2703 aiot paper
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Test Type : ALL INDIA OPEN TEST Test Pattern : JEE-Main
TEST DATE : 27 - 03 - 2016
TARGET : JEE (MAIN) 2016LEADER & ENTHUSIAST COURSE
Paper Code : 0000CT103115005Form Number :
CLASSROOM CONTACT PROGRAMME(Academic Session : 2015 - 2016)
H I N D I
Corporate Office : CAREER INSTITUTE, “SANKALP”, CP-6, Indra Vihar, Kota (Rajasthan)-324005
+91-744-5156100 [email protected] www.allen.ac.in
our Target is to secure Good Rank in JEE (Main) 2016
Important Instructions
Do not open this Test Booklet until you are asked to do so.
1. Immediately fill in the form number on this page of the Test Booklet
with Blue/Black Ball Point Pen. Use of pencil is strictly prohibited .
2. The candidates should not write their Form Number anywhere else
(except in the specified space) on the Test Booklet/Answer Sheet.
3. The test is of 3 hours duration.
4. The Test Booklet consists of 90 questions. The maximum marks
are 360.
5. There are three parts in the question paper A,B,C consisting of
Physics, Chemistry and Mathematics having 30 questions ineach part of equal weightage. Each question is allotted 4 (four)
marks for correct response.
6. One Fourth mark will be deducted for indicated incorrect response
of each question. No deduction from the total score will be made
if no response is indicated for an item in the Answer Sheet.
7. Use Blue/Black Ball Point Pen only for writting particulars/
marking responses on Side–1 and Side–2 of the Answer Sheet.
Use of pencil is strictly prohibited.
8. No candidate is allowed to carry any textual material, printed or
written, bits of papers, mobile phone any electronic device etc,
except the Identity Card inside the examination hall/room.
9. Rough work is to be done on the space provided for this purpose
in the Test Booklet only.
10. On completion of the test, the candidate must hand over the Answer
Sheet to the invigilator on duty in the Room/Hall. However, the
candidate are allowed to take away this Test Booklet with them.
11. Do not fold or make any stray marks on the Answer Sheet.
eg oi . u n '
b l i i rd d rc rd u [ y tc rd dg u t ,A
1. i j h k k i q f L r d k d s b l i ` " B i j v k o ' ; d f o o j . kuh y s @ dk y s ck W y ik
i s u ls r R d k y H k j s a Ai s f U ly dk i z ;k s x f cY d q y oftZ r g S a A
2. i j h k k F k h Z v i u k Q k e Z u a - ( f u/ k k Z f j r tx g d s v f r f j ‰ ) i j h@ m Ÿ k j i = i j d g h a v k S j u f y [ k s a A
3. i j h k k d h v o f / k3 V
g S A
4. b l i j h k k i q f L r d k e s a90 i z ' u g a S A v f / k d r e v a d360 g S a A
5. b l i j h k k i q f L r d k e s a r h u H k k xA, B, C g S a ] f tld s i z R ; s d H k k x
rd oK u
]l ;u oK u
, o ax . r
d s 30 i 'u
g S a v k S j lH k h i z ' u d s v a d le k u g S a A i z R ; s d i z ' u d s
lg
m Ÿ k j d s f y ,4 ( p k j)v a d f uË k k Z f j r f d ; s x ; s g S a A
6. i z R ; s d x y r m Ÿ k j d s f y , m l i z ' u d s d q y v a d d k,d p b v d
d k V k tk ; s x k A m Ÿ k j i q f L r d k e s a d k s b Z H k h m Ÿ k j u g h a e s a ls
Ω. ed v du
u g h a g k s x k A
7. m Ÿ k j i = d si B & 1
, o ai B & 2
i j o k a f N r f o o j . k , o a m Ÿ k j v a f d r d j u s g s r q d s o y
u y d y c y i b V i u
d k g h i z ; k s x d j s a A i ly d i ; x lo o t r g A
8. i j h k k F k h Z k j k i j h k k d k @ g k W y e s a i f j p ; i = d s v
i z d k j d h i k B ~ ; lk e x z h e q f Ê r ; k g L r f y f [ k r d k x t d h i f pZ e k s c k b y Q k s u ; k f d lh H k h i z d k j d s b y s D V ™ k f u d m i d j . k k s a i z d k j d h lk e x z h d k s y s tk u s ; k m i ; k s x d j u s d h v u q e f r u
9. j Q d k ; Z i j h k k i q f L r d k e s a d s o y f u/ k k Z f j r tx g i j g h d h f
10. i j h k k le k I r g k s u s i j] i j h k k F k h Z d k @ g k W y N k s M + u s ls i wv o ' ; lk S a i n s a A
i viu l b li i rd d y
g A
11. m i= d u e M ,o u g m l i v ; u' u y
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H-1/310000CT103115005
SPACE FOR ROUGH WORK / dP p d ; d y, L u
ALL INDIA OPEN TEST/JEE (Main)/27-03-2016
BEWARE OF NEGATIVE MARKING
HAVE CONTROL HAVE PATIENCE HAVE CONFIDENCE 100% SUCCESS
PART A - PHYSICS
1. If the unmodulated level peak carrier amplitudeis double of modulating signal in an AM signal,
the amplitude modulation is ________ :-
(1) 20% (2) 50%
(3) 100% (4) 200%
2. The dc output polarity from a half-wave
rectifier can be reversed by reversing :-
(1) the diode
(2) transformer's primary coil(3) transformer's secondary coil
(4) both (2) and (3)
3. The acceleration time graph of a particle is
shown in the figure. What is the velocity of
particle at t = 8 s if its initial velocity is 3 m/s ?
O 4 8 t
–1
4
a
(1) 4 m/s (2) 5 m/s (3) 6 m/s (4) 7 m/s
1. ; f n AM la d s r e s a f ' k [ k j o k g d v k ; k e ( e k s M q f y r u g h e k s M q f y r la d s r d k n q x u k g k s r k s v k ; k e e k s M ________ :-
(1) 20% (2) 50%
(3) 100% (4) 200%
2. f d lh v ºZ r j a x f n " V d k j h ls i z k I rdc f u x Z r / k z q o r k f u E u
e s a ls f d l i z f ÿ ; k k j k O ; q R ÿ f e r d h tk ld r h g S %
(1) M k ; k s M d k s O ; q R ÿ f e r d j
(2) V ™ k a lQ k W e Z j d h i z k F k f e d d q . M y h d k s O(3) V ™ k a lQ k W e Z j d h f r h ; d d q . M y h d k s O ; q R
(4) i z f ÿ ; k (2) , o a (3) n k s u k s a d s k j k
3. f d lh d . k d k R o j . k & le ; v k j s [ k f p = e s a i z n f ' k Z r
d . k d k t = 8 s i j o s x D ; k g k s x k ; f n b ld k i z k j f E H k
o s x3 m/s g S ?
