NRT INDIA
(Code I015/JEE/01)
COACHING INSTITUTE
IIT-JEE-2015
Paper Code: I015/JEE/01
Time : 3.00 Hrs
Unit Test-1
Sub :PCM
Answer Sheet Code: ……
Max. Marks :360
Date:……………………
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1.
2.
Attempt all questions .
There are 45 questions each subject (PCBZ). . Each question carry +4 & −1 marks.
3.
4.
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corresponding answer on OMR sheet provided separately.
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5.
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First of all fulfill the formalities in answer sheet and question paper properly before commencement.
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1.
(Code I015/JEE/01)
2
The vector sum of two forces is perpendicular
(a) BA sin θ
to their vector differences. In that case, the
(b)
BA2 cos θ
(c)
BA2 sinθ cos θ
forces
(a)
are equal to each other in magnitude
(b)
are not equal to each other in
(d) Zero
magnitude
6.
2.
(c)
cannot be predicted
(d)
are equal to each other
If A and B are non-zero vectors which obey
the relation A + B = A − B , then the angle
between them is :
A truck travelling due north at 20 ms
−1
(a)
turns
00
(c) 900
west and travels with same speed. What is
(b) 600
(d) 1200
the change in velocity?
(a)
(b)
40 ms
(c) 10 ms
(d)
7.
20 ms−1 south –west
−1
−1
A car travels 6 km towards north at an angle
of 450 to the east and then travels distance of 4
south west
km towards north at an angle 1350 to east. How
north west
far is the point from starting point? What angle
1
40 ms− north-west
does the straight line joining its initial and
final position makes with the east?
3.
50 km and tan−1 (5)
Two forces P and Q have a resultant
(a)
perpendicular to P. The angle between the
(b) 10 km and tan−1( 5 )
forces is :
−1
(a)
tan (−P/Q)
(b)
tan−1 (P/Q)
(c)
sin−1 (P/Q)
(d)
Cos−1 (−P/Q)
8.
(c)
52 km and tan−1 (5)
(d)
52 km and tan−1 ( 5 )
An object moves at a constant speed along a
circular path in a horizontal XY plane, with the
center at the origin,. When the object is at x=
4.
If A × B = 3A. B, , then the value of A × B is
(a)
(b)
A2 + B 2 +
object’s acceleration when it is y= 2m?
AB 1/2
3
(a)
A+B
−(8m/s2)j
(b) (8m/s2)j
2
2
2
2
(c) (A +B + 3 AB)
(d) (A +B +AB)
5.
−2m, its velocity is –(4m/s)j. What is the
1/2
(c) −(4m/s2)j
1/2
(d) (4m/s2)j
If the angle between the vectors A and B is θ,
then value of the product B × A . A is equal to
9.
The motion of a particle along a straight line is
described by equation x=8+12t−t3 where x is in
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meter and t in second. The retardation of the
(b)
particle when its velocity becomes zero is
(c) 4 times the original
(a)
24 ms
−2
(b) zero
(c) 6 ms−2
10. A particle
(d)
(d)
12 ms−2
has initial velocity (2+3)
and
order of :
(a) 1011 kg m−3
of
velocity after 10 seconds will be :
9 2units
(b) 5 2units
(c)
5 units
(d)
8 times the original
16. Density of matter inside atomic nuclei is of the
acceleration (0.3+0.2). The magnitude
(a)
1/2 times the original
9 units
(c)
1017 kg m−3
(b) 1014kg m−3
(d)
1020 kg m−3
17. The universal gravitational constant G is of the
order of :
11. Which of the following is the unit of latent heat?
(a)
10−8 Nm2 Kg−2
(a)
J
(b)
J Kg mol−1
(b) 10−10 Nm2 Kg−2
(c)
J kg−1
(d)
J Kg−1 mol−1
(c)
10−12 Nm2 Kg−2
(d) 10−14 Nm2 Kg−2
12. The unit of force as well as distance are
doubled. How many times will the unit of
18. The order of Avogadro’ s number is
kinetic energy be ?
