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AIEEE full paper | DEXL
DEXL IIT-JEE Academy; Raja Park :DEXL House, 468-A, Gali No. 4, Raja Park, Jaipur Ph : 0141-4036660/4034848
Vidyadhar Nagar : Office No. 102, 1st Floor, Shivam Apartment, P. No. 4, Central Spine, Vidyadhar Nagar, Jaipur Ph :0141-6595558
(1)
PHYSICS
1. This question contains statement 1 and statement-2. Of the four choices given after the statements,choose the one that best describes the two statements.Statement 1 : If two bodies of equal masses undergo elastic collision in one dimension, then afterthe collision, the bodies will exchange their velocities.
Statement 2 : In elastic collision, velocity of approach is equal and opposite of velocity ofseparation.
(A) Statement 1 is true, statement 2 is false.(B) Statement 1 is true, statement 2 is true, statement 2 is the correct explanation of statement
1.(C) Statement 1 is true, statement 2 is true, but statement 2 is not the correct explanation of
statement 1(D) Statement 1 is false, statement 2 is true
2. If a body is changed by rubbing it, its weight :(A) remains precisely constant(B) increase slightly(C) decreases slightly
(D) May increases slightly or may decrease slightly
3. When plate voltage in diode valve is increased from 100 volt to 150 volt then plate current increasesfrom 7.5 mA. The dynamic plate resistance will be :
(A) 10 k (B) 13 k (C) 15 k (D) 11.1 k
4. The symbolic representation of four logic gates are given below:
The logic symbols for Or, NOT and NAND gates are respectively :(A) (iv), (i), (iii) (B) (iv), (ii), (i) (C) (i), (iii), (iv) (D) (iii), (iv), (ii)
5. The length of a spring is when a force of 4N is applied on it. The length is when 5N force isapplied. Then the length of spring when 9N force is applied is :(A) 5 4 (B) (C) 5 4 (D) 9 ( )
6. In a Fresnel biprism experiment, the two positions of lens give separation between the slits as 16 cmand 9 cm respectively. What is the actual distance of separation?(A) 10.5 cm (B) 13 cm (C) 12 cm (D) 14 cm
7. The coefficient of volumetric expansion of mercury is 18 x 105 /C. The thermometer bulb has avolume of 106m3 and cross-section of the stem is 0.002 cm2. Assuming that bulb is filled withmercury at 0C, the increase in length of the mercury column at 100C will be:(A) 9 cm (B) 9 mm (C) 18 cm (D) 18 mm
8. The adjacent diagram shows a charge + Q held on aninsulating support S and enclosed by a hollow sphericalconductor.O represents the centre of the spherical conductor and P is apoint such that OP = x and SP = r. The electric field r at point Pwill be:
(A)2
0x4
Q
(B)
20r4
Q
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DEXL | AIEEE full paper
DEXL IIT-JEE Academy; Raja Park :DEXL House, 468-A, Gali No. 4, Raja Park, Jaipur Ph : 0141-4036660/4034848
Vidyadhar Nagar : Office No. 102, 1st Floor, Shivam Apartment, P. No. 4, Central Spine, Vidyadhar Nagar, Jaipur Ph :0141-6595558
(2)
(C) 0 (D) None of the above
9. In the P V diagram. I is the initial state and F is the final state. The gas goes from I to F by (i) IAF,(ii) IBF, (iii) ICF. The heat absorbed by the gas is :
(A) The same in all three processes
(B) The same in (i) and (ii)(C) Greater in (i) than in (ii)
(D) The same in (i) and (iii)
10. A gaseous mixture consists of 16 g of helium and 16 g of oxygen. The ratioV
P
C
Cof the mixture is :
(A) 1.4 (B) 1.54 (C) 1.59 (D) 1.62
11. This question contains statement 1 and statement-2. Of the four choices given after the statements,choose the one that best describes the two statements.Statement 1 : When height of a tube is less than liquid rise in the capillary tube, the liquid does not
overflow.Statement 2 : Product of radius of meniscus and height of liquid in the capillary tube, alwaysremain constant.(A) If the both statement I and statement 2 are true and statement 2 is the correct explanationof statement 1(B) If the both statement 1 and statement 2 are true but statement 2 is the not correctexplanation of statement 1(C) If statement 1 is true but statement 2 is false.(D) Both statement 1 and statement 2 are false.
Directions : Question numbers 12 to 14 are based on the following paragraph.
