x –direction in a string stretched along x-axis. A particle of

string at x = 2m is found at its mean position and it is moving in positive y direction at t = 1 sec. The

amplitude of the wave, the wavelength and the angular frequency of the wave are 0.1meter, " /4 meter and

4" rad/sec respectively.

13. The equation of the wave is

(A) y = 0.1 sin (4"#t  –1)+ 8(x  –  2)) (B) y = 0.1 sin (#t –1) –  (x  –  2))

(C) y = 0.1 sin (4"#t –

1) –

8(x –

  2)) (D) none of these

14. The speed of particle at x = 2 m and t = 1sec is

(A) 0.2" m/s (B) 0.6"  m/s (C) 0.4"  m/s (D) 0

SECTION - IV

Integer Answer Type 

This section contains 7 questions. The answer to each of the questions is

a double digit integer, ranging from 00 to 99. The appropriate bubble

below the respective question number in the ORS have to be darkened.

15. One mole of an ideal gas (% = 1.4) at 500 K, is filled in an adiabatic cylinder. The piston is free to move

against atmospheric pressure. A non –conducting fan is inserted into the gas space and rotated vigorously,

so that the gas expands slowly, till its volume is doubled. Find work done by the fan in kJ.

(Take R = 8 J/mole.K, neglect heat capacity of the cylinder, piston and the fan).

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PHYSICS

Space for Rough Work 

P1AIOTXI200113C0-6

16. 4th harmonic of an organ pipe has frequency 33 Hz lesser than 5th harmonic of same organ pipe. Find

difference of wavelength (in cm) in the given two cases (Assume velocity of sound in air = 330 m/s).

Neglect end correction.

17. A bus is moving with a constant acceleration a = 3g/4 towards right. In the bus, a ball is tied with a

rope and is rotated in vertical circle as shown. The tension in the rope will be minimum, when the rope

makes an angle & with horizontal. Find & in degree.

& a=3g/4

18 In a cyclic process ABCA for an ideal gas. In AB, BC and CA process 50 J, 20 J and 5 J heat is supplied to

an ideal gas. In process AB internal energy of gas increases by 60 J and in process BC work done by gas

is 30 J. The decrease in internal energy of gas in process CA in joule is :

19. One end of a very long chain of linear mass density ' is fixed to a

cube of mass m and specific density3

2 while the other end of chain

is free. The cube attached with chain is immersed in deep water

container. If specific density of chain is 6, then find the height h (in

mtres) above the surface of container at which cube will float in

equilibrium. (Given'

m = 50 metre)

h

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PHYSICS

Space for Rough Work 

P1AIOTXI200113C0-7

20. A standing wave ( = (5 mm) sin "x.cos (200 t) is maintained in a homogeneous rod with cross-sectional

area 0.04 m2 and density 1000 kg/m3. Find the total mechanical-energy in joule confined between the

sections corresponding to the adjacent displacement nodes.

21. In the pulley system shown in figure, at an instant if block A is going down at 5 m/s, find speed of

block B  (in m/s).In step pully the ratio of radii is 1 : 2. There is no slipping between step pulley and

string. Other pulleys are frictionless.

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P1AIOTXI200113C0-8

CHEMISTRY

Space for Rough Work 

PART II : CHEMISTRY

Atomic masses : [H = 1, D = 2, Li = 7, C = 12, N = 14, O = 16, F = 19, Na = 23, Mg = 24, Al = 27, Si = 28,

P = 31, S = 32, Cl = 35.5, K = 39, Ca = 40, Cr = 52, Mn = 55, Fe = 56, Cu = 63.5, Zn = 65, As = 75,

Br = 80, Ag = 108, I = 127, Ba = 137, Hg = 200, Pb = 207]

SECTION - I

Straight Objective Type This section contains 7 questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of

which ONLY ONE is correct.

22. In what ratio should a 15% solution of acetic acid be mixed with a 3% solution of the acid to prepare a 10%

solution(all percentages are mass/mass percentages) :

(A) 7 : 3 (B) 5 : 7 (C) 7 : 5 (D) 7 : 10

23. The wave motion of electron in a Bohr's orbit of hydrogen is as shown in diagram. The potential energy of

electron in the given orbit of hydrogen atom is :

(A)  –3.4 eV (B) + 3.4 eV (C)  –3.02 eV (D)  –1.51 eV

24. In context with the industrial preparation of hydrogen from water gas (CO + H2), which of the following is the

correct statement ?