O 4 8 t
–1
4
a
(1) 4 m/s (2) 5 m/s (3) 6 m/s (4) 7 m/s
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SPACE FOR ROUGH WORK / dP p d ; d y, L u
ALL INDIA OPEN TEST/JEE (Main)/27-03-2016
4. Two concentric rings each of radius R and massM are joined together such that their planes are
perpendicular to each other as shown in figure.The moment of inertia of the system about theaxis AA' is :-
(1)2MR
5
(2)23
MR 2
A
M
R
A(3)25
MR 3
(4) MR 2
5. A hollow sphere of radius R moves with initial
linear and angular velocities as shown in thefigure on a rough horizontal surface. Theangular velocity of the sphere when its linear velocity becomes zero is :-
V3VR
(1)V
R anticlockwise
(2) VR
clockwise
(3)3V
2R clockwise
(4)3V
2R anticlockwise
4. f = T ; kR rF k k Ê O ; e k uM o k y h n k s la d s U Ê h ; o y ; k s av k i l e s a b l i z d k j tk s M + k tk r k g S f d b u d s r y f p = k
, d& n w lj s d s y E c o r ~ g S A v kAA' d s lk i s k f u d k ; d k tM + R o v k ? k w . k Z g k s x k % &
(1)2MR
5
(2)23
MR 2
A
M
R
A(3)25
MR 3
(4) MR 2
5. f = T ; kR o k y s , d x f r ' k h y [ k k s [ k y s x k s y s d k i z k j f E
j s [ k h ; , o a d k s . k h ; o s x f p = e s a n ' k k Z ; k x ; k g S A [ k q j n j h k S f r t lr g i j g S A x k s y s d k j s [ k h ; o s x ' k w i j b ld k d k s . k h ; o s x g k s x k % &
V3VR
(1)V
R o k e k o r Z
(2) VR
n f k . k k o r Z
(3)3V
2R n f k . k k o r Z
(4)3V
2R o k e k o r Z
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H-3/310000CT103115005
SPACE FOR ROUGH WORK / dP p d ; d y, L u
ALL INDIA OPEN TEST/JEE (Main)/27-03-2016
6. A simple pendulum consisting of a mass M
attached to a string of length L is released from
rest at an angle . A pin is located at a distance
below the pivot point. When the pendulum
swings down, the string hits the pin as shownin the figure. The maximum angle which
string makes with the vertical after hitting the
pin is :-
L
(1)1 Lcos
cosL
(2) 1 Lcos
cosL
(3) cos –1Lcos
L
(4)
1 Lcoscos
L
7. In the figure a conducting wire of length a is
moving in a uniform and constant magnetic
field B with a constant velocity v parallel to its
length. The potential difference between the
ends P and Q is equal to :-× × × × × ×× × × × × ×
× × × × × ×P QB
xv
a
(1) 0 (2)Bav (3)1
Bav2
(4)3
Bav2
6. , d lj y y k s y d e s a Ê O ; e k uM, y E c k b ZL o k y h j L lh ls
tq M + k g S rF k k b ls f o j k e k o L F k k ls d k s . k i j N k s M + k tk r k g S
d h y d f c U n q ls n w j h u h p s , d f i u y x h g q b Z g S A
y k s y d u h p s d h v k s j v k r k g S r k s j L lh f i u ls f p = k
V d j k r h g S A f i u ls V d j k u s d s i ' p k r ~ j L lh k j k ≈ Ë o
ls c u k ; k x ; k v f / k d r e d k s . k g k s x k % &
L
(1)1 Lcos
cosL
(2) 1 Lcos
cosL
(3) cos –1Lcos
L
(4)
1 Lcoscos
L
7. i z n f ' k Z r f p = e s aa y E c k b Z o k y k , d p k y d r k j le :i
rF k k f u ; r p q E c d h ; k s =B e s a b ld h y E c k b Z d s le k U r j
f u ; r o s xv ls x f r ' k h y g S A f lj k s aP rF k kQ d s e/ ;
f oH k o k U r j g k s x k:-
× × × × × ×× × × × × ×
× × × × × ×P QB
xv
a
(1) 0 (2)Bav (3)1
Bav2
(4)3
Bav2
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SPACE FOR ROUGH WORK / dP p d ; d y, L u
ALL INDIA OPEN TEST/JEE (Main)/27-03-2016
8. In a certain region of space there exists a
constant and uniform magnetic field of
induction B. The width of the magnetic field is
a. A charged particle having charge q, is
projected perpendicular to B
and along thewidth of the field. If deflection produced by
the field perpendicular to the width is d, then
the magnitude of the momentum of the particle
is :-
×××××××
×××××××
×××××××
a
d
q
(1)
2 2d aqB
2d
(2)2
2
aqB
2d
(3)
24dqB
a d (4) 2 2a d
qB2d
9. In a certain region of space electric field is given
by ˆ ˆ ˆE 2i 3 j 4k
. The change in potential
observed by a man who moves from point (1 , 0, 5) to the po int (4, 2, 6) is.
(Electric field is in N/C and coordinates are in
meter) :-
(1) 4V (2) –4V (3)1
3 V (4)
53V
18
8. v a r f j k e s a f d lh L F k k u i j i z s j . kB o k y k , d f u ; r rF k k
le :i p q E c d h ; k s = f o |e k u g S A p q E c d h ; k s =
p k S M + k b Za g S A v k o s ' kq o k y s , d v k o s f ' k r d . k d k sB
d s
y E c o r ~ rF k k k s = d h p k S M + k b Z d s v u q f n ' k i z
tk r k g S A ; f n p k S M + k b Z d s y E c o r ~ k s = k j k m
d g k s r k s d . k d s la o s x d k i f j e k . k g k s x k % &
×××××××
×××××××
×××××××
a
d
q
(1)
2 2d aqB
2d
(2)2
2
aqB
2d
(3)
24dqB
a d (4) 2 2a d
qB2d
9. v a r f j k e s a f d lh L F k k u i j f o |q r k s =ˆ ˆ ˆE 2i 3 j 4k
k j k f n ; k tk r k g S A f c U n q(1, 0, 5) ls (4, 2, 6) r d x f r
d j j g s O ; f ‰ k j k i z s f " k r f oH k o e s a i f j o r Z( f o |q r k s = N/C e s a rF k k f u n s Z ' k k a d e h V j e s a g S) :-
(1) 4V (2) –4V (3)1
3 V (4)
53V
18
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H-5/310000CT103115005
SPACE FOR ROUGH WORK / dP p d ; d y, L u
ALL INDIA OPEN TEST/JEE (Main)/27-03-2016
10. Every iron atom in a ferromagnetic domain in
iron has a magnetic dipole moment equal to
9.27 × 10 –24 A–m2. A ferromagnetic domain in
iron has the shape of a cube of side 1 µm. The
maximum dipole moment occurs when all thedipoles are aligned. The molar mass of iron is
56g, and its specific gravity is 8. The
approximate magnetization of the domain
is :-
(1) 8.0 × 105 A/m (2) 8.0 × 108 A/m
(3) 8.0 × 1011 A/m (4) 8.0 × 1014 A/m
11. A particle is placed at the lowest point of a
smooth wire frame in the shape of a parabola,
lying in the vertical xy-plane having equation
x2 = 5y (x, y are in meter). After slight
displacement, the particle is set free. Find
angular frequency of oscillation (in rad/sec)
(take g = 10 m/s2) :-
(1) 2 rad/s (2) 4 rad/s
(3) 6 rad/s (4) 8 rad/s
12. Two particles A and B have de-Broglie's
wavelengths 30Å and 20Å, combined to forma particle C. Momentum is conserved in this
process. The possible de-Broglie's wavelength
of C is :-
(1) 10Å (2) 20Å
(3) 65Å (4) 80Å
10. y k S g s e s a y k S g p q E c d h ; i z k a r e s a i z R ; s d y k S
p q E cd h ; f/k z q o vk ? k w .k Z9.27 × 10 –24 A–m2 g k s r k g S A
y k S g s e s a , d y k S g p q E c d h ; i z k a r1 µm H k q tk o k y s ? k u d h
v k d ` f r e s a g S A tc lH k h f / k z q o la j s f [ k r g k s r s g S a f / k z q o v k ? k w . k Z i z k I r g k s r k g S A y k S g s d k e k 56g
rF k k b ld k f o f ' k " V x q :R o8 g k s r k g S A i z k a r d k y xH k
p q E c d u g k s x k % &
(1) 8.0 × 105 A/m (2) 8.0 × 108 A/m
(3) 8.0 × 1011 A/m (4) 8.0 × 1014 A/m
11. , d d . k ≈/ o k Z / k j xy- r y e s a f L F k r i j o y ;
x2
= 5y (x, y e h V j e s a g S) d h v k d ` f r o k y s , d f p d u s r k j ›s e d s f u E u r e f c U n q i j f L F k r g S A d . k d k s
f o L F k k f i r d j N k s M + f n ; k tk r k g S A n k s y u d h d k s
(rad/sec e s a) K k r d h f t, (g = 10 m/s2) :-
(1) 2 rad/s (2) 4 rad/s
(3) 6 rad/s (4) 8 rad/s
12. n k s d . k k s aA rF k kB d h M h & c z k s X y h r j a x n S / ; Z ÿ
30Å rF k k20Å g S A ; s la ; q ‰ g k s d j , d d . kC c u k r s g S a A b l i z f ÿ ; k e s a la o s x la j f k r j g r k g S AC d h la H k k f o r
M h & c z k s X y h r j a x n S / ; Z g k s x h :-
(1) 10Å (2) 20Å
(3) 65Å (4) 80Å
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SPACE FOR ROUGH WORK / dP p d ; d y, L u
ALL INDIA OPEN TEST/JEE (Main)/27-03-2016
13. In an experiment of photoelectric effect, thevariation of photoelectric current is plottedagainst potential difference across emitter andcollector plates for different intensities. On the
basis of graph choose the incorrect option :-
I1
I2
V
Photoelectriccurrent
(1) All emitted photoelectrons do not have samekinetic energy
(2) If frequency of incident light is kept
constant, the maximum kinetic energy of emitted photoelectron is independent of intensity.
(3) Maximum value of photoelectric current isindependent of intensity of radiation if itsfrequency is constant.
(4) From the graph, we can conclude radiationintensity I
1 > I
2.
14. A passenger in an aeroplane shall :-
(1) Never see a rainbow.(2) May see a primary and a secondary rainbowas concentric circles.
(3) Will see a primary and a secondary rainbowas concentric arcs.
(4) Shall never see a secondary rainbow.
