mains practice paper
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JEE mains practice paper.Very good.TRANSCRIPT
PRACTICE TEST – 2 (MAIN)
CENTERS: MUMBAI / DELHI / AKOLA / KOLKATA / LUCKNOW / NASHIK / GOA / PUNE # 1
PHYSICS (PART – A)
SECTION I: (SINGLE CHOICE QUESTIONS)
This section contains 30 Multiple Choice Questions. Each question has four choices (1), (2), (3)
and (4) out of which ONLY ONE is correct.
1. A person sitting in the rear end of the compartment throws a ball towards the front end. The ball
follows a parabolic path. The train is moving with velocity of 120ms . A person standing outside on
the ground also observes the ball. How will the maximum heights my attained and the ranges R
seen by the thrower and the outside observer compare with each other?
(1) same my different R (2) Same my and R
(3) Different my same R (4) Different my and R
2. Two trains are moving with equal speed in opposite directions along two parallel railway tracks, if
the wind is blowing with speed u along the track so that the relative velocities of the trains with
respect to the wind are in the ratio 1:2, then the speed of each train must be.
(1) 3 u (2 ) 2 u (3) 5 u (4) 4 u
3. A person moves along OABC as shown in the figure. What is the magnitude of displacement from
the initial position? OA 30m,AB 20m and BC 30 2 m
x'B' x
BA
C
Y'
Y
O
(1) 10 m (2) 20 m (3) 30 m (4) 30 2 m
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4. Graph below shows the force F in N versus time t in s curve. The impulse of the force in the
interval 0 to 1.2 is nearest to
(1) 16 Ns (2) 8 Ns (3) 7 Ns (4) 5 Ns
5. A ladder is leaned against a smooth wall and it is allowed to slip on a frictionless floor. Which figure
represents path of its centre of mass?
(1) (2)
(3) (4)
6. Figure shows the force versus displacement for a particle in motion. The increase of kinetic energy in
travelling over s 0 to 20 m will be
F in N
15
10
5
0 10 20s in m
(1) 250 J (2) 200 J (3) 150 J (4) 10 J
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7. Two balls of same mass each „m‟ are moving with same velocities v on a smooth surface as shown in
figure. If all colissions between the masses and with the wall are perfectly elastic the possible
number of collisions between the bodies and wall together is
(1) 1 (2) 2 (3) 3 (4) inifnity
8. A thin disc of mass 9M and radius R from which a disc of radius R/3 is cut. Moment of inertia of the
disc about an axis passing through O and perpendicular to the plane of disc is
2R
3
OR
(A) 240MR
9 (2)
237MR
9 (3)
29MR (4) 24MR
9. A roller coaster is designed such that riders experience “ weightlessness” as they go round the top of
a hill whose radius of curvature is 20m. The speed of the car at the top of the hill is between
(1) 15m / s and 16m / s (2) 16m / s and 17m / s
(3) 13m / s and 14 m/s (4) 14 m/s and 15 m/s
10. Given that for a gas iB isothermal bulk modulus, aB adiabatic bulk modulus , p pressure and
ratio of the specific heat at constant pressure to that at constant volume. Which of the following
relation is correct?
(1) aB p (2) iB p (3) i aB B (4) None of these
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11. Two rods of different materials having coefficients of linear expansion 1 and 2 . Young‟s
modulus 1Y and 2Y respectively are fixed between two rigid massive walls. The rods are heated
such that they undergo same increase in temperature. There is no bending of the rods. If 1
2
2
3
, the
thermal stresses developed in the two rods are equal provided 1 2Y / Y
(1) 2
3 (2) 1 (3)
3
2 (4)
4
9
12. Which of the following is true of the following P V diagram?
(1) Temperature is constant 1 2T T
(2) Temperature increases 2 1T T
(3) Temperature decreases 2 1T T
(4) Temperature first increases and then decreases
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13. An ideal gas is expanding such that 2PT constant. The co-efficient of volume expansion of the gas
is
(1) 1
T (2)
2
T (3)
3
T (4)
4
T
14. A wooden block performs SHM on a frictionless surface with frequency 0v . The block carries a
charge Q on its surface. If now a uniform electric field E is switched on as shown, then the SHM
of the block will be
(1) of the same frequency and with shifted mean position
(2) of the same frequency and with same mean position
(3) of changed frequency and with shifted mean position
(4) of changed frequency and with same mean position
15. Two gases of different densities are mixed in proportions 1V and 2V by volume. If 1v and 2v be the
velocities of sound in pure gases respectively then, the velocity of sound in mixture is(Assume
same )
(1) 1 21 2 2 2
1 2
V Vv v v
v v
(2) 1 2
1 2
v vv
V V
(3) 1 21 2 2 2
1 2
v vv v v
V V
(4) 1 2
1 2 2 2
1 1 2 1
V Vv v v
V v V v
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16. The figure below shows spherical distribution of the charge density varies as C
rr
for a r b
where C is a constant. A point charge q lies at the centre of the sphere at r 0 . Which of the
following is the condition for the electric field to have a constant magnitude in the region a r b ?