(A) CO is removed by absorption in aqueous Cu2Cl

2 Solution.

(B) H2 is removed through occlusion with Pd.

(C) CO is oxidized to CO2 with steam in the presence of a catalyst followed by absorption of CO

2 in alkali.

(D) CO and H2 are fractionally separated using differences in their densities.

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P1AIOTXI200113C0-9

CHEMISTRY

25. A(s) 2B(g) + C(g)

The above equilibrium was established by initially taking A(s) only. At equilibrium, B is removed so that its

partial pressure at new equilibrium becomes 1/3rd of original total pressure. Ratio of total pressure at new

equilibrium and at initial equilibrium will be :

(A) 2/3 (B) 14/13 (C) 5/3 (D) 17/19

26 . The IUPAC name of the following compound is :

(A) 4-Bromo-3-cyanophenol (B) 2-Bromo-5-hydroxybenzonitrile

(C) 2-Cyano-4-hydroxybromobenzene (D) 6-Bromo-3-hydroxybenzonitrile

27. What is the decreasing order of C –N bond lenth in the given compounds :

(A) x > y > w > z (B) z > y > w > x (C) x > z > y > w (D) y > z > w > x

Space for Rough Work 

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P1AIOTXI200113C0-10

CHEMISTRY

28. The most stable resonating structure of p-nitroso nitrobenzene is :

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

SECTION - II

True & False Statement Type This Section Contains 3 questions. Each questions contains 3 or 4 statements S

1, S

2, S

3or S

4. Each

statement is either true (T) or false (F). Each questions has 4 choices (A), (B), (C) and (D) each of

which contains whether S1, S

2, S

3 or S

4are true or false. Exactly one choice contains the correct order

of truthness or falseness of S1, S

2, S

3 or S

4 respectively and is the correct choice.

29. S1 : In modern periodic table each block contains a number of columns equal to the number of electrons thatcan occupy that sub-shell.

S2 : The greatest increase in ionization enthalpy is experienced on removal of electron from core noble gas

configuration.

S3 : The size of the isoelectronic species is effected by electron-electron interaction in the outer orbitals.

(A) FFT (B) TTF (C) FTF (D) TTT

30. S1: Carbon has allotropic forms due to its property of catenation

S2: Carbon has allotropic forms due to its ability to form p!-d! bond

S3: Carbon has allotropic forms due to its non-metallic character

(A) FFT (B) TTF (C) FTF (D) TTT

31. S1 : The energy of resonance hybrid is always less than that of any resonating structure.S

2 :The resonance energy is the difference between the enthalpies of formation of the molecule and the

resonating structure having maximum energy.

S3 : The resonance structures are hypothetical structure and they do not represent any real molecule.

(A) F T F (B) T F T (C) F F F (D) T T T

Space for Rough Work 

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P1AIOTXI200113C0-11

CHEMISTRY

SECTION - III

Comprehension Type This section contains 2 paragraphs. Based upon each paragraph, there are 2 questions. Each question has

4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

Paragraph for Question Nos. 32 to 33

The approximate shape of a molecule can often be predicted by using what is called the valence-shell

electron-pair repulsion (VSEPR) model. Electrons in bonds and in lone pairs can be thought of an “ charge

cloud” that repel one another and stay as far apart possible, thus causing molecules to assume specific

shapes.

The repulsive interactions of electron pairs decrease in the order :

lone pair - lone pair > lone pair - bond pair > bond pair - bond pair.

These repulsions effect result in deviations from idealised shapes and alteration in bond angles in

molecules.

32. Which of the following statement is correct with respect to bond angle ?

(A) The F - S - F angle in SF2 is more than 109o 28’.

(B) The H - N - N angle in N2

 H2

  is approximately 180o .

(C) The F -Kr - F angle in KrF4 is 90o .

(D) The Cl - N - O angle in NOCl is more than 120o.

33. Molecular shape of XeF3+, SF

3+ and CF

3+ are :

(A) the same with 2,1 and 0 lone pairs of electrons respectively.

(B) different with 2 , 1 and 0 lone pairs of electrons respectively.

(C) different with 0, 1 and 2 lone pairs of electrons respectively.

(D) the same with 2, 0 and 1 lone pairs of electrons respectively.