1
2
(b) 2
(c) 4
(d) 8
(a)
1022
(b) 1023
(c) 1024
(d) 1025
(a)
19. The angle 10 54’ equal to :
(a) 2.91×10−4 radian
13. Unit of Stefan’s constant is :
(a)
watt m2K4
(b) watt m2/K4
(b) 3.32×10−2 radian
(c)
watt /m2K
(d)
watt /m2K4
(c) 1.21× 10−6 radian
(d)
None of these
14. The unit of permittivity of free space , ∈0, is :
(a)
newton meter2/coulomb2
(b)
coulomb2/newton meter2
20.
The cgs unit of viscosity is poise (F) and the
SI unit of viscosity is poiseuille (PI). Which of
(c) coulomb2/(newton meter)2
the following relations is correct?
(d) coulomb/newton meter
(a)
P=PI
(b)
10P=PI
(c)
P= 10PI
(d)
None of these
15. If the unit of force and length are doubled, the
unit of energy will be
(a) 1/4 times the original
21. A man is throwing balls in air. He throws next
ball when previous one is at highest point. If
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the throws each ball after 2 seconds, then
26. A particle is thrown vertically upwards. Its
height to which ball rises is (Take g= 10 m/s2)
velocity at half of the height is 10 m/s, then
(a)
the maximum height attained by it is (g= 10
10 m
(b) 20 m
(c) 30 m
(d) 15m
m/s2)
22. The average velocity of a body moving with
uniform acceleration after travelling a distance
(a)
8m
(c) 10 m
(b) 20 m
(d) 16 m
of 3.06 m is 0.34 ms−1. If the change in velocity
of the body is 0.18 ms−1 during this time, its
uniform accelerations is ;
27. If a body loses half of its velocity
on
penetrating 3 cm in a wooden block, then how
(a)
0.01 ms−2
(b) 0.02 ms−2
much will it penetrate more before coming to
(c)
0.03 ms−2
(d) 0.04 ms−2
rest?
23. A man throws a ball vertically upward and it
(a) 1 cm
(b) 2cm
(c) 3 cm
(d) 4 cm
rises through 20 m and return to his hands.
What was the initial velocity (u) of the ball and
28. A body dropped from a height ‘h’ with an initial
for how much time (T) it remained in the air?
speed zero reaches the ground with a velocity
(a) u= 10 m/s, T= 2s
of 3 km/hour. Another body of the same mass
(b) u=10 m/s, T=4s
was dropped from the same height ‘h’ with an
initial speed 4 km/hour , will reach the ground
(c) u=20 m/s, T= 2s
with a velocity of :
(d) u= 20 m/s, T= 4s
(a)
24. A stone is dropped from rest from the top of a
3km/hour
(c) 5km/hour
(b) 4km/hour
(d) 12 km/hour
tower 19.6 m high. The distance travelled
during the last second of its fall is : (Given g=
other in magnitude , is perpendicular to the
9.8 m/s2)
(a)
9.8 m
(c) 4.9 m
29. The resultant of two forces, one double the
(b)
smaller of the two forces. The angle between
14.7 m
the two forces is :
(d) 19.6 m
(a)
2
25. If for a particle position x ∝ t then
1200
(c) 900
(b) 600
(d) 1500
(a) velocity is constant
(b)
acceleration is constant
(c)
acceleration is variable
(d)
None of these
30. A body released from
a great height
freely towards the earth. Another
falls
body is
released from the same height exactly one
second later. The separation between the two
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bodies two seconds after the release of the
(a) 0.52
second body is (g= 9.8 ms−2)
(b) 2.5
(a)
(b) 19.6 m
(c) 0.25
(d) 4.9 m
(d) 0.50
24.5 m
(c) 9.8 m
31.
limx→0
tan [−π2 ]x 2 −x 2 tan [−π2 ]
sin 2 x
equals where [ ]
37.
1−cos 2x sin 5x
x 2 sin 3x
limx‒0
denotes the greatest integer function
(a) 10/3
(a) 0
(b) 3/10
(b) 1
(c) 6/5
(c) tan 10 − 10
(d) 5/6
(d) ∞
38. limx→0
32.