13. i z d k ' k f o |q r i z H k k o i z ; k s x e s a f o f H k U u r h o z r k m R ltZ d rF k k la x z k g d I y s V k s a i j f oH k o k U r j f o |q r / k k j k d s e/ ; i f j o r Z u v k j s [ k i j n ' k k Z ; k x ; k x y r f o d Y i p q f u , % &
I1
I2
V
Photoelectriccurrent
(1) lH k h m R lf tZ r Q k s V k s b y s D V ™ k W u k s a d h u g h a g S A
(2) ; f n v k i f r r i z d k ' k d h v k o ` f Ÿ k f u ; r j [ k h tk , r k s
m R lf tZ r Q k s V k s b y s D V ™ k W u d h v f / k d r e r h o z r k i j f uH k Z j u g h a d j r h A
(3) i z d k ' k f o |q r / k k j k d k v f / k d r e e k u f o f d j . k d h r h o z r k i j f uH k Z j u g h a d j r k ] ; f n b ld h v k o ` f Ÿ k g k s A
(4) v k j s [ k d s v k / k k j i j d g k tk ld r k g S f d f o f d j . k r h o z r kI
1 > I
2 g S A
14. o k ; q ; k u e s a c S B s ; k = h d k s % &(1) dH k h H k h b U Ê / k u q " k f n [ k k b Z u g h a n s x k A(2) i z k F k f e d rF k k f r h ; d b U Ê / k u q " k la d s U Ê h
:i e s a f n [ k k b Z n s ld r s g S a A(3) i z k F k f e d rF k k f r h ; d b U Ê / k u q " k la d s U Ê h ;
:i e s a f n [ k k b Z n s x s a A(4) dH k h H k h f r h ; d b U Ê / k u q " k f n [ k k b Z u g h a
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H-7/310000CT103115005
SPACE FOR ROUGH WORK / dP p d ; d y, L u
ALL INDIA OPEN TEST/JEE (Main)/27-03-2016
15. Two identical spherical stars each having a massequal to that of the sun move in a commoncircular orbit of radius equal to the earth'sorbital radius, under their mutual gravitationalinteraction. Their time period of rotation
equals:-
(1) 2yr (2)1
2 yr (3) 2 2 yr (4) 2 yr
16. An equimolar mixture of a monoatomic and adiatomic ideal gas is suddenly compressed to1
8th of its original volume. The ratio of final
temperature to the initial temperature :-
(1) 80.53 (2) 80.5 (3) 81.53 (4) 82/3
17.
In an experiment to determine the inertial massof an object using Newton's second law,following graph is obtained between net forceon the object and the acceleration produced init. The mass of the object within error limitsis :-
1 2 3
F(N)
1
2
3
a(m/s )2
(1) 1.0 kg (2) 1 kg(3) (1.0 ± 0.1) kg (4) (1.0 ± 0.15)kg
15. lw ; Z d s le k u Ê O ; e k u o k y s n k s , d tS ls x k s y k d k
v i u s v U ; k s U ; x q :R o k d " k Z . k d s i z H k k o e s a i ` F o
f = T ; k d s c j k c j f = T ; k o k y h m H k ; f u " B o ` Ÿ k k d k j
x f r d j r s g S a A b u d s ? k w . k Z u d k v k o r Z d k y g k s x
(1) 2yr (2)1
2 yr (3) 2 2 yr (4) 2 yr
16. , d i j e k f . o d rF k k f & i j e k f . o d v k n ' k Z x S l d s
le& e k s y j f eJ . k d k s v p k u d i z k j f E H k d v k ; r u d s1
8 x q u k r d la i h f M + r f d ; k tk r k g S A v f U r e rF k k i z k r k i e k u d k v u q i k r g k s x k % &(1) 80.53 (2) 80.5 (3) 81.53 (4) 82/3
17. U ; w V u d s f r h ; f u ; e d s m i ; k s x k j k f d lh f i . M tM + R o h ; Ê O ; e k u d k s K k r d j u s lE c U / k h i z ; k s x i j y x k ; s x ; s d q y c y rF k k b le s a m R i U u R o j . k d sv k j s [ k f p = e s a n ' k k Z ; k x ; k g S A = q f V lh e k d s
d k Ê O ; e k u g S % &
1 2 3
F(N)
1
2
3
a(m/s )2
(1) 1.0 kg (2) 1 kg
(3) (1.0 ± 0.1) kg (4) (1.0 ± 0.15)kg
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0000CT103115005H-8/31
SPACE FOR ROUGH WORK / dP p d ; d y, L u
ALL INDIA OPEN TEST/JEE (Main)/27-03-2016
18. A point object O is placed at a distance of 20cm
in front of a equi-convex lens (a
g = 1.5) of
focal length 10 cm . The lens is placed on a
liquid of refractive index 2 as shown. Image
will be formed at a distance h from lens. Thevalue of h is :-
2 0 c m
O
=2
(1) 5 cm (2) 10 cm
(3) 20 cm (4) 40 cm
19. The frequency of first overtone of a closed
organ pipe of length L is f 1. A hole is made at a
distanceL
6 from the closed end so that it
becomes an open pipe. Now the frequency of
first overtone of open pipe is f 2. Then
1
2
f
f is :-
(1)4
5(2)
5
4(3)
8
5(4)
5
8
18. , d f c U n q f c E cO d k s10 cm Q k s d l n w j h o k y s le k s Ÿ k
y s a l (a
g = 1.5) d s lk e u s20 cm n w j h i j j [ k k x ; k g S A
y s a l d k s v i o r Z u k a d2 o k y s n z o i j f p = k u q lk j j [ k k x ; k
g S A i z f r f c E c y s a l l sh n w j h i j c u r k g S Ah d k e k u
g k s x k % &
2 0 c m
O
=2
(1) 5 cm (2) 10 cm
(3) 20 cm (4) 40 cm
19. y E c k b ZL o k y s c U n v k W x Z u i k b i d s i z F k e v f / k L o
v k o ` f Ÿ kf 1 g S A c U n f lj s ls
L
6 n w j h i j , d f N Ê b l i z d k j
c u k ; k tk r k g S f d ; g , d [ k q y k i k b i c u tk r k g S A
[ k q y s i k b i d s i z F k e v f / k L o j d d h v k o ` f Ÿ kf 2 g S A r c12
f
f
d k e k u g k s x k:-
(1)4
5(2)
5
4(3)
8
5(4)
5
8
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20. A transverse wave is passing through a stringshown in figure. Mass density of the string is1 kg/m3 and cross section area of string is0.01m2. Equation of wave in string is y = 2sin(20t – 10x). The hanging mass is (in kg)
['t' is in second and 'x' is in meter] :-
m
(1) 40 (2) 0.2 (3) 0.004 (4) 0.4
21. There is a set of 4 tuning forks, one with lowestfrequency vibrating at 552 Hz. By using anytwo forks at time, the beat frequencies heard
are 1, 2, 3, 5, 7, 8. The possible frequencies of other three forks are :-
(1) 553, 554 and 560 Hz
(2) 553, 555 and 560 Hz
(3) 553, 556 and 558 Hz
(4) 551, 554 and 560 Hz
22. In an experiment to determine the radius of achalk by screw gauge, the diameter is measuredand readings are d
1 = 1.002 cm, d
2 = 1.004 cm
and d3
= 1.006 cm. Select the correctalternatives:-
(1) Mean absolute error in radius is 0.0013 cm
(2) Mean absolute error in diameter is 0.0013cm
(3) Error is 0 cm(4) % age error in the measurement of diameter
is 1.3%
20. f p = e s a , d v u q i z L F k r j a x j L lh ls g k s d j x q tj j g h j L lh d k Ê O ; e k u ? k u R o1 kg/m3 rF k k j L lh d k v u q i z L F k d k V k s = Q y0.01m2 g S A j L lh e s a r j a x d h le h d j . k y = 2sin (20t – 10x) g S A y V d s g q , Ê O ; e k u d k e k(kg e s a) g S ['t' ls d . M e s a rF k k'x' e h V j e s a g S]:-
m
(1) 40 (2) 0.2 (3) 0.004 (4) 0.4
21. 4 L o f j = k s a d s le w g e s a ls U ; w u r e v k o ` f Ÿ k o k 552 Hz i j d E i U u d j j g k g S A f d U g h a H k h n k s L o
, d lk F k i z ; q ‰ d j u s i j lq u k b Z n s u s o k y h f o L i U n
1, 2, 3, 5, 7, 8 g S A ' k s " k r h u k s a L o f j = k s a d h a v k o ` f Ÿ k ; k ° g k s x h a % &(1) 553, 554 rF k k 560 Hz
(2) 553, 555 rF k k 560 Hz
(3) 553, 556 rF k k 558 Hz
(4) 551, 554 rF k k 560 Hz
22. L ÿ w x s t k j k f d lh p k s d d s V q d M + s d h f = T ; k lE c U / k h i z ; k s x e s a O ; k l d k e k i u f d ; k tk r k g S i k B ~ ; k a dd
1 = 1.002 cm, d
2 = 1.004 cm rF k k
d3 = 1.006 cm i z k I r g k s r s g S a A lg h f o d Y i p q f u , %(1) f = T ; k e s a e k / ; f u j i s k = q f V0.0013 cm g S A
(2) O ; k l e s a e k / ; f u j i s k = q f V0.0013 cm g S A
(3) = q f V0 cm g S A
(4) O ; k l d s e k i u e s a% = q f V1.3% g S A
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23. The ratio of average translational K.E. torotational K.E. of a linear polyatomic moleculeat temperature T is :-
(1) 3 (2) 5 (3)3
2(4)
7
524. Two spheres of emissive power 0.6 and 0.8 and
radii 2cm and 4 cm are heated to 27°C and
127°C and placed in room of temperature 0K.