Space for Rough Work 

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P1AIOTXI200113C0-12

CHEMISTRY

Paragraph for Question Nos. 34 to 35

Identification of +m &  –m groups : If the first atom of the group has lone pair or negative charge shows +m

effect. If the group has vacant p-orbital or vacant d-orbital on first atom. Also a multiple bonded group in which

second atom is more electronegative than the first then it shows  –m effect.

34. Identify which of the following does not show + m effect.

(A)  –NH – (B)3CHCNH

||O

""" (C)  –O# (D)  –B(CH3)2

35. Identify which of the following cannot show  – m effect.

(A)  –F (B)33 )CH(P

$

" (C)  –CH = O (D)  –NO2

SECTION - IV

Integer Answer Type 

This section contains 7 questions. The answer to each of the questions isa double digit integer, ranging from 00 to 99. The appropriate bubble

below the respective question number in the ORS have to be darkened.

36. Spin only magnetic moment (in unit of Bohr magneton) of Co3+ is x  then value of x is ________.

37. Give the atomic number of the inert gas atom in which the total number of d-electrons is equal to the

difference in the number of total p- and s-electrons.

38. NH3 is heated initially at 15 atm from 27ºC to 127ºC at constant volume. At 127ºC equilibrium is established.

The new pressue at equilibrium at 127ºC becomes 30 atm for the reaction 2NH3(g) N2(g) + 3H2(g) . Then

find the % of moles of NH3 actually decomposed.

Space for Rough Work 

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P1AIOTXI200113C0-13

CHEMISTRY

39. The pressure of 11 gm of a gas which is placed in a 4 litres container at 127 °C is 2 atm, then the

molecular weight of gas would be ?

(Take R = 0.08 ltr. atm/mol K)

40. Give the sum of aromatic and antiaromatic compounds in the following :

(a) (b) (c) (d) (e)

(f) (g) (h) (i) (j)

(k) (l) (m) (n)

41. What is the moleculer mass of conjugated diene (X) :

42. Number of ! electrons in resonance in the following structure is.

Space for Rough Work 

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P1AIOTXI200113C0-14

MATHEMATICS

PART- III - MATHEMATICS

SECTION - I

Straight Objective Type 

This section contains 7 questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out ofwhich ONLY ONE is correct.

43. A value of a for which one root of quadratic equation (a2  – 5a + 3) x2 + (2a  – 3) x + 2 = 0 is twice as

large as other is

(A)  –3

1(B)

5

3(C)  – 

5

3(D)

3

1

44. If a, a1, a

2, a

3 , ......, a

100 , b are in A.P. and a, g

1, g

2, ...., g

100b , are in G.P. and h is harmonic mean of a and

b, then 501001

100321

)aa(

g....ggg

!+ 49

992

99432

)aa(

g....ggg

!+ 48

983

98543

)aa(

g....ggg

!+ ...+

)aa(

gg

5150

5150

! is equal to

(A)1h

)1h(h 50

"

"(B)

2h

)2h(h 5050

"

"(C)

)2h(2

)2h(h50

5050

"

"(D)

)2h(h

)2h(250

5050

"

"

45. The sum of the coefficient of all the terms in the expansion of (2x  – y + z)20 in which y do not appear at allwhile x appears in even powers and z appears in odd powers is

(A) 0 (B)2

1220 "(C) 219 (D)

2

1320 "

46. The number of six letter words, each consisting of three consonants and 3 vowels, that can be formedusing the letters of the word "CIRCUMFERENCE" is

(A) 22100 (B) 22150 (C) 22101 (D) 21200

Space for Rough Work 

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47. If in a #ABC the equation of angle bisector of angle B is y = x and angle C is y =  –x. The equation of 

line BC if the coordiates of A are (5, 7) is

(A) x + y + 1 = 0 (B) 7y + 5x  – 3 = 0

(C) 7y = 5x (D) none of these

48. If two distinct chords of a parabola y2 = 4ax passing through the point (a, 2a) are bisected by the linex + y = 1, then length of the latus rectum can be(A) 2 (B) 7 (C) 4 (D) 5

49. The number of solutions of the equation xcos1"  = sin x which lie in the interval [$, 5$], are

(A) 6 (B) 5 (C) 4 (D) 3

SECTION - II

True & False Statement Type This Section Contains 3 questions. Each questions contains 3 or 4 statements S

1, S

2, S

3or S

4. Each

statement is either true (T) or false (F). Each questions has 4 choices (A), (B), (C) and (D) each ofwhich contains whether S

1, S

2, S

3 or S

4are true or false. Exactly one choice contains the correct order

of truthness or falseness of S1, S

2, S

3 or S

4 respectively and is the correct choice.