(1) C 0 (2) C q (3) 2
qC
4 a
(4)
2
qC
2 a
17. Two equal positive point charges q are held at a 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?
(1) a / 2 (2) a / 2 2 (3) a / 2 (4) 2a
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18. A battery of e.m.f V , resistors 1R and 2R , a capacitor C and switches 1S and 2S are connected in
the circuit as shown in figure below. The capacitor will get fully, charged to V volts when
(1) 1S and 2S are both open (2) 1S and 2S are both closed
(3) 1S is closed and 2S is open (4) 1S is open and 2S is closed
19. In the circuit given here, the points A,B and C are at 70 V, zero and 10 V respectively. Then
(1) currents in the paths AD, DB and DC are in the ratio of 3:2:1
(2) currents in the paths AD,DB and DC are in the ratio of 1:2:3
(3) the point D will be at a potential of 20 V
(4) the point D will be at potential of 60 V
20. In the circuit the battery is assumed to be ideal (no internal resistance) and has emf of 3.0 V. The
resistor that dissipated most power is
(1) 1R (2) 2R (3) 3R (4) 4R
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21. Circular loop of a wire and a long straight wire carry currents cI and eI respectively as shown in
figure. Assuming that these are placed in the same plane, the magnetic field will be zero at the centre
of the loop when separation H is
(1) e
c
I R
I (2) e
c
I R
I (3) c
e
I
I R
(4) e
c
I
I R
22. In the inductive circuit given in the figure, the currents rises after the switch is closed. At instant
when the currents is 15 mA, then potential difference across the inductor will be
(1) zero (2) 240 V (3) 180 V (4) 60 V
23. A luminous object is lying in front of a screen at a distance D from it. What is the maximum focal
length of a converging lens, which can be mounted between the object and the screen to cast the real
image of the object on the screen?
(1) 2D (2) D (3) D/2 (4) D/4
24. A parallel beam of white light falls on a convex lens. Images of blue, yellow and red light are formed
on other side of the lens at a distance 20 cm, 20.5 cm and 21.4 cm respectively. The dispersive power
of the material of the lens will be
(1) 619
1000 (2)
9
200 (3)
14
205 (4)
5
214
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25. A point object is placed at a distance of 20 cm from a thin plano-convex lens of focal length 15 cm.
If the plane surface is silvered. The system will act as
(1) concave mirror (2) complex mirror (3) convex mirror (4) concave lens
26. The fusion of hydrogen into helium is more likely to take place
(1) at high temperature and high pressure (2) at high temperature and low pressure
(3) at low temperature and low pressure (4) at low temperature and high pressure
27. When 228
90 Th transforms to 212
83 Bi , then the number of the emitted and particles is
respectively
(1) 8 ,7 (2) 4 ,7 (3) 4 ,4 (4) 4 ,1
28. In photoelectric emission process from a metal of work function 1.8eV , the kinetic energy of most
energetic electrons is 0.5eV . The corresponding stopping potential is
(1) 1.8eV (2) 1.3V (3) 0.5V (4) 2.3V
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29. The given plot of binding energy per nucleus bE , against the nuclear mass M; A,B,C,D,E,F
correspond to different nuclei. Consider four reactions
(i) A B C (ii) C A B (iii) D E F (iv) F D E
Where is the energy released in the which reaction is positive
(1)(i) and (iv) (2) (i) and (iii) (3) (iii) and (iv) (4) (ii) and (iii)
30. Which of the following is the graph between the frequency (v) of the incident radiations and the
stopping potential?
(1) (2)
(3) (4)
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CHEMISTRY (PART – B)
SECTION I: (SINGLE CHOICE QUESTIONS)
This section contains 30 Multiple Choice Questions. Each question has four choices (1), (2), (3)
and (4) out of which ONLY ONE is correct.