The ratio of heat radiated per second is :-
(1) 0.059 (2) 0.044 (3) 0.079 (4) 0.831
25. Two short dipoles of dipole moment p are
placed at two corners of a square as shown in
the figure. What is the ratio of magnitudes of electric field at two points O & A :-
O
A p
p
(1) 2 (2) 2 2 (3) 1 (4) 2
26. Rate of dissipation of joule heat in resistance per unit volume is (E is elect ric field, resistivity):-
(1)E
(2)2E
(3) E2 (4) None of these
23. r k i e k uT i j , d j S f [ k d c g q i j e k f . o d v . k q d h v k S lr L F k k u k U r j . k x f r t ≈ tk Z , o a ? k w . k Z u x f r t ≈ tk Z d k v
g k s r k g S % &
(1) 3 (2) 5 (3)
3
2 (4)
7
524. n k s x k s y k s a d h m R ltZ u k e r k0.6 o 0.8 rF k k f = T ; k ÿ e ' k %
2cm o 4 cm g S A b U g s a0K r k i e k u o k y s d e j s e s a ÿ e ' k %
27°C o 127°C r d x e Z f d ; k tk r k g S A i z f r ls d . M
f o f d f j r ≈ " e k d k v u q i k r g k s x k % &(1) 0.059 (2) 0.044 (3) 0.079 (4) 0.831
25. f / k z q o v k ? k w . k Z p o k y s n k s y ? k q f / k z q o f p = k u q lk j , d
n k s d k s u k s a i j j [ k s g q , g S a A f c U n qO rF k kA i j f o |q r k s = d s
i f j e k . k k s a d k v u q i k r g k s x k :-
O
A p
p
(1) 2 (2) 2 2 (3) 1 (4) 2
26.
i z f r j k s / k i z f r b d k b Z v k ; r u e s a tw y ≈ " e k d s ‚ k l d h g k s r h g S(E f o |q r k s = , i z f r j k s / k d r k g S):-
(1)E
(2)2E
(3) E2 (4) m i j k s ‰ e a s ls d k s b Z u
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27. Three rings each having equal radius R, are
placed mutually perpendicular to each other and
each having its centre at the origin of coordinate
system. If current I is flowing through each ring
then the magnitude of the magnetic field at thecommon centre is :-
x
y
(1) 3 I2R (2) 03 I2R
(3) 0 (4) 0I3 1
2R
28. If the system is released from rest, then the
reading of spring balance is :-
1kg 2kg
(1)1
kg3
(2)2
kg3
(3) 1kg (4)4
kg3
27. i z R ; s dR f = T ; k o k y h r h u o y ; , d& n w l j s d s y E c o r ~
j [ k h g q b Z g S rF k k i z R ; s d d k d s U Ê f u n s Z ' k k a d
f c U n q i j g S A ; f n i z R ; s d o y ; l sI / k k j k i z o k f g r g k s r h g S
r k s m H k ; f u " B d s U Ê i j p q E c d h ; k s = d k i f j e k . k
x
y
(1)3 I
2R
(2) 0
3 I
2R
(3) 0 (4) 0I3 1
2R
28. i z n f ' k Z r f u d k ; d k s f o j k e k o L F k k ls N k s M + s tk
r q y k d k i k B ~ ; k a d g k s x k % &
1kg 2kg
(1)1
kg3
(2)2
kg3
(3) 1kg (4)4
kg3
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29. An open U tube contains two immiscible liquids
of densities 1 and
2 (
1 >
2) as shown in
figure. If PA, P
B, P
C and P
D refer to the pressure
at points A, B, C and D respectively then :-
A B
C D
1
2
C
(1) PA = P
B > P
C > P
D
(2) PA = P
B > P
D > P
C
(3) PA = PB > PC = PD
(4) It is not possible to predict the correct
relation between PA, P
B, P
C and P
D with
given information
30. An irregular shaped body of mass m, density is falling with a terminal speed v in a viscous
medium of density and viscosity . The
viscous drag force acting on the body has a
magnitude :-
(1) mg (2) mg 1
(3) 6v (4) mg 1
29. , d [ k q y hU u y h e s a ? k u R o1 o
2 (
1 >
2) o k y s n k s
v f eJ . k h ; Ê o H k j s g q , g S a A ; f nPA, P
B, P
C rF k kP
D
ÿ e ' k % f c U n qA, B, C o D i j n k c g k s a r k s % &
A B
C D
1
2
C
(1) PA = P
B > P
C > P
D
(2) PA = P
B > P
D > P
C
(3) PA = P
B > P
C = P
D
(4) n h x ; h tk u d k j h d s v k / k k j i jPA, P
B, P
C o P
D d s
e/ ; lg h lE c U / k K k r d j u k v la H k o g S A
30. Ê O ; e k um rF k k ? k u R o o k y h v f u ; f e r v k d ` f r d h
o L r q lh e k U r p k yv ls ? k u R o rF k k ' ; k u r k o k y s
' ; k u e k / ; e e s a f x j j g h g S A o L r q i j d k ; Z j r ' ; k u c
d k i f j e k . k g k s x k % &
(1) mg (2) mg 1
(3) 6v (4) mg 1
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PART B - CHEMISTRY
31. e k s y j p k y d R o( m ) d h b d k b Z g S-
(1) Scm3 mol –1 (2) Scm mol –1
(3) Sm mol –1 (4) Scm2 mol –1
32. H- i j e k . k q e s a tc , d b y S D V ™ k W u , d , s ls d k d
x k s y h ; u k s M d s lk F k n k s d k s . k h ; u k s M j [ k r k
, d u k s M j [ k u s o k y s d k d e s a d w n r k g S r k s m R lf
d h r j a x n S / ; Z D ; k g k s x h-
f n ; k g S %hc = 1240 eV.nm
(1) 1240 nm10.2
(2) 1240 nm1.89
(3)1240
2.55 nm (4)
1240nm
0.66
33. l g h dF k u g S-
(1) j k lk ; f u d v f / k ' k k s " k . k ] i z d ` f r e s a v u q R ÿ e . k h
(2) n z o d s ≈ i j x S l d s v f / k ' k k s " k . k d s f y ,G > 0
(3) o S |q r d . k l a p y u d s n k S j k u x k s Y M d s d k s
f o y ; u e s a i f j f k I r i z k o L F k k d S F k k s M d h v k s j x
(4) d k s y k s b M h d . k d k v k d k j1Å ls 1000Å d s c h p
i f j o f r Z r g k s r k g S
31. Units of molar conductivity ( m ) is -
(1) Scm3 mol –1 (2) Scm mol –1
(3) Sm mol –1 (4) Scm2 mol –1
32. Wavelength of photon emited when an electron in
H-atom jumps from an orbital having 2 angular
nodes with one spherical node to an orbital having
total 1 node is -
Given hc = 1240 eV.nm
(1) 1240 nm10.2
(2) 1240 nm1.89
(3)1240
2.55 nm (4)
1240nm
0.66
33. Correct statement is -
(1) Chemical adsorption is irreversible in nature
(2) G > 0 for adsorption of gas over liquid
(3) Dispersed phase in colloidal solution of gold
moves towards cathode during electrophoresis
(4) Size of colloidal particle varies between 1Å to
1000Å
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34. 1 e k s yv k n ' k Z x S l 10 bar d s f u ; r c k g ~ ; n k c d s f o :º
(5 y h V j , 300K) ls (10 y h V j , 200K) r d :ºk s " e h ;
i z l k j e s a y h x ; h g S r k s f d ; k x ; k d k ; Z c j k c j g S-
(1) – 50 J (2) –300 cal(3) – 5000 J (4) – 500 cal
35. n h x ; h v f H k f ÿ ; k d s f y ; s lk E ; o L F k k f u ; r k a d g
aA bB + cC
( u k s V : a , b rF k k c U ; w u r e v k a f d d j lle h d j . k f e r h ; x q . k k a d g S)
Time
conc. [C]
1
2
3
4
5
6
[B]
[A]
(1) 48 (2) 4 3
(3) 64 (4) 36
36. A2+(aq.)
+ 2e – A(s) ; E = 0.8 volt
B3+(aq.)