If
un =
1
3 .5
+
1
5 .7
+ ⋯…..+
1
2n+1 2n+3
then
limn→∞ un =
33.
(a) 1
(b)
0
(c) 1/6
(d)
∞
39.
limn→∞ 4n 31/n − 1 =
(a) 0
(b)
1
(c) ∞
(d)
none of these
40.
34.
=
If [x] denotes the greatest integer less than or
equal to x, then the value of limx→1 1 − x +
x−1+[1−x] is
(a) 0
sin x+log 1−x
x2
(a) 0
(b)
‒½
(c) ½
(d)
not defined
limx→0
sin −1 x−tan −1 x
x2
(c) ‒ 1
(d)
none of these
=
(a) ‒ 1
(b)
0
(c) 1
(d)
none of these
The value of
x 3 +2x 2 +x+1
limx→1 𝑥 2 +2𝑥+3
1−cos (x −1)
𝑥−1 2
(a) e
(b)
e1/2
(c) 1
(d)
none of these
(b) 1
41.
is
Let f(x) =limn→∞
x 2n −1
,
x 2n +1
is
then
(a) f(x) = 1, for x > 1
35.
36.
limx→∞
2x
0
(b) f(x) is not defined for any value of x
2
x e x dx
e
4x 2
equals
(c) f(x) = ‒1, for x = 1
(a) 0
(b)
∞
(c) 2
(d)
½
limx→0
x
0
sin 3 x.cos
x4
x dx
(d) None of these
42.
=
1
limx→∞ 1 + a+bx
c+dx
=( where a, b, c, d > 0)
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a/b
(b)
e
(c) ec/b
(d)
ed/b
(a) e
b/c
49.
If f(x)=x3 sgn x, then
(a) f is derivable at x=0
43.
limx→0
1
6
sin x−x+ x 3
x5
(b) f is continuous but not derivable at x=0
=
(c) LHD at x=0 is 1
(a) 1/60
(d) None of these
(b) 1/120
(c) 1/30
1+cos 4x
x2
(d) 1/180
50.
x<0
x=0
a
If f(x)=
x
16+ 4−4
44.
45.
limx→0 1co sec
2x
+ 2cosec
2x
+ ⋯ + ncosec
2
2 x sin x
x>0
is continuous at x=0, the value of a is :
=
(a) 0
(b)
∞
(a) 8
(b)
−8
(c) n
(d)
none of these
(c) 4
(d)
None of these
If a>b then f(x)=
x−a
b−x
If f(x) =
2
,g
x−3
x =
x−3
x+4
2(2x+1)
,
x 2 +x−12
and h(x) =
then
51.
limx→3 f x + g x + h(x) is
(a) ‒ 2
(b)
‒1
(c) ‒ 2/7
(d)
0
is continuous on
(a) (b, a)
(b) [b, a]
(c) [b, a)
(d) (b, a]
1
46.
sin hx 2
limx→ 𝑥 x
=
(a) e−1/6
(b)
e1/6
(c) e
(d)
e−1
52.
If f(x)=
a+x 2 sin a+x −a 2 sin a
x
, x≠0
Is continuous at x=0 then f(0)
(a) a2 cos a +a sin a
47.
limx→∞
(a)
x+cos α
𝑥+sin 𝛼
cos t
(c) 1
48.
(b) a2 cos a+2a sin a
=
(c) 2a2 cos a +a sin a
(b)
∞
(d)
none of these
If f(x)= log10 x , then at x=1
(d) None of these
53.
(a) f(x) is continuous and f’ (1+)= log10 e
If f (x)=
x− x
x
2
x≠0
x=0
(a) f(x) is continuous at x=0
+
(b) f(x) is continuous and f’(1 ) =loge10
(c) f(x) is continuous and f’(1−) = loge10
(b) f(x) is discontinuous at x=0
(c) limx→0 f(x)=2
(d) None of these
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(d) None of these
58.
If f(x)=
x
1
x≠0 and f(0)=0then at x=0
1+e x
(a) f is continuous
54.
The function
(b) f is discontinuous
F(x)= max { (1−x), (1+x), 2},
(c) f is left continuous only
x∈ (−∞, ∞) is
(d) f is right continuous only
(a) continuous at all points
(b) differentiable at all points
59.