31. The amount of energy required to remove an electron from a 2Li ion from its ground state is how
many times the amount of energy required to remove the electron from a hydrogen atom fro
m its ground state
(1) 9 (2) 2 (3) 3 (4) 5
32. In an 2H ion
(1) One electron is bound to two protons
(2) Two electrons are bound to two protons
(3) Three electrons are bound to two protons
(4) Bond does not exist
33. The shape of 4 4PCl ,PCl and 5AsCl are respectively
(1) square planar, tetrahedral and see-saw
(2) tetrahedral, see-saw and trigonal bipyramidal
(3) tetrahedral, square planar and pentagonal bipyramidal
(4) trigonal bipyramidal , tetrahedral and square pyramidal
34. At constant pressure what would be the percentage decrease in the density of an ideal gas for a 10%
increase in the temperature.
(1) 10% (2) 9.1% (3) 11% (4) 12.09%
35. A cylinder with a movable piston is filled at 25 C with a gas that occupies a volume of 330.5cm . If
the maximum capacity of the cylinder is 345.8cm , what is the highest temperature to which the
cylinder can be heated at constant pressure without having the piston come out?
(1) 50 C (2) 147.5 C (3) 174.5 C (4) 120 C
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36. For the following gaseous equilibria X,Y and Z at 300 K
2 2 3X : 2SO O 2SO
5 3 2Y : PCl PCl Cl
2 2Z: 2HI H I
ratio of pK and cK in the increasing order is
(1) X Y Z (2) X Y Z (3) X Z Y (4) Z Y X
37. A weak acid HX has 5
aK 1.0 10 and its forms a salt NaX when treated with caustic soda. The
percentage hydrolysis of a 0.1M NaX solution is
(1) 1% (2) 0.01% (3) 0.001 % (4) 1%
38. 0.1 millimole of 4CdSO is present in 10 mL acid solution of 0.08NHCl . Now 2H S is passed to
precipitate all the 2Cd
ions. The pH of the solution after filtering off precipitate, boiling off 2H S
and making the solution 100 mL by adding 2H O is approximately
(1) 2 (2) 4 (3) 6 (4) 8
39. When poly atomic gas undergoes an adiabatic process, its temperature and volume are related by the
equation nTV constant, the value of n will be
(1) 1.33 (2) 0.33 (3) 2.33 (4) 1
40. The standard heat of formation values of 6SF g ,S g and F g are : 1100,275 and 80kJ 1mol
respectively. Then the average S F bond energy in 6SF
(1) 1301kJ mol (2)
1320kJ mol (3) 1309kJ mol (4)
1280kJ mol
41. A mixture contains 1 mole of volatile liquid AA P 100mmHg and 3 moles of volatile liquid
BB P 80mmHg . If solution behaves ideally, the total vapour pressure of the distillate is
(1) 85 mm Hg (2) 85.88 mm Hg (3) 90 mm Hg (4) 92 mm Hg
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42. In a galvanic cell, if salt bridge is replaced by inert platinum sheet, the cell will
(1) not work further; as positive and negative charges will accumulate on respective sides
(2) not work further; as platinum performs poorly as salt-bridge
(3) work as previous; as platinum performs will as salt-bridge
(4) produce less potential; as platinum performs poorly as salt-bridge
43. The solubility of hydroxide of alkaline earth metal increases down the group because
(1) the decrease in lattice energy is more predominant than the decrease in hydration energy
(2) the decrease in lattice energy is less predominant than the decrease in hydration energy
(3) the salts become less ionic.
(4) lattice energy increases and hydration energy decreases as we move from 2Be
to 2Ba
44. Which one of the following oxides is neutral?
(1) CO (2) 2SnO (3) ZnO (4) 2SiO
45. The true statement for the acids of phosphorus,
3 2 3 3H PO ,H PO and 3 4H PO is
(1) The order of their acidity is 3 4 3 3 3 2H PO H PO H PO
(2) All of them are reducing in nature
(3) All of them are tribasic acids
(4) The geometry of phosphorus is tetrahedral in all the three.
46. The number of S-S bonds in cyclic trimer of sulphur trioxide 3 9S O is
(1) three (2) two (3) one (4) zero
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47. Which of the given statements in not true for the following reaction?
2 2
2 3 3 24 4Cu H O 4NH Cu NH 4H O
(1) It is a ligand- substitution reaction.
(2) 3NH is a relatively strong field ligand while 2H O is a weak field ligand
(3) During the reaction, there is a change in colour from light blue to dark blue.
(4) 2
3 4Cu NH
has a tetrahedral structure and is paramagnetic.
48. The IUPAC name of the complex 4 7 2 2 2Ni C H O N formed from the reaction of
2Ni with
dimethyl glyoxime is
(1) Bis methylgloxal nickel(II) (2) Bis dimethyloxime nickelate(IV)
(3) Bis 2,3- butanedioldioximato nickel(II) (4) Bis bu tan e 2,3-dionedioximato nickel(II)
49. The actual reducing agent of haematite in blast furnace is
(1) C (2) CO (3) Al (4) 2CO
50. Forth floatation process for the concentration of ores is a practical application of
(1) Adsorption (2) Absorption (3) Coagulation (4) Sedimentation
51.