+ 3e – B(s) ; E = 0.6 volt
; f n A2+(aq.) rF k k B3+(aq.) ; q D r f o y ; u o S |q r v i ? k f V r g k s r k g S ] r k s m i j k s D r lw p u k d k m i ; k g q , o g v k ; u c r k b ; s tk s d S F k k s M i j i g y s f u k s f i r
(1) A2+(aq.)
(2) B3+(aq.)
(3) H+(aq.)
(4) OH(aq.)
34. 1 mol of an ideal gas undergoes adiabaticexpansion from (5 litre, 300K) to (10 litre, 200K)against constant external pressure of 10 bar. Work done equals to -
(1) – 50 J (2) –300 cal(3) – 5000 J (4) – 500 cal
35. Equilibrium constant for the given reactionwill be
aA bB + cC
(Note : a , b & c are minimum integralstoichiometric coefficients )
Time
conc. [C]
1
2
3
45
6
[B]
[A]
(1) 48 (2) 4 3 (3) 64 (4) 36
36. A2+(aq.)
+ 2e – A(s) ; E = 0.8 volt
B3+
(aq.) + 3e –
B(s) ; E = 0.6 voltUsing above information find the ion which will bedeposited first at cathode if solution containingA2+(aq.) & B3+(aq.) is electrolysed.
(1) A2+(aq.)
(2) B3+(aq.)
(3) H+(aq.)
(4) OH(aq.)
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37. , d v . k q d k l j y r e lw = c r k b ; s f tu e s a'A' i j e k . k q
:f U M r (truncated) v " V Q y d d s i z R ; s d d k s u s i j
m i f L F k r g S rF k k'B' i j e k . k q i z R ; s d f d u k j s d s d s U n z
m i f L F k r g S(1) AB (2) AB
2
(3) A2B
3(4) A
3B
2
38. l g h dF k u d k p ; u d h f t; s-
(1) ' k w U ; d k s f V v f H k f ÿ ; k d s f y ; s, t1/2
i z k j f E H k d lk U n z r k
i j f u H k Z j d j r k g S
(2) 1st d k s f V v f H k f ÿ ; k d s f y ; s n j] v f H k f ÿ ; k c < +
d s l k F k l k F k f u ; r j g r h g S
(3) 2nd d k s f V v f H k f ÿ ; k d s f y ; s, t1/2
i z k j f E H k d lk U n z r k
e s a o ` f º d s l k F k c < + r k g S
(4) , d 1st d k s f V v f H k f ÿ ; k ] i z k F k f e d g h g k s x h
39. f o y ; u -I (S-I) = 0.2 M HCl (aq.)
f o y ; u -II (S-II) = 0.2 M BOH (aq.) (K b= 10 –2M)
f o y ; u -III (S-III) = 1 y h V j f o y ; u - I + 1 y h V j
f o y ; u - II
f o y s ; d k s v o k " i ' k h y rF k k f o y ; u d k s v k n ' k Z e k
g q , l g h dF k u d k p ; u d h f t; s(1) i j k lj . k n k c d k ÿ e g S %S-II < S-I < S- III
(2) o k " i n k c d k ÿ e g S %S-I < S-III < S- II
(3) D oF k u k a d f c U n q d k ÿ e g SS-II < S-III < S- I
(4) f g e k a d f c U n q d k ÿ e g S S-I < S-II < S -III
37. Find the simplest formula of a molecule in which'A' atoms are present at each corner and 'B' atomsare present at each edge centre of a truncatedoctahedron
(1) AB (2) AB2
(3) A2B
3(4) A
3B
2
38. Select the correct statement -
(1) For zero order reaction, t1/2
depends on initial
conc.
(2) For 1st order reaction, rate remains constant
as reaction proceed
(3) For 2nd order reaction, t1/2
increases with
increase in initial conc.
(4) A 1st order reaction must be elementry
39. Solution-I (S-I) = 0.2 M HCl (aq.)
Solution-II (S-II) = 0.2 M BOH (aq.) (K b=10 –2M)
Solution-III (S-III) = 1 litre solution- I + 1 litre
solution- II
Considering solute to be non-volatile and solution
to be ideal, select the correct statement(1) Order of osmostic pressure is S-II < S-I<S-III
(2) Order of vapour pressure is S-I < S-III <S-II
(3) Order of boiling point is S-II < S-III <S-I
(4) Order of freezing point is S-I< S-II < S-III
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40. FeO rF k kFe0.8
O d s le k u e k s y o k y s1 y h V j f o y ; u
d k s v E y h ; e k / ; e e s a70 ml, 0.3M KMnO4 d s lk F k
m i p k f j r f d ; k x ; k g S m R i k f n rFe3+ d s f e y h e k s y g S-
(1) 126 (2) 75
(3) 30 (4) 135
41. f u E u e s a ls d k S u lk ; k S f x d , s D o k j s f t; k e s a f o g S :-(1) Hg (2) HgS
(3) (Hg + HgS) (4) m i j k s D r lH k h
42. f u E u e s a ls d k S u lk / k u k ; u] c k s j s D l e u d k i j h k . k
e u d k n s r k g S &(1) Ag+ (2) Cu+2
(3) Al+3 (4) Cd+2
43. f u E u e s a ls d k S u ls r R o NH3 f o y ; u e s a f o y s ; g k s tk r s
g S rF k k m u d s f o y ; u v i p k ; d d s :i e s a d k ; Z d j r s g S(1) Ca (2) Eu
(3) Yb (4) m i j k s D r lH k h
44. b u e s a ls d k S u ls ; k S f x d d k s g k b M ™ k s f yF k d s lk
l e k u g k b M ™ k b M d s :i e s a tk u k tk r k g S &(1) CaH
2(2) SrH
2
(3) NaH (4) KH45. 'X' x S l lM + h g q b Z e N y h tS lh x a / k j [ k r h g S A
CuSO4 f o y ; u d s lk F k f ÿ ; k d j k ; h tk r h g S r k s v o k s
d k j a x D ; k g k s r k g S &
(1) i h y k (2) H k w j k
(3) y k y (4) d k y k
40. A 1 litre solution containing equal moles of FeO
and Fe0.8
O was titrated with 70 ml 0.3M KMnO4
in acidic medium. Millimoles Fe3+ produced are
(1) 126 (2) 75
(3) 30 (4) 135
41. Which of the following compound is soluble in
aqua regia :-
(1) Hg (2) HgS
(3) (Hg + HgS) (4) All of these
42. Which of the following cation gives coloured bead
in borax bead test
(1) Ag+ (2) Cu+2
(3) Al+3 (4) Cd+2
43. Which of the following elements dissolved in NH3
solution and their solution act as reducing agent.
(1) Ca (2) Eu
(3) Yb (4) All of these
44. Which of the following compound is known ashydrolith as well as salt like hydride.
(1) CaH2
(2) SrH2
(3) NaH (4) KH
45. 'X' gas has rotten fish smell, when react with CuSO4
solution, then what is the colour of ppt.
(1) Yellow (2) Brown
(3) Red (4) Black
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46. l k s f M ; e u k b V ™ k s i z q l k b M d s d s U n z h ; i j e k . k q
D ; k g S:-
(1) sp3d2 (2) d2sp3
(3) sp3
d (4) sp3
47. f u E u e s a l s d k S u lh L i h ' k h t e s a3d –2p
i ' p c a / k u
m i f L F k r g S:-
(1) O(SiH3)
2(2) OCl
2
(3) N(SiH3)
3(4) m i j k s D r lH k h
48. f u E u e s a ls d k S u ls / k k r q v k W D lk b M d k s v k S
d k c Z u v i p ; u f o f / k k j k v i p f ; r u g h a f d ; k tk r k g S
(1) Cr 2O3 (2) Mn3O4
(3) ZnO (4) (1) o (2) n k s u k s a
49. f u E u e s a ls d k S u lh f o f / k d k i z ; k s x d s o y v L F k k ; h
d k s g V k u s d s f y , f d ; k tk r k g S:-
(1) m c k y d j (2) D y k d Z
(3) f tv k s y k b V (4) (1) o (2) n k s u k s a
50.
f u E u e s a ls d k S u lk v . k q @ L i h ' k h t le r y h ; d s lk F k / k q z o h ; g S &
(1) XeF2
(2) I3 –
(3) ICl4 – (4) ClF
3
46. What is the hybridisation of central atom of sodium
nitroprusside :-
(1) sp3d2 (2) d2sp3
(3) sp
3
d (4) sp
3
47. Which of the following specie has 3d –2p
back
bonding :-
(1) O(SiH3)
2(2) OCl
2
(3) N(SiH3)
3(4) All of these
48. Which of the following metal oxide are not reduced
commercially by carbon reduction method.
(1) Cr 2O3 (2) Mn3O4
(3) ZnO (4) Both (1) and (2)
49. Which of the following methods are used for
removal of temporary hardness only :-
(1) Boiling (2) Clark's
(3) Zeolite (4) Both (1) and (2)
50.