A particle of mass 1 kg is projected at an angle of4 from horizontal
with a muzzle velocity of 20m/sec. A long slender rod of mass 5kg from apoint at the same horizontal level as that of projection and at a distance of60m from the projection point as shown in the figure. The rod can rotatefreely. If collision occurs, it is perfectly inelastic. [Take g = 10 m/s2]
12. The partical will(A) Not hit the rod at all (B) Hit the rodbetween O and A, not at its mid point(C) Hit the rod at A (D) Hit the rod at itsmid point
13. Angular velocity of rod after collision is :
(A) s/rad24
1
(B) s/rad2
4
(C) s/rad24 (D) zero
14. If the rod tilts to an angle after collision then :
(A) 0 (B)
4140cos 1 (C)
2827cos 1 (D) 90
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DEXL IIT-JEE Academy; Raja Park :DEXL House, 468-A, Gali No. 4, Raja Park, Jaipur Ph : 0141-4036660/4034848
Vidyadhar Nagar : Office No. 102, 1st Floor, Shivam Apartment, P. No. 4, Central Spine, Vidyadhar Nagar, Jaipur Ph :0141-6595558
(3)
15. In Youngs double slit experiment, the distance between the two slits is 0.1 mm and wavelength oflight used is 4 x 107m. If the width of fringe on screen is 4 mm, the distance between screen andslits is :(A) 0.1 mm (B) 1 cm (C) 0.1 cm (D) 1 m
16. The figure shows a plot of photo current versus anode potential for a photo sensitive surface forthree different radiations. Which one of the following is a correct statement?
(A) Curves (a) and (b) represent incident radiations of samefrequency but of different intensities.
(B) Curves (b) and (c) represent incident radiations of differentfrequencies and different intensities.
(C) Curves (b) and (c) represent incident radiations of samefrequency having same intensity.
(D) Curves (a) and (b) represent incident radiations of differentfrequencies and different intensities.
17. If
Landkk represent the frequencies of LandK,K X-ray lines of a given material,
then :(A)
Lkk (B)
Lkk (C)
kkL (D)
Lkk
18. A particle moves in the x-y plane with velocity vx = 8t 2 and vy = 2. If it passes through the point x =14 and y = 4 at t = 2 sec, then the equation of the path is:(A) x = y3 y2 + 2 (B) x = y2 y + 2 (C) x = y2 3y + 2 (D) x = y3 2y2 + 2
19. A car is moving on a straight, horizontal road at 30 ms1 towards the east. The acceleration of the carfor the following 20 s is shown in the graph as a functionof time. The velocity of the car at 20 s is :(A) 5 ms1 to the east
(B) 25 ms1 to the east
(C) 5 ms1 to the west
(D) 25 ms1 to the west
20. An object is kept on a smooth inclined plane of 1 in l. The horizontal acceleration to be imparted tothe inclined plane no that the object is stationary relative to the incline is:
(A) 1lg 2 (B) 1lg 2 (C)1l
g
2 (D)
1l
g2
21. Two charges q1 and q2 are placed 30 cm apart, as shown in the figure. A third charge q 3 is moved
along the arc of a circle of radius 40 cm from C to D. The changein the potential energy of the system is k
4
q
0
3
, where k is :
(A) 8q1
(B) 6q1
(C) 8q2
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DEXL | AIEEE full paper
DEXL IIT-JEE Academy; Raja Park :DEXL House, 468-A, Gali No. 4, Raja Park, Jaipur Ph : 0141-4036660/4034848
Vidyadhar Nagar : Office No. 102, 1st Floor, Shivam Apartment, P. No. 4, Central Spine, Vidyadhar Nagar, Jaipur Ph :0141-6595558
(4)
(D) 6q2
22. The internal energy change in a system that has absorbed 2 kcal of heat and done 500 J of work is :(A) 6400 J (B) 5400 J (C) 7900 J (D) 8900 J
23. A wire of resistance 12 ohms per meter is bent to form a complete circle of radius 10 cm. Theresistance between its two diametrically opposite points, A and B as shown
in the figure is :
(A) 3 (B) 6
(C) 6 (D) 0.6
24. A U-tube is partially filled with water. Oil which does not mix with water is next poured into one side,until water rises by 25 cm on the other side. If the relative density of oil is 0.8, the oil level will standhigher than the water level by:
(A) 6.25 cm (B) 12.50 cm (C) 31.75 cm (D) 62.50 cm
25. The ratio of the energy required to raise a satellite up to a height h above the earth of radius R to thatthe kinetic energy of the satellite into that orbit is:(A) R : h (B) h : R (C) R : 2h (D) 2h : R
26. The potential energy for a conservative system is given by U = ax2 bxWhere a and b are positive constants. The law of the force governing the system is :(A) F = constant (B) F = bx 2a (C) F = b 2ax (D) F = 2ax
27. A system of uniform cylinders and plates is shown in the figure. All the cylinders are identical andthere is no slipping at any contact. Velocity of lower andupper plate is v0 and 2v0 respectively as shown in the
figure. Then the ratio of angular speed of upper cylinder tolower cylinder is :(A) 1 : 3 (B) 3 : 1(C) 1 : 2 (D) 2 : 1
28. An R L circuit in which R = 5W and L = 4H is connected to a 22 V battery at t = 0. For this circuit atwhat rate the energy is being stored in the inductor when the current in circuit is 1 A?(A) 17 W (B) 22 W (C) 5 W(D) Cannot be computed from the given information
Directions : Question numbers 29 to 31 are based on the following paragraph.