The value of „N‟ and „n‟ are
(1) 6, 6 (2) 6,4 (3) 4,4 (4) 3,3
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52. During debromination of meso-dibromobutane, the major compound formed is
(1) n- butane (2) 1 butene (3) cis 2 butene (4) trans 2 butene
53. on hydrolysis in presence of aqueous
acetone gives
(1) (K) and (L) (2) (K) only (3) (K) and (M) (4) (M) only
54. Heating a particular ether with HBr yielded a single organic product. Which of the following
conclusions may be reached?
(1) The reactant was a methyl ether (2) The reactant was a symmetrical ether
(3) The reactant was a cyclic ether (4) Both (2) and (3) may be correct.
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55. In the reaction, dil.NaOH
2HO CH CHO how many distinct products(saturated) are possible?
(1) 1 (2) 2 (3) 3 (4) 4
56.
(A) (2)
(3) (4)
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57. Consider the following reaction,
2H /H O
6 5 2 3C H NH CHCl KOH A B C
The compounds (B) and (C) are
(A) 6 5C H COOH and 3NH respectively (2) 6 5 2C H NH and HCOOH respectively
(3) 6 5 2C H NH and 2H O respectively (4) none of these
58. When aniline is treated with benzene diazonium chloride at low temperature in weakly acidic
medium, the final product obtained is
(1)
N=N
2NH
(2)
N=N 2NH
(3)
N=N NH
(4)
N=N
2NH
59. Consider following reagents
(I) 2Br water (II) Tollen‟s reagent and (III) Fehling‟s solution.
Which reagent (s) can be used to make distinction between an aldose and a ketose?
(1) (I), (II) and (III) (2) (II) and (III) (3) (I) only (4) (II) only
60. This structure of glycine (amino acid) is 3 2H NCH CO
O
(zwitter ion)
Select the correct statement of the following
(A) Glycine, as well as other amino acids are amphoteric
(B) The acidic functional group in amino acids is 3N H
(C) The basic functional group in amino acids is
(D) All the statements are correct
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MATHEMATICS (PART – C)
SECTION I: (SINGLE CHOICE QUESTIONS)
This section contains 30 Multiple Choice Questions. Each question has four choices (1), (2), (3)
and (4) out of which ONLY ONE is correct.
61. Total number of positive integral solutions of 1 2 3x x 3x 15 is equal to…..
(1) 63 (2) 64 (3) 65 (4) None of these
62. If A 1,1,1 and C 0,1 1 are given vectors, then a vectors B satisfying the equation A B C
and A.B 3 is
(1) 5 2 2
, ,3 3 3
(2) 5 2 2
, ,3 3 3
(3) 5 2 2
, ,3 3 3
(4) none of these
63. If f x 0 be a quadratic equation such that f f 0 and 23
f2 4
, then
x
f xlim
sin sin x is equal to
(1) 0 (2) (3) 2 (4) none of these
64.
2 2 2 2 2n 2
1 1 1 1lim ....
n n 1 n 2 n n 1
is
(1) 4
(2)
2
(3) does not exist (4) none of these
65. The value of 3
4
4xsin x dx
where . denotes greatest integer function
(1) 0 (2) 5
sq units4
(3)
7sq units
4
(4)
3sq units
4
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66. The system of equations a b x ay bz 0 , b c x by cz 0 ,
a b y b c z 0 has non-trivial solution, if
(1) a,b,c are in A.P. (2) a,b,c are in G.P.