Which of the following molecule/specie is planar as well as polar :-
(1) XeF2
(2) I3 –
(3) ICl4 – (4) ClF
3
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51. f u E u e a s ls d k S u ls ; q X e e s a(I) d h r q y u k e s a(II) SN1
v f H k f ÿ ; k d s i z f r v f / k d f ÿ ; k ' k h y g S:
(1) ,Br
Br
(2) ,ClClO
(3) ,Br Br
(4) ,I Br
52. f u E u e s a l s d k S u l k ; k S f x d v k s t k s u h v i ? k"3- e s f F k y -6- v k W D lk s g s I V s u s y " m R i k f n r d j s x k?
(1) (2)
(3) (4)
53. f u E u ; k S f x d k s d s f y ; s ] x y r f o d Y i d k p ; u d h f t; s?
CH –NH3 2 (CH ) NH3 2 (CH ) N3 3
(a) (b) (c)
(1) x S l i z k o L F k k e s aa, b, c e s a ls(c) lo k Z f / k d k k j h ; g S(2) ty h ; i z k o L F k k e s aa, b, c e s a ls(b) lo k Z f / k d k k j h ; g S(3) lH k h ] l e k u l e tk r J s . k h d s l n L ; g S(4) d s o y(a) d k s x s f c z ; y F k s y h e k b M l a ' y s " k . k
i z k I r f d ; k tk l d r k g S
51. Among the following pairs, in which pair (II) ismore reactive than (I) for SN1 reaction :
(1) ,Br
Br
(2) ,ClClO
(3) ,Br Br
(4) ,I Br
52. Which of the following compound on ozonolysiswill produce "3-methyl-6-oxoheptanal" ?
(1) (2)
(3) (4)
53. For the following compounds, choose the incorrectoption ?
CH –NH3 2 (CH ) NH3 2 (CH ) N3 3
(a) (b) (c)
(1) (c) is most basic among a, b, c in gas phase(2) (b) is most basic among a, b, c in aq. phase(3) All are member of same homologous series(4) Only (a) can be obtained by gabriel
phthalimide synthesis
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54. v . k q lw =C9H
10O d k , d d k c Z f u d ; k S f x d2,4-DNP
O ; q R i U u c u k r k g S ] V k W y s U lv f H k d e Z d d k s v
g S rF k k d s f u tk j k s v f H k f ÿ ; k n s r k g S r h o z v k
i j ; s 1,3- M k b Z d k c k s Z f D lf y d v E y n s r k g S ] r k s ; k :
(1)
CHO
CH –CH2 3
(2)
CH3
CH –CHO2
(3)CH –CH2 3
CHO
(4)CH3
C–CH3
O
55. C H NO6 5 2
Fe/HCl (P) HNO2 (Q)
273 K H
O 2
(R)
b o
i l
m R i k n(R) g S :
(1) (2)
OH
(3)
NH2
(4)
N Cl2
+ –
54. An organic compound with molecular formula
C9H
10O forms 2,4-DNP derivative, reduces
tollen's reagent & undergo cannizzaro reaction. On
vigrous oxidation it gives 1,3-dicarboxylic acid,
then compound is :
(1)
CHO
CH –CH2 3
(2)
CH3
CH –CHO2
(3)
CH –CH2 3
CHO
(4)
CH3
C–CH3
O
55. C H NO6 5 2
Fe/HCl (P) HNO2 (Q)
273 K H
O 2
(R)
b o
i l
Product (R) is :
(1) (2)
OH
(3)
NH2
(4)
N Cl2
+ –
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56.OsO4 (P)
CrO3
Acetone (Q)
m R i k n(P) rF k k (Q) ÿ e ' k % g S:
(1)
OH
OH
CH3
O
OH
(2)
OH
OH
CH3
O
(3)
CH3
OH
OH
O
OH
(4) CH3
OH
OH
OH
O
56.OsO4 (P)
CrO3
Acetone (Q)
Product (P) & (Q) respectively is :
(1)
OH
OH
CH3
O
OH
(2)
OH
OH
CH3
O
(3)
CH3
OH
OH
O
OH
(4) CH3
OH
OH
OH
O
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57. f u E u e s a l s d k S u l h v f H k f ÿ ; k d s d k c Z f u d m R
u k b V ™ k s tu i j e k . k q m i f L F k r u g h a g S?
(1)
COOH
CH3
H CH3
N H , H3
+
(2)
COOH
NH3
(3)COOH
NH2
(4) NH2
O
Br 2KOH
58. x y r f o d Y i d k p ; u d h f t; s ?
NH2
NaNO2
HCl (P) Cu/HBr (Q)
(1) m R i k n (Q), c z k s e k s c s a th u g S(2) (Q) d k f u e k Z . k ] ls . M e s ; j v f H k f ÿ ; k d s u k e
tk u k tk r k g S
(3) m R i k n(P), c s a th u M k b Z , s tk s f u ; e D y k s j k b M
(4) b u e s a l s d k s b Z u g h a
57. Which of the following reaction organic productdoes not contain nitrogen atom ?
(1)
COOH
CH3
H CH3
N H , H3
+
(2)
COOH
NH3
(3)COOH
NH2
(4) NH2
OBr 2
KOH
58. Choose the incorrect option ?
NH2
NaNO2
HCl (P) Cu/HBr (Q)
(1) Product (Q) is bromobenzene
(2) Formation of (Q) is known as sandmayer
reaction
(3) Product (P) is benzene diazonium chloride
(4) None of these
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59. f u E u e s a l s d k S u l k ; k S f x d T ; k f e r h ; d s l k F k
i z dk f ’k d lek o;ork i z nf ’k Z r dj s xk?
(1) 3- e s f F k y i s U V -1- b Z u
(2) 3- e s f F k y g s D l -3- b Z u
(3) 4- e s f F k y g s D l -2- b Z u
(4) 4- e s f F k y i s U V -2- b Z u
60. l g h f o d Y i d k p ; u d h f t; s ?
(1) i k W y h F k h u ] , d J ` a [ k y k o/ k Z d c g q y d g S
(2) lk c q u e s a , s U V h ls I V h d x q . k y k u s d s f y ; s c k
f e y k ; k tk r k g S
(3) f le s f V M h u d k i z ; k s x i z f rv E y(antacid) d s :i
e s a f d ; k tk r k g S
(4) m i j k s D r lH k h
59. Which of the following compound will show
geometrical as well as optical isomerism ?