If f(x)= [ x sin πx], then f(x) is :
(c) Continuous at all points except at x=1 and
x=−1, where it is discontinuous
(a) continuous at x=0
(d) none of these
(b) differentiable at x=1
(c) Both a and b
55.
(d) None of these
Let f(x)= x and g(x)= x 3 , then
(a) f(x) and g(x) both are continuous at x=0
(b) f(x) and g(x) both are differentiable at x=0
(c) f(x) is differentiable but g(x) is not
differentiable at x=0
(d) f(x) and g(x) both are not differentiable at
x=0
56.
1
60.
Let f(x)= x + x
x . Then for all x
(a) f is continuous
(b) f’ is differentiable for same x
(c) f’ is continuous
(d) f” is continuous
2
The function f(x)=x − e 2x −1 , x≠0 is continuous
at x=0. Then
OH O
(a) f(0)=1
61. The IUPAC name of
(b) f(x) is not differentiable at x=0
(c) f’(0)=
1
3
4-hydroxy-2-pentanone
(c) 2-oxo-4-pentanol
(d)
sin a+1 x+sin x
x
If f(x)=
(a) 2-hydroxy-4-pentanone
(b)
(d) None of these
57.
is :
c
1
1
(x+bx 2 )2 −x 2
3
x<0
x=0
x>0
bx 2
is continuous at x=0 then c=
(a) −3/2
(b)
1/2
(c) a
(d)
b
2-keto-2-pentanol
62. The IUPAC name of CH3CH2OCH(CH3)2 is :
(a)
isopropoxy ethane
(b)
2-methoxy butane
(c) 1- methyl-1-methoxy ethane
(d)
2-ethoxy propane
63. The IUPC name of H3C −CH−CH2−CH−CH2Cl
C2H5
OH
(a) 1-chloro-4-methylhexan-2-ol
(b) 1-chloro-4-methylhexan -2-al
(c) 1-chlroor-4-ethylpentan-2-ol
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(d)
(Code I015/JEE/01)
1-chloro-2-hydroxy-4-methylhexane
(d) none of these
64. The IUPAC name of CH3−CH=C−CH2CH3
69. The IUPAC name of the following is :
7
CH2 CH2CH3
(a) 3-prophylhex-2-en
(b)
6
5
4
3
2
1
CH3CH=CH−CH2−CH−CH2COOH
NH2
3-propylhex-3-ene
(a) 3- amino hept-5 enoic acid
(c) 4-ethylhex-4-ene
(b) 5-amino hex-2-ene-carboxylic acid
(d) 3-ethylhex-2-ene
(c) 3-amino-δ-heptenoic acid
65. The IUPAC nomenclature of (CH3)3 C−CH=C(CH3)2
is
70. The IUPAC name of CH3−C≡CCH(CH3)2 is :
(a) 4-methylpent-2-yne
(a) 2, 4, 4-trimethyl pent-3-ene
(b) 4,4’-dimethylpent-2-yne
(b) 2,4,4,-trimethyl pent-2-ene
(c) 2,2,4-trimethyl pent-3-ene
(c) methyl isopropyl acetylene
(d) 2,2,4-trimethyl pent-2-ene
(d) 2-methylpent-4-yne
O
C2H5−O
66. The IUPAC name of
71. The IUPAC name of
C=O is :
OH
is
(a) prop-2-enoic acid
CH3−CH
(b) but-1-enoic acid
CH3
(a) ethoxy methanone
(c) but-3-enoic acid
(b)
ethyl-2-methyl propanoate
(d) pent-4-enoic acid
(c)
ethoxypropanone
(d)
2-methyl ethoxy propanone
72. The IUPAC name of the compound shown
below is :
Cl
67. The correct IUPAC name of the compound
Br
CH3
(a) 2-bromo-6-chlorocyclohex-1-ene
CH3CH2 − C = CH − CH − CH2 − CH3
6
7
6
9
(b)
10
CH3 CH2−CH−CH2−CH2−CH2−CH3 is
(a) 5, 6-diethyl-3-methyl-dec-4-ene
6-bromo-2-chlorocyclohexene
(c) 3-bromo-1-chlorocylohexene
(d)
1-bromo-3-chlororcylohexene
(b) 5,6-diethyl-8-methyl-dec-6-ene
(c)
6-butyl-5-ethyl-3-methyl-oct-4-ene
73. How many structures are possible for following