(3) a,b,c are in H.P. (4) None of these
67. If z 1 z 3 8 , then the range of values of z 4 is
(1) 0,8 (2) 0,8 (3) 1,9 (4) 5,9
68. In the binomial 2
2 27 2 14exp 1 x x ......x 1 x x ...... x , the coefficient of 28x
(1) 220 (2) 222 (3) 224 (4) 226
69. How many real solutions does the system 2 2x y 25 and xy 10 have
(1) 3 (2) 1 (3) 2 (4) none of these
70. If the family of lines x a 2b y a 3b a b passes through the point for all values of a and b,
then the coordinates of the point are
(1) 2,1 (2) 2, 1 (3) 2,1 (4) None of these
71. The diagonals of a parallelogram PQRS are along the lines x 3y 4 and 6x 2y 7 . Then PQRS
must be a
(1) rectangle (2) square
(3) cyclic quadrilateral (4) rhombus
72. S and T are the foci of an ellipse and B is an end of the minor axis. If STB is an equilateral triangle,
the eccentricity of the ellipse is
(1) 1
4 (2)
1
3 (3)
1
2 (4)
2
3
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73. If t t
P 1 ,22 2
be any point on a line, then the values of t for which the point P lies between
parallel lines x 2y 1 and 2x 4y 15 may belong to the interval
(1) 4 2 5 2
,3 6
(2) 2 5
0,6
(3) 4 2 5 2
,3 6
(4) None of these
74. If 5c 3b
log , loga 5c
and a
log3b
are in AP, where a,b,c are in GP, then a,b,c, are the lengths of
sides of
(1) an isosceles triangle (2) an equilateral triangle
(3) a scalene triangle (4) None of the above
75. The integral value of k for which the inequality 2 2x 2 4k 1 x 15k 2k 7 0 holds for all
x R is
(1) 0 (2) 1 (3) 2 (4) 3
76. If 1 2 3 na ,a ,a ,....a are in HP and n
r k
r 1
f k a a
, then
1 2 na a a
, ,......,f 1 f 2 f n
are in
(1) AP (2) GP (3) HP (4) None of the above
77. General solution of 2
a Rsin x cos x min 1,a 4a 6
is
(1) nn
12 4
(2)
n2n 1
4
(3) n 1
n 14
(4)
nn 1
4 4
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78. 31 2 n
0 1 2 n 1
CC C C1 1 1 ..... 1
C C C C
is equal to
(1) n 1
n!
(2)
nn 1
n 1 !
(3)
n
n 1
n!
(4)
n
n 1
n!
79. If
3
sin x,
x 0x
f x 2, x 0
x 0sin x x
x
( where . denotes the greatest integer function) if f x is
continuous at x 0 , then is equal to
(1) 1 (2) 1 (3) 2 (4) 2
80. The set of all values of a for which the function 5a 4f x 1 x 3x log5
1 a
decreases for all
real x, is
(1) , (2) 3 21 3 21
, ,2 2
(3) 5 27
3, 2,2
(4) 3 21
4, 1,2
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81. x
2
e x 1 x ln xdx
x
is equal to
(1) x x ln xe c
x
(2) x x ln x 1
e cx
(3) x
2
x ln xe c
x
(4) x x ln x 1
e cx
82. The solution of the differential equation dy sin y x
dx sin 2y x cos y
is
(1) 2
2 xsin y x sin y c
2 (2)
22 x
sin y x sin y c2
(3) 2
2 xsin y x sin y c
2 (4)
22 x
sin y x sin y c2
83. Let CA denotes the complement of an event A. Let A,B,C be three pair wise dependent events.
Given P A / C =0.2, P B / C 0.4 and P A B / C 0.1 , then C CP A B / C is
(1) 0.5 (2) 0.6 (3) 0.8 (4) 0.4
84. If 1 2 n 11,z ,z ,....., z are the nth roots of unity, then the value of 1 2 n 1
1 1 1.......
3 z 3 z 3 z
is equal
to
(1) n 1
n
n.3 1
3 1 2
(2) n 1
n
n.31
3 1
(3) n 1
n
n.31
3 1
(4) none of these
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85. If 2 2 2a b c 2 ,and
2 2 2
2 2 2
2 2 2
1 a x 1 b x 1 c x
f x 1 a x 1 b x 1 c x
1 a x 1 b x 1 c x
then f x is a polynomial of degree
(1) 0 (2) 1 (3) 2 (4) 3
86. If f x and g x are continuous functions, then
2
1ln
2ln
xf f x f x
4dx
xg g x g x
4
is 0
(1) depend on (2) a non-zero constant
(3) zero (4) None of these
87.
3x1 1 1 1
x x x x
x
p q r slim
4
where p,q, r,s 0 is equal to
(1) pqrs (2) 3
pqrs (3) 3
2pqrs (4) 3
4pqrs
88. If
1000
m
k 1
m 1000x
x k
k limx 10
, then k is m 101
(1) 10 (2) 210 (3)
310 (4) 410
89. The line x y z
k 2 12
makes an isosceles triangle with the planes 2x y 3z 1 0 and
x 2y 3z 1 0 , then value of k is
(1) 3 (2) 2 (3) 5 (4) 0
90. If A and B are two events such that 1
P A2
and 2
P B3
, then which of the following is correct?
(1) 2
P A B3
(2) 1
P A B3
(3) Both (1) & (2) (4) Only (1)
SPACE FOR ROUGH WORK