Thin interference film is used to measure the thickness of slides,paper etc. The arrangement is shown in figure. For sake of clearity thetwo strips are shown thick. Consider the wedge formed in betweenstrips 1 and 2. If the interference pattern because of the two wavesreflacted from wedge surfaces is observed, then from the observeddata we can compute thickness of paper, refractive index of themedium filled in wedge, number of bands formed etc.
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DEXL IIT-JEE Academy; Raja Park :DEXL House, 468-A, Gali No. 4, Raja Park, Jaipur Ph : 0141-4036660/4034848
Vidyadhar Nagar : Office No. 102, 1st Floor, Shivam Apartment, P. No. 4, Central Spine, Vidyadhar Nagar, Jaipur Ph :0141-6595558
(5)
Consider the strips to be thick as compared to wavelength of light and light is incident normally. Neglect
the effect due to reflection from top surface of strip 1 and bottom surface of strip 2. Take L = 5 cm, air =400 nm
29. Consider an air wedge is formed by two glass plates having refractive index 1.5 by placing a piece ofpaper of thickness 20 mm. Determine the number of dark bands formed :(A) 1000 (B) 100 (C) 5000 (D) 500
30. For strip 1 refractive index = 1.34, for strip 2 refractive index = 1.6 and the wedge is filled withmedium having refractive index 1.5, then :(A) The band at contact point would be dark (B) The band at contact point would be bright(C) At contact point no maxima or minima occurs (D) At contact point uniform illumination would bethere
31. For data in Q. 29 determine the distance of point B from the 20th dark band. Counting of dark pointshas to start from the contact point:(A) 4 cm (B) 3 cm (C) 5 cm (D) 2 cm
32. The shape of graph of u versus v in case of a convex lens is
(A) (B) (C) (D)
33. A Carnots engine working between 27C and 127C has a work output of 200J per cycle. Theenergy supplied to the engine from the source in each cycle is :(A) 400 J (B) 800 J (C) 600 J (D) 500 J
34. A body possessing kinetic energy T, moving on a rough horizontal surface, is stopped in a distancey. The frictional force exerted on the body is :
(A) Ty (B) Ty
(C)Ty
(D) T
y
35. A ball of mass M is thrown vertically upwards. Another ball of mass 2M is thrown at an angle withthe vertical. Both of them stay in air for the same period of time. The heights attained by the two arein the ratio :