(1) 3-methyl pent-1-ene
(2) 3-methyl hex-3-ene
(3) 4-methyl hex-2-ene
(4) 4-methyl pent-2-ene
60. Choose the correct option ?
(1) Polythene is a chain growth polymer
(2) Bithional is added to soaps to impart
antiseptic properties
(3) Cimetidine is used as antacid
(4) All of these
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PART C - MATHEMATICS
61. If ƒ(x) and g(x) are functions such that ƒ(x)
approaches to infinity as x and
xlim ƒ x 5g x 10 , then
x
ƒ x 5g x
lim 10g x 5ƒ x
is
equal to-
(1) 10 (2)1
10(3) –1 (4)
2
3
62. The dimensions of a rectangle are continuously
changing. The width increases at rate of
3 inch/sec. while the length decreases at rate of
2 inch/sec. At one instant if the each side of rectangle
is 20 inch, then the rate of change of area after 3
seconds is-
(1) 16 inch2/sec (2) –16 inch2/sec
(3) 32 inch2/sec (4) –32 inch2/sec
63. Let 2 3x x x
x 1 ...2 4 8
(where x [–1,1]), then the value of
1
0
x dx
e
is
equal to-
(1) 1 (2) 2 (3) 3 (4) 4
64. Let ƒ(x) = min(4x + 1, x + 2, –2x + 4), x R,
then the maximum value of ƒ(x) is -
(1)1
3(2)
1
2(3)
2
3(4)
8
3
61. ; f n Q y u ƒ(x) rF k kg(x) b l i z d k j g S f dx i j ƒ(x), v u U r d h v k s j v x z l j g S rF k k
xlim ƒ x 5g x 10 g k s ] r k s x
ƒ x 5g x
lim 10g x 5ƒ x
c j k c j g k s x k &
(1) 10 (2)1
10(3) –1 (4)
2
3
62. , d v k ; r d h T ; k f e f r f u j a r j i f j o f r Z r g k s r h g S A b ld p k S M + k b Z e s a3 inch/sec d h n j ls o ` f º g k s r h g S tc f d b ld h y E c k b Z e s a2 inch/sec d h n j ls d e h g k s r h g S A ; f n f d l h , d k . k i j v k ; r d h i z R ; s d H k q tk d h y E c k b Z20 inch g S ] r k s3 ls d . M i ' p k r b ld s k s = Q y e s a i f j o r Z u d h n j g k s x h-
(1) 16 inch2/sec (2) –16 inch2/sec
(3) 32 inch2/sec (4) –32 inch2/sec
63. e k u k 2 3x x x
x 1 ...2 4 8
( tg k °x [–1,1]) g k s ] r k s
1
0
x dx
e
d k e k u g k s x k &
(1) 1 (2) 2 (3) 3 (4) 4
64. e k u kƒ(x) = U ; w u r e(4x + 1, x + 2, –2x + 4),
x R g k s ] r k sƒ(x) d k v f / k d r e e k u g k s x k &
(1)1
3(2)
1
2(3)
2
3(4)
8
3
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65. Let A = [aij] be a 3 × 3 invertible matrix. If
determinant value of matrix A is 3, then the value
of det((adjAT)T) + det.((adj A –1) –1) (where det(B)
denotes determinant value of matrix B)-
(1) 3 (2) 6 (3) 9 (4) 1866. Area of triangle whose vertices are (a,a2), (b,b2),
(c,c2) is1
2 and area of another triangle whose
vertices are (p,p2), (q,q2) and (r,r 2) is 4, then the
value of
2 2 2
2 2 2
2 2 2
1 ap 1 bp 1 cp
1 aq 1 bq 1 cq
1 ar 1 br 1 cr
is-
(1) 2 (2) 4 (3) 8 (4) 16
67. Let
2
2
4 sec 1 0
A 0 3tan 1
0 1 2
and
2
2
cot 2 0
B 1 3cosec 1
1 1 2
, then minimum
value of tr.(AB) is (where tr(A) denotes trace of
square matrix A)-
(1) 12 (2) 20
(3) 32 (4) 64
65. e k u kA = [aij], , d 3 × 3 d k O ; q R ÿ e . k h ; v k O ; w g g S
; f n v k O ; w gA d k lk j f . k d e k u3 g S ] r k sdet((adjAT)T) + det.((adj A –1) –1) d k e k u g k s x k ( tg k °det(B), v k O ; w gB d s lk j f . k d d k s n ' k k Z r k g S)-
(1) 3 (2) 6 (3) 9 (4) 18
66. ' k h " k Z(a,a2), (b,b2), (c,c2) o k y s f =H k q t d k k s = Q y1
2
rF k k ' k h " k Z(p,p2), (q,q2) rF k k(r,r 2) o k y s v U ; f =H k q t d k
k s = Q y4 g k s ] r k s
2 2 2
2 2 2
2 2 2
1 ap 1 bp 1 cp
1 aq 1 bq 1 cq
1 ar 1 br 1 cr
d k e k u g k s x k &(1) 2 (2) 4 (3) 8 (4) 16
67. e k u k
2
2
4sec 1 0
A 0 3tan 1
0 1 2
rF k k
2
2
cot 2 0
B 1 3cosec 1
1 1 2
g k s ] r k str.(AB) d k
U ; w u r e e k u g k s x k( tg k ° tr(A), o x Z v k O ; w gA d s v u q j s [ k d k s n ' k k Z r k g S)-
(1) 12 (2) 20
(3) 32 (4) 64
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68. Let a be a positive real number and
a a a
a a an
n 1 n 2 .... n nlim 15
1 2 ... n
,
then the value of a is-(1) 1 (2) 2 (3) 3 (4) 4
69. Let x > 0 and y > 0, then the maximum value of
2
2 2
5x 12y
x y
is-
(1) 25 (2) 144 (3) 169 (4) 256
70. Consider the polynomials
2P x x 2 x 2x 2
2Q x x 2 x 2x 2
2 8R x x 2 x 16 ,
then the coefficient of x4 in P(x). Q(x). R(x) is-
(1) 0 (2) 2 (3) 2 (4) 4
71. A biased coin has2
3 probability of landing heads.
If the coin is flipped 50 times, then the probability
that the number of heads is zero or even is-
(1)
50 50
50
3 2
2.3
(2)
50
50
3 1
2.3
(3)
50
50
3 1
2.3
(4)
50 50
50
3 2
2.3
68. e k u k a , d / k u k R e d o k L r f o d l a [ ; k rF k k
a a a
a a an
n 1 n 2 .... n nlim 15
1 2 ... n
g k s ]
r k sa d k e k u g k s x k &(1) 1 (2) 2 (3) 3 (4) 4
69. e k u kx > 0 rF k ky > 0 g k s ] r k s
2
2 2
5x 12y
x y
d k
v f / k d r e e k u g k s x k &
(1) 25 (2) 144 (3) 169 (4) 256
70. e k u k c g q i n
2P x x 2 x 2x 2
2Q x x 2 x 2x 2
2 8R x x 2 x 16
g k s ] r k sP(x). Q(x). R(x) d s i z lk j e s ax4 d k x q . k k a d g k s x k &
(1) 0 (2) 2 (3) 2 (4) 4
71. , d i k i k r h f lD d s d s f p Ÿ k o k j f x j u s d h i z k f ; d r k2
3
g S ; f n f lD d s d k s50 c k j m N k y k tk r k g S ] r k s i z k I r f d h d q y l[ a ; k ] ' k w U ; ; k le la [ ; k e s a i z k I r g k s u s i z k f ; d r k g k s x h &
(1)
50 50
50
3 2
2.3
(2)
50
50
3 1
2.3
(3)
50
50
3 1
2.3
(4)
50 50
50
3 2
2.3
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72. Consider the system of equations
2 3 4 5
1 2 3 4 5x x x x x 5 and
x1 + 2x
2 + 3x
3 + 4x
4 + 5x
5 = 15
where x1,x
2,x
3,x
4,x
5 are positive real numbers, then
the number of (x1,x
2,x
3,x
4,x
5) is-
(1) 0 (2) 1 (3) 2 (4) 3
73. The differential equation of family of lines which
passes through (1,2) is-
(1) dy
y x 1 2dx
(2) dyy x 1 2dx
(3) dy
y x 1 2dx
(4) dy
y x 1 2dx
74. Perimeter of the locus represented by
z iargz i 4
(where i 1 ) is equal to-
(1)3
2
(2)
3
2
(3)2
(4) None of these
72. e k u k le h d j . k f u d k ;
2 3 4 5
1 2 3 4 5x x x x x 5 rF k k
x1 + 2x
2 + 3x
3 + 4x
4 + 5x
5 = 15
tg k °x1,x
2,x
3,x
4,x
5 / k u k R e d o k L r f o d la [ ; k ; s a g k s ] r
(x1,x
2,x
3,x
4,x
5) d h d q y la [ ; k g k s x h &
(1) 0 (2) 1 (3) 2 (4) 3
73. f c U n q(1,2) ls x q tj u s o k y s j s [ k k f u d k ; k s a d k v o le h d j . k g k s x k -
(1) dy
y x 1 2dx
(2) dyy x 1 2dx
(3) dy
y x 1 2dx
(4) dy
y x 1 2dx
74.z i
argz i 4
k j k i z n f ' k Z r f c U n q iF k d k i f j e k i g
( tg k ° i 1 ) -
(1)3
2
(2)
3
2
(3)2
(4) b u e s a ls d k s b Z u g h a
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75. If 0 < < < <2
, then the equation
(x – sin) (x – sin) + (x – sin) (x – sin)
+ (x – sin) (x – sin) = 0, has-
(1) real and unequal roots
(2) non-real roots
(3) real and equal roots
(4) real and unequal roots greater than 2.
76. Let P1 and P
2 be two fixed points in xy-plane.