formula C6H14
(d) 2,4,5-triethyl-3-nonene
O
(a) 3
(b) 4
(c) 5
(d) 6
C2H5 − C
68. The IUPAC name of the compound
is
O
CH3−C
O
(a) Propionic acetic anhydride
74. How many 20 amines are possible for following
formula C6H15N
(a) 12
(b) 16
(c) 15
(d) 24
(b) ethanoic propanoic anhydride
(c) aceto ethanoate
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75. How many Ald. and Ketones are possible for
following formula C6H12O. (only structures)
(a) 8 8
(d) 3
81. How many positional isomers all possible for
following formula C4H8Cl2[only having Butane
as a parent chain]
(b) 8 6
(c) 16 18
(d)
(c) 1
16 16
76. Which Isomeric Relation is present in following
molecules
CH3−CH2−CH2−COOH
& CH3 − CH − CH3
COOH
(a) Chain isomerism
(b)
Position Isomerism
(c)
Functional group. Isomerism
(d)
Geometrical Isomerism
(a) 3
(b) 4
(c) 5
(d) 6
82. How many easters are possible for following
formula C5H10O2 (Only structures).
(a)
5
(b) 3
(c) 9
(d) 6
83. What is degree of unsaturation for given
molecules
C10H20N2Br2Cl2, C17H27NBr2Cl2, C10H10Cl10
77. How many total alcohol & ethers are possible
(structure only) for following formula : C6H14O
(a) 0 3 6
(b) 0 3 1
(c) 2 4 6
(d) 2 4 4
(a) 17 15
84. The presence of unsaturation (olefinic or
acetylinic bond) in an organic compound can
be tested with
(b) 16 12
(c) 16 16
(d) 16 8
(a)
Schiff’s reagent
(b) Tollen’s reagent
78. What is degree of unsaturation for following
formula :
CN
COOH
CN
(a) 8 8
(b) 8 7
(c) 2 7
(d) 8 6
(c)
Fehling’s solution
(d)
Baeyer’s reagent
85. Which of following compound will give Iodop
test positive
(a) CH3OH
(b)
CH3−CH2−C−H
O
79. What isomeric relation is in following compound
CH3
CH3−CH2−CH2−CH2−OH & CH3−C−CH3
(c) CH3−C−CH2−C−CH3
O
(d)
O
CH3CH2OH
OH
(a) Only Position isomerism
86. Which of the following compound will give
carbyl Amine test positive
(b)
Only chain isomerism
(c)
Chain and position both
(a) CH3CH2NH2
(b) CH3CH2NHCH3
(d)
None of these
(c) CH3−N− CH3
(d) All
CH3
80. How many structure are possible having
benzene ring only C7H14.
(a) 0
(b) 2
87. Which of the following test will give fastest
Lucas test with (HCl+ZnCl2)
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NRT INDIA
(Code I015/JEE/01)
(a) CH3OH
(b)
CH3CH2OH
OH
OH
(c) CH3−C−CH3
(d)
CH3
88. Which of the following compound will produce
white ppt with (AgNO3+NH4OH)
(a) CH4
(b) C2H4
(c) C2H2
(d) CH3−C≡C−CH3
89. Which of following compound will give test of
unsaturation as well as Iodopharm test
(a) CH3−C−CH2−CH=CH2
O
O
(b) CH3−CH2−C−CH2−CH=CH2
O
(c)
CH= CH2
O
(d)
O
90. How many Ring structures are possible for
C6H12
(a) 8
(b) 10
(c) 12
(d) 14
NRT India , 14/32, RLB Road Near Munshi Pulia, Indira Nagar, Lucknow. Call: 0522-2714802, 9415905513, 8090510938
Branches : Indira Nagar, Gomti Nagar, Hazratganj
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