(A) 1 : 2 (B) 2 : 1 (C) 1 : 1 (D) 1 : cos
Chemistry
36. Number of isomeric monochloro products possible for iso-pentane are :(A) 2 (B) 3 (C) 4 (D) 5
37. Dehydrohalogenation of neopentyl bromide with alcoholic KOH mainly gives :
(A) 2methyl 1butene (B) 2methyl2butene (C) 2, 2dimethyl1butene(D) 2butene
38. Which of the following will have fastest rate of reaction with Br2/FeBr3.
(A) (B)
NO2
(C)
CH3
(D)
OCH3
39. Ozonolysis of 1, 3butadiene gives :
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DEXL IIT-JEE Academy; Raja Park :DEXL House, 468-A, Gali No. 4, Raja Park, Jaipur Ph : 0141-4036660/4034848
Vidyadhar Nagar : Office No. 102, 1st Floor, Shivam Apartment, P. No. 4, Central Spine, Vidyadhar Nagar, Jaipur Ph :0141-6595558
(6)
(A) Mixture of an aldehyde and a ketone (B) Mixture of an aldehyde and an acid(C) Only aldehydes (D) Only ketones
40. The compound X in the reaction
+ ICl X isAnhyd. AlCl3
(A)lCl
(B)Cl
(C)Cl Cl
(D)l
41. Which of the following benzyl alcohol reacts most readily with aq. HBr?
(A)CH2OH
(B)CH3O CH2OH
(C)Cl CH2OH
(D)O2N CH2OH
42. Among the following compounds, the one that undergoes deprotonation most readily in the presenceof a base, to form a carbanion is :
(A)
O O
(B) MeO OMe
O O
(C) MeO
O O
(D) H
O
43.CH3CH2COOH A
Cl2
red P
alc. KOHB
What is B?(A) CH3CH2COCl (B) CH3CH2CHO (C) CH2 = CHCOOH (D) ClCH2CH2COOH
44. Arrange the following in the increasing order of their basic strengths :CH3NH2, (CH3)2NH, (CH3)3N, NH3(A) NH3 < (CH3)3N < CH3NH2 < (CH3)2NH (B) (CH3)3N < NH3 < CH3NH2 < (CH3)2NH(C) CH3NH2 < (CH3)2NH < (CH3)3N < NH3 (D) NH3 < (CH3)3N < (CH3)2NH < CH3NH2
45. Aniline reacts with phosgene and KOH to form :
(A)
OH
(B)C Cl
O
(C)NHCOCl
(D)NCO
46. terylene is made by polymerization of terephthalic acid with :(A) Ethylene glycol (B) phenol (C) Ethanol (D) Catechol
47. A colloidal solution is subjected to an electrical field. The particles move towards anode. Thecoagulation of same sol is studied using NaCl, BaCl 2 and AlCl3 solution. Their coagulating powershould be :(A) NaCl > BaCl2 > AlCl3 (B) BaCl2 > AlCl3 > NaCl (C) AlCl3 > BaCl2 > NaCl
(D) BaCl2 > NaCl > AlCl3
48. Point out the false statement :(A) Brownian movement and Tyndall effect is shown by colloidal systems(B) gold number is a measure of the protective power of a lyophillic colloid(C) The colloidal solution of a liquid in liquid is called gel(D) Hardy-Schulze rule is related with coagulation
49. The number of planar and spherical nodes in 4 f-orbital are respectively :(A) 4 and 3 (B) 0 and 3 (C) 2 and 1 (D) 3 and 0
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DEXL IIT-JEE Academy; Raja Park :DEXL House, 468-A, Gali No. 4, Raja Park, Jaipur Ph : 0141-4036660/4034848
Vidyadhar Nagar : Office No. 102, 1st Floor, Shivam Apartment, P. No. 4, Central Spine, Vidyadhar Nagar, Jaipur Ph :0141-6595558
(7)
50. The reaction,
N2O5 (in CCl4) 2NO2 + O2(g)is first order in N2O5 with rate constant 6.2 10
4 s1. What is the value of rate of reaction when[N2O5] = 1.25 mol L
1?(A) 7.75 104 mol L1 s1 (B) 6.35 103 mol L1 s1 (C) 5.15 105 mol L1 s1
(D) 3.85 104 mol L1 s1
51. For the precipitation of cations of group IV in the qualitative anylysis, the medium is made alkalinebefore passing H2S gas. The purpose of alkaline solution is :(A) to suppress the ionization of H2S (B) to increase the ionization of H2S(C) to increase the ionization of metal salt (D) to decrease the ionization of metal salt
52. When equal volumes of the AgNO3 and NaCl solution are mixed, precipitation of AgCl (KSP = 1.81 1010) will occur only with :(A) 104 M Ag+ and 104 M Cl (B) 105 M Ag+ and 105 M Cl
(C) 106 M Ag+ and 106 M Cl (D) 1010 M Ag+ and 1010 M Cl
53. At a certain temperature, the value of kKw is 13.4 and the measured pH of a solution is 7. Thesolution is :
(A) acidic (B) basic (C) neutral (D) unpredictable