A line L1 = 0 passes through P
1 intersects y-axis
at B and the line L2 = 0 passes through P
2 and
intersects x-axis at A. If L1 = 0 and L
2 = 0 are
perpendicular then the locus of mid-point of
AB is-
(1) Straight line (2) Circle
(3) Ellipse (4) Parabola
77. If ˆˆ ˆa, b,c are unit vectors, then the number of
integers in the range of the expression
2 2 2ˆ ˆˆ ˆ ˆ ˆ2a 3b 2b 3c 2c 3a is-
(1) 51 (2) 53 (3) 55 (4) 57
78. The complete set of real values of such that
point P(, sin) lies inside the triangle formed by
lines x – 2y + 2 = 0, x + y = 0 and x – y – = 0 is-
(1) ,3 2
(2) 0, ,6 3 2
(3)2
0, ,2 3
(4) (0,)
75. ; f n 0 < < < <2
g k s ] r k s le h d j . k
(x – sin) (x – sin) + (x – sin) (x – sin)
+ (x – sin) (x – sin) = 0 d s &
(1) o k L r f o d rF k k v le k u e w y g k s x s a A(2) v o k L r f o d e w y g k s x s a A(3) o k L r f o d rF k k le k u e w y g k s x s a A(4) 2 ls c M + s o k L r f o d rF k k v le k u e w y g k s x s a A
76. e k u kP1 rF k kP
2 , xy- le r y e s a n k s v p j f c U n q g S A f c U
P1 ls x q tj u s o k y h , d j s [ k kL
1 = 0, y- v k d k s f c U n qB
i j d k V r h g S rF k k f c U n qP2 ls x q tj u s o k y h j s [ k kL
2 = 0,
x- v k d k s f c U n qA i j d k V r h g S A ; f nL1 = 0 rF k k
L2 = 0 y E c o r ~ g k s ] r k sAB d s e/ ; f c U n q d k f c U n q iF k
g k s x k &(1) lj y j s [ k k (2) o ` Ÿ k (3) n h ? k Z o ` Ÿ k (4) i j o y ;
77. ; f n ˆˆ ˆa,b,c b d k b Z l f n ' k g k s ] r k s O ; a t2 2 2ˆ ˆˆ ˆ ˆ ˆ2a 3b 2b 3c 2c 3a d s i f j l j e s a
i w . k k ± d k s a d h la [ ; k g k s x h -
(1) 51 (2) 53 (3) 55 (4) 57
78. d s o k L r f o d e k u k s a d k i w . k ± le q P p ; b l i z d k j f c U n qP(, sin), j s [ k k v k s ax – 2y + 2 = 0, x + y = 0
rF k kx – y – = 0 k j k f u f e Z r f =H k q t d s v U n j d h v k f L F k r g S &
(1) ,3 2
(2) 0, ,6 3 2
(3)2
0, ,2 3
(4) (0,)
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ALL INDIA OPEN TEST/JEE (Main)/27-03-2016
79. The variable plane (2 + 1)x + (3 – )y + z = 4,
( R) always contains the line :
(1)x y z 4
0 0 1
(2)
x y z
1 2 3
(3)x y z 4
1 2 7
(4) None of these
80. Let ˆ ˆ ˆ ˆˆ ˆa ti 3j 2tk, b i 2 j 2k
and
ˆ ˆ ˆc 3i tj k
, then the value of the integral
2
1
a. b c dt
equals-
(1) 0 (2) 6 (3) –2 (4) 4
81. Let ƒ(x) be a continuous function such that
3
3
x dx 0
and 3
0
x dx 3 , then the area
bounded by y = ƒ(x), x-axis, x = –3 and x = 3 is
equal to -
(1) 1 (2) 3
(3) 6 (4) cannot be evaluated
82. In a set of 2n observations, half of them are equal
to '' and the remaining half are equal to '-'.
If the standard deviation of all the observations is
2, then || is equal to-
(1) 2 (2) 2
(3) 2 2 (4) 4
79. p j le r y (2 + 1)x + (3 – )y + z = 4, ( R)
ln S o f u E u j s [ k k d k s j [ k r k g S &
(1)x y z 4
0 0 1
(2)
x y z
1 2 3
(3)x y z 4
1 2 7
(4) b u e s a ls d k s b Z u g h a
80. e k u k ˆ ˆ ˆ ˆˆ ˆa ti 3j 2tk, b i 2 j 2k
rF k k
ˆ ˆ ˆc 3i tj k
g k s ] r k s 2
1
a. b c dt
d k e k u
g k s x k -
(1) 0 (2) 6 (3) –2 (4) 4
81. e k u k ƒ(x) , d l a r r ~ Q y u b l i z d k j g S f d
3
3
x dx 0
rF k k 3
0
x dx 3 g k s ] r k sy = ƒ(x),
x- v k ]x = –3 rF k kx = 3 k j k i f j c º k s = Q y g k s x k -
(1) 1 (2) 3
(3) 6 (4) g y u g h a f d ; k tk ld r k A
82. 2n i z s k . k k s a d s le q P p ; e s a ] v k / k s i z s k . k'' d s c j k c j rF k k
' k s " k v k / k s i z s k . k'-' d s c j k c j g S A ; f n lH k h i z s k . k k s a
e k u d f o p y u2 g k s ] r k s|| c j k c j g k s x k &
(1) 2 (2) 2
(3) 2 2 (4) 4
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83. Let A(z1), B(z
2), C(z
3) are three points on Argand
plane such that |z1| = |z
2| = |z
3| = 4. The image of
2 3
1
z zP
z
about the line BC is-
(1) z1 + z
2 + z
3(2) z
1 – z
2 – z
3
(3) 2z1 + z
3(4) None of these
84. AB is a vertical pole resting at the end A on the
level ground. P is a point on the level ground such
that AP = 3AB. If C is the mid point of AB and
CB subtends an angle at P, then the value of
tan is-
(1)18
19(2)
3
19(3)
1
6(4)
1
3
85. Consider at three dimensional figure represented
by xyz2 = 2, then its minimum distance from origin
is-
(1) 2 (2) 4 (3) 6 (4) 8
86. x
2e sec2x 1 4 tan 2x dx is equals-
(1) 4ex/2 sec2x + C (2) 2ex/2 sec2x + C
(3) ex/2 sec 2x + C (4)x /21
e sec2x C2
(where C is constant of integration)
83. e k u kA(z1), B(z
2), C(z
3) v k x Z . M le r y i j r h u f c U n q
b l i z d k j g S f d|z1| = |z
2| = |z
3| = 4 g S A f c U n q
2 3
1
z zP
z
d k j s [ k kBC d s lk i s k i z f r f c E c g k s x k &
(1) z1 + z
2 + z
3(2) z
1 – z
2 – z
3
(3) 2z1 + z
3(4) b u e s a ls d k s b Z u g h a
84. AB , d m / o k Z / k j [ k E H k k g S ] tk s / k j k r y i j f c U n q A i j
f o j k e o L F k k e s a [ k M + k g q v k g S A / k j k r y i j , d fP b l
i z d k j g S f dAP = 3AB g S A ; f nC, AB d k e/ ; f c U n q
g S rF k k f c U n qP, CB i j d k s . k v U r f j r d j r k g S ] r k s
tan d k e k u g k s x k &
(1)18
19(2)
3
19(3)
1
6(4)
1
3
85. e k u k r h u T ; k f e r h ; v k j s [ kxyz2 = 2 k j k i z n f ' k Z r g S ] r k s
e w y f c U n q ls b ld h U ; w u r e n w j h g k s x h -
(1) 2 (2) 4 (3) 6 (4) 8
86.
x
2e sec 2x 1 4 tan 2x dx c j k c j g k s x k &
(1) 4ex/2 sec2x + C (2) 2ex/2 sec2x + C
(3) ex/2 sec 2x + C (4)x / 21
e sec2x C2
( tg k ° C le k d y u v p j g S )
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87. A relation R 1 is defined on the set R of real numbers
as follows : (x,y) R 1 x3 = x2y , then relation
R 1is-
(1) only symmetric relation
(2) only transitive relation
(3) only reflexive relation
(4) reflexive and transitive relation
88.1 11 5 1 5
tan cos cot cos4 2 7 4 2 7
is equal to-
(1)5
7(2)
10
7(3)
14
5(4)
7
5
89. The sum of the solutions in x (0,4) of the
equationx x 2 x
7sin sin sin 13 3 3
is-
(1) 6 (2) 4
(3) 2 (4) None of these
90. The contrapositive of ' If Kapil is rich then he is
honest' is-
(1) If Kapil is not rich then he is dishonest
(2) If Kapil is dishonest then he is not rich
(3) Kapil is not rich or he is dishonest
(4) Kapil is dishonest and not rich
87. , d la c a / k R 1 o k L r f o d la [ ; k v k s a d s le q P p ;R e s a
(x,y) R 1 x3 = x2y k j k i f jH k k f " k r g S ] r k s la
R 1 ln S o g k s x k -
(1) d s o y le f e r la c a / k
(2) d s o y la ÿ k e d la c a / k (3) d s o y L o r q Y ; la c a / k
(4) L o r q Y ; la c a / k , o a la ÿ k e d la c a / k
88.1 11 5 1 5
tan cos cot cos4 2 7 4 2 7
c j k c j g k s x k &
(1)5
7
(2)10
7
(3)14
5
(4)7
5
89. v U r j k y x (0,4) e s a l e h d j . k
x x 2 x7sin sin sin 1
3 3 3
d s g y k s a d k
; k s x Q y g k s x k &
(1) 6 (2) 4
(3) 2 (4) b u e s a ls d k s b Z u g h a
90. ; f n d f i y / k u o k u g k s r k s o g b Z e k u n k j H k h g k s
i z f r i f j o r h Z(contrapositive) g k s x k -
(1) ; f n d f i y / k u o k u u g h a g k s r k s o g b Z e k u n k j u g h
(2) ; f n d f i y b Z e k u n k j u g h a g k s r k s o g / k u o k u u g h a
(3) d f i y / k u o k u u g h a g S ; k o g b Z e k u n k j u g h a g S
(4) d f i y b Z e k u n k j u g h a g S v k S j o g / k u o k u u g h a
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SPACE FOR ROUGH WORK / Q d ; d y; txg