50. Consider the following statements :

S1 : If two quadratic expressions f(x) = ax2 + bx + c and g(x) = ax2 + px + q, have equal discreminants  and f(x) = g(x) has a root x = %, then arithematic mean of roots of f(x) + g(x) = 0 is %

S2 : The determinants D

1 =

bac1

acb1

cba1

 , D2 =

2

2

2

cc1

bb1

aa1

, then D1 = D

2

S3 : cos 1° > cos 1

State, in order, whether S1, S

2, S

3  are true or false

(A) T T T (B) F T T (C) T F T (D) F F F

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51. Consider the following statements :S1 : If x + y = k is a normal to y2 = 12x, then k = 9S2 : The centre of ellipse 4x2 + 9y2  – 16x  – 54y + 61 = 0 is (2, 3)

S3 : If in a triangle (a + b + c) ( – a + b + c) = kbc, then k & [0, 3]State, in order, whether S

1, S

2, S

3  are true or false

(A) T T F (B) T F T (C) F T F (D) F F T

52. Consider the following statementsS1 : If r and s are non negative integers and r + s = 2n + 1, then r! s! is least when value of |r  – s| is 2.

S2 : 0xlim'   (

( )

 *++, 

-    !

)2 / x(tan

x2cos –xsinx12  = 6.

S3 :  Number of values of ‘.’ in [0, 4$] satisfying the equation cos3. = 3cos., are 4State, in order, whether S

1, S

2, S

3  are true or false

(A) T F T (B) F T F (C) F F T (D) F T T

SECTION - III

Comprehension Type This section contains 2 paragraphs. Based upon each paragraph, there are 2 questions. Each question has4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

Paragraph for Question Nos. 53 to 54

Let 0(x, y) 1  x2 + y2 + 2gx + 2fy + c = 0 be a circle of radius k passing through the points (%, 0) and(0, %), % 2 0. If 0 (%, 0) = 0 has equal roots and 0(1, 1) =  – 2 ,then

53. Value of k is(A) 1 (B) 2 (C) 4 (D) 8

54. Let the equation of tangent to the circle x2 + y2  – 2kx = 0 which is perpendicular to the normal drawn through

the origin be x + by = c, (where c 2 0 and k is obtained by Q.No. 53) then c =(A) 4 (B) 3 (C) 2 (D) 1

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Paragraph for Question Nos. 55 to 56

Consider f(x) = | log

ax  – 4

 |  –  |4xlog| 2a

  "

55. If f(x) = 4 has n solutions and product of these solutions is k, then k =

(A)2

n(B) n (C) 2n (D) 3n

56. If a = 2, then the greater solution of f(x) = 4 is (where k is obtained by Q.No. 55)

(A) 22k (B) 24k (C) 28k (D) 1

SECTION - IV

Integer Answer Type 

This section contains 7 questions. The answer to each of the questions isa double digit integer, ranging from 00 to 99. The appropriate bubblebelow the respective question number in the ORS have to be darkened.

57. If set of all real value of a such that f(x) =40x2x

)1a2(x)1a(2x)1a2(2

2

!""!!!"  always negative is ( – 3, p),

then find the value of p.

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58. Find the least positive integer n such that

ºnsin

1

º134sinº133sin

1.......

º48sinº47sin

1

º46sinº45sin

14!!! .

59. If

15x11x8x

9x6x4x

5x3x2x

!!!

!!!

!!!

 = kx2 + !x + m, then find the value of 2  – 5(k + ! + m).

60. The sum of the squares of the reciprocals of two perpendicular diameters of the ellipse 5x2 + 4y2 = 1is equal to k, then find the value of 8k.

61. If PQ is a double ordinate and e is eccentricity of the hyperbola 1b

y –

a

x2

2

2

2

4   such that OPQ is an

equilateral triangle, O being the centre of the hyperbola, then find the least possible integral value of 3e2.

62. PN is an ordinate of the parabola y2 = 4ax. A straight line is drawn parallel to the axis to bisect NP andmeets the curve in Q. NQ meets the tangent at the vertex in a point T such that AT = kNP, then find thevalue of 30k. (Where A is the vertex)

63. The number of different necklaces formed by using 30 identical diamonds and 3 different jewels when exactlytwo jewels are always together is 10x + y, where 0 5 x, y 5 9, then find the value of |x  – y|.

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