54. The van der Waals constant a for the gases O2, N2, NH3 and CH4 are 1.3, 1.390, 4.170 and 2.253L2 atm mol2 respectively. The gas which can be most easily liquefied is :(A) O2 (B) N2 (C) NH3 (D) CH4
55. Heating an aqueous solution of aluminium chloride to dryness will give :(A) Al2Cl6 (B) Al2O3 (C) AlCl3 (D) Al(OH)Cl2
56. Which one among the following is an example of ferroelectric substance?(A) Quartz (B) Lead chromate (C) Barium titanate (D) Rochelle salt
57. Correct set of four quantum numbers for the valene (outermost) electrons of rubidium (Z = 37) is :(A) 5, 0, 0 + 1/2 (B) 5, 1, 0, + 1/2 (C) 5, 1, 1 + 1/2 (D) 6, 0, 0, + 1/2
58. Wilkinsons catalyst, (Ph3P)3 RhCl is used for :(A) Hydrogenation of oils (B) Hydrogenation of alkynes(C) Hydrogenation of alkenes (D) Polymerization of alkenes
59. Consider the following statements :
I. A sigma () bond is formed when two s-orbitals overlapII. A pi () bond is formed when two p-orbitals axially overlapIII. A -bond is weaker than -bondWhich of the above statements is/are correct?(A) I and II (B) II and III (C) I alone (D) II alone
60. The common features among the species CNCO, and NO+ are :(A) bond order three and isoelectronic (B) bond order three and weak field ligands
(C) bond order two and -acceptors (D) isoelectronic and weak field ligands
61. the hybridization of atomic orbitals of nitrogen in 2 3NO ,NO and 4NH
are :
(A) sp2, sp3 and sp3 respectively (B) sp2, sp2 and sp3 respectively
(C) sp2, sp2 and sp3 respectively (D) sp3, sp2 and sp respectively
62. Which of the following statements is false?(A) BH3 is not a stable compound
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DEXL | AIEEE full paper
DEXL IIT-JEE Academy; Raja Park :DEXL House, 468-A, Gali No. 4, Raja Park, Jaipur Ph : 0141-4036660/4034848
Vidyadhar Nagar : Office No. 102, 1st Floor, Shivam Apartment, P. No. 4, Central Spine, Vidyadhar Nagar, Jaipur Ph :0141-6595558
(8)
(B) All the B H bonds in B2H6 are equal(C) The boron hydrides are readily hydrolyzed(D) Boron hydrides are prepared by the action of dil. HCl on Mg3B2.
63. Graphite is a soft, solid, lubricant, extremely difficult to melt. The reason for this anomalous behavioris that graphite :(A) Is an allotropic form of diamond
(B) Has molecules of variable molecular masses like polymers(C) Has carbon atoms arragned in large plates of rings of strongly bound carbon atoms with weak
interpolate bonds(D) Is a non crystalline substance
64. Drikold is :(A) Solid CO2 (B) Ether and dry ice (C) dry ice and alcohol (D) Dry ice and acetone
65. Which of the following reaction does not take place?
(A) 4 Al + 3O2 2Al2O3 (B) 8Al + 3Mn3O4 4Al2O3 + 9 Mn(C) 2Al + Fe2O3 Al2O3 + 2Fe (D) Al2O3 + Cr Cr2O3 +2Al
66. Thermite is a mixture of :(A) 3 parts of powdered Al and I part of Fe2O3 (B) I part of powdered Al and 3 parts of Fe2O3(C) I part of powdered Al and I part of Fe2O3 (D) 2 parts of powdered Al and I part of Fe2O3
Paragraph : for Q. No. 67 to 68Naphthalene is a white organic solid at room temperature. It melts at 80.1C. Its depression offreezing point constant is 6.5C kg mol1. 100 g of naphthalene was melted and 3.94 g of sulphurstirred into it. The sulphur dissolved in the naphthalene. The solution froze at 80.0C.
67. How many grams of sulphur would have depressed the freezing point of 1 kg of naphthalene by0.1C?(A) 3.94 g (B) 39.4 g (C) 394 g (D) 25.7 g
68. The predicated molar mass of sulphur is :(A) 32 g (B) 39.4 g (C) 128 g (D) 256 g
Directions : This section contains 2 questions numbered (69) and (70). Each question containsstatements of Assertion (A) and Reason (R) just below it. Of the statements, mark the correctanswer.(a) If both assertion and reason are true and reason is the correct explanation of assertion.(b) If both assertion and reason are true but reason is not the correct explanation of assertion.(c) If assetion is true but reason is false.(d) If both assertion and reason are false.
69. Assertion : When a concentrated solution is diluted by adding more water, the number of moles of
solute in the solution remains unchanged.Reason : Number of moles of a solute is equal to the product of molarity and volume of solution inlitres.
70. Assertion : In close packing of spheres, a tetrahedral void is surrounded by four spheres whereas anoctahedral void is surrounded by six spheres.Reason : A tetrahedral void is occupied by ions whereas an octahedral void is occupied byimpurities.
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(9)
Mathematics
71. If C1 and C2 be the centres of the two circles with radii r1 and r2 respectively such that | r2 r1 | 0 then :(A) Relation r is not a reflexive (B) R is not a transitive(C) R is not symmetric (D) R is an equivalence relation
77. The equation of a curve is y = f(x). The tangents at {1, f(1)}, {2, f(2)} and {3, f(3)} make angles ,6 3
and4 respectively with positive direction of x-axis, then the value of
3 3
2 1
f '(x) f "(x) dx f " (x) dx
(A)1
3(B)
1
3 (C) 0 (D) 1
78. Points F1, F2 are the foci of the ellipse 4x2 + 9y2 = 36. P is a point on the ellipse such that | PF1 | : |
PF2 | =
2 : 1. Then area of PF1F2 (in sq. unit) is :(A) 4 (B) 3 (C) 2 (D) 1
79. (1 + tan 1) (1 + tan 2) (1 + tan 3) . . . . . (1 + tan 45) = 2n, the value of n is :(A) 21 (B) 22 (C) 23 (D) 24
80. The distance between two points A and B is d and the projection of AB on the co-ordinate planes are
d1, d2, d3 if d12 + d2
2 + d32 = d2 then the value of l =
(A) 2 (B) 3 (C) 4 (D) 6
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DEXL IIT-JEE Academy; Raja Park :DEXL House, 468-A, Gali No. 4, Raja Park, Jaipur Ph : 0141-4036660/4034848
Vidyadhar Nagar : Office No. 102, 1st Floor, Shivam Apartment, P. No. 4, Central Spine, Vidyadhar Nagar, Jaipur Ph :0141-6595558
(10)
81. Let a, b, c
be three non-coplanar vectors and 1 2 3b c c a a b
v , v , v
[ a b c] [ a b c] [ a b c]
which one of
the following is false?
(A) 1 2 3a . b . c . 3
(B) 1 2 3 2 3 1 3 1 23
.( ) .( ) .( )
[abc]
(C) 1 2 31
[ ]
[ a b c]
(D) 1 2 2 3 3 1
1[ ]
[ a b c]
82. If S.D. of a variate x is x then the S.D. ofax b
c
( a, b, c R and c 0) is :
(A) xac
(B) xax
(C) x (D) xa
83. Ifk 2k 3k
1 1 1, , , . . .
2 2 2 are the probabilities of mutually. exclusive and exhaustive system of events
then k( Real number) =(A) 1/2 (B) 1 (C) 2 (D) 2/3
84. The value of the limit2
2 2 2 2cos cos cos cos
cos1 1 1 1
2
lim 1 2 3 . . . . .10
(A) 1010 (B) 1 (C) 10 (D) 0
85. The reflection of the complex number (2 i) in the straight lie z iz is :(A) 1 2i (B) 1 + 2i (C) 2 i (D) 2 + i
86. The value of the sum of the series n n n n th0 1 2 33 c 8 c 13 c 18 c . . . . n term is :(A) 2n (B) 3n (C) 5n (D) 0
87. 1
0
t an (tan x)dx
(A)2 (B)
2
2 (C) 0 (D)
2
2
88. The equation of the line which passes through (a cos3 , a sin3 ) and perpendicular to the linex sec + y cosec = a is(A) x cos y sin = a cos 2 (B) x cos + y sin = a cos 2
(C) x sin y cos = a sin 2 (D) x sin + y cos = a cos 2
89. Area of the triangle formed by the lines x2 + 4xy + y2 = 0 and x + y = 1
(A) 3 (B)3
2(C) 1 (D) 2 3
90. The number of diagonals that can be drawn in polygon of 100 sides is :(A) 98 (B) 4850 (C) 4950 (D) 4900
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AIEEE full paper | DEXL
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91. If 2 2k2 2
1 n n
A 2k n n 1 n n
2k 1 n n n 1
andn
kk 1
A 72
then n =
(A) 8 (B) 7 (C) 6 (D) 1
92. If are the roots of x4
+ 4x3
6x2
+ 7x 9 = 0 then the value of (1 + 2
) (1 + 2
) (1 + 2
) (1 +2) =(A) 12 (B) 13 (C) 14 (D) 0
93. Ifmx. . . . ny . . . .mx nymx nyx y then
dy
dxequals
(A)my
nx(B)
mxny
(C) mn
(D) nm
94. Let f(x) = min {x, x2}, R then(A) f(x) is continuous every where (B) f(x) is non differentiable at two values of x
(C) f(x) is a constant function x > 1 (D) (a) , (b) and (c) all are true
Paragraph : for Q. No. 95 to 97.Given a function f which has a derivative f(x) for every real x and which satisfy f(0) = 2 andf(x + y) = ey f(x) + ex f(y) for every real x and which satisfy f(0) = 2 and f(x + y) = e y f(x) + ex f(y) forall x and y.
95. The function f(x) is :(A) 2xex (B) x(ex + 1) (C) x (D) xex
96. f(x) form a linear differential equation of IF =(A) ex (B) ex (C) ex (D) xex
97. The range of the function f(x) is :(A) [0, ) (B) ( , ) (C) (, 0] (D)
Directions : This section contains 3 questions numbered (98), (99) and (100). Each questioncontains statement 1 and statement 2. Each question has 4 choices (a), (b) and (d) out of whichonly one is correct. Of these statement, mark correct choice.(a) Statement 1 and 2 are true and statement 2 is a correct explanation for statement 1.(b) Statement 1 and 2 are true but statement 2 is not a correct explanation for statement 1.(c) Statement 1 is true, statement 2 is false.(d) Statement 1 is false, statement 2 is true.(e)
98. Statement 1 : Statements (i) ~ (P q) (ii) ~ p q and (iii) p ~ q are logically equivalent.Statement 2 : Two statements p and q are said to be logically equivalent iff they have identical
truth values.
99. Let 2 n0 1 2 nlog (1 x)
a a x a x . . . . a x . . . . |x| 11 x
Statement 1 : n1 1 1 1a 1 . . .2 3 4 n
Statement 2 : Ifx
n0 1 n
xa a x . . . a x . . . . | x| 1
1 x
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then n1 1 1 1
a 1 . . . .1! 2! 3! n!
100. Statement 1 :tan xx , 0 x
sin x x 2
Statement 2: f(x) = tan x sin x x
2
is increasing in 0 x 2
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DEXL IIT-JEE Academy; Raja Park :DEXL House, 468-A, Gali No. 4, Raja Park, Jaipur Ph : 0141-4036660/4034848
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AIEEE TS - 8 (English)
Physics
1. (c) 2. (d) 3. (d) 4. (b) 5. (a) 6. (c) 7. (a)
8. (a) 9. (c) 10. (d) 11. (a) 12. (c) 13. (a) 14. (c)
15. (d) 16. (a) 17. (a) 18. (b) 19. (b) 20. (c) 21. (c)
22. (c) 23. (d) 24. (b) 25. (d) 26. (c) 27. (b) 28. (a)29. (b) 30. (b) 31. (a) 32. (d) 33. (b) 34. (c) 35. (c)
Chemistry
36. (c) 37. (b) 38. (d) 39. (c) 40. (d) 41. (b) 42. (a)
43. (c) 44. (a) 45. (d) 46. (a) 47. (c) 48. (c) 49. (d)
50. (a) 51. (b) 52. (b) 53. (b) 54. (c) 55. (a) 56. (c)
57. (a) 58. (c) 59. (c) 60. (a) 61. (b) 62. (b) 63. (c)
64. (a) 65. (d) 66. (b) 67. (b) 68. (d) 69. (b) 70. (c)
Mathematics
71. (c) 72. (b) 73. (b) 74. (d) 75. (c) 76. (d) 77. (b)
78. (a) 79. (c) 80. (a) 81. (d) 82. (b) 83. (b) 84. (c)
85. (a) 86. (d) 87. (c) 88. (a) 89. (b) 90. (b) 91. (a)
92. (b) 93. (a) 94. (d) 95. (a) 96. (c) 97. (b) 98. (a)
99. (b) 100. (d)
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