1. No category

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PHYSICS
1.
2.
3.
4.
5.
Two bulbs have the ratings 40 W, 250 V , and 20 W -110 V. The ratio of their resistances is
(A) 1 : 2
(B) 1 : 1
(C) 2 : 1
(D) 1 : 4
In the circuit shown below the 10 Ohm resistor develops 10 cal/s due to the current flowing
through it . the heat developed per second in the 9 ohm resistor is
(A) 4 Cal
(B) 16 Cal
(C) 8 Cal
(D) 32 Cal
If R 1 and R 2 are respectively the filament resistances of a 200 W and a 100 W bulb
designed to operate on the same voltage, then
(A) R1  2R 2
(B) R 2  2R1
(C) R1  4R 2
(D) R 2  4R1
You are given a resistance coil and a battery. In which of the following cases is largest
amount of heat generated ?
(A) When the coil is connected to the battery directly.
(B) When the coil is divided into two equal parts and both the parts are connected to the
battery in parallel.
(C) When the coil is divided into four equal parts and all the four parts are connected to the
battery in parallel
(D) When only half the coil is connected to the battery
Two bulbs which consume powers P1 and P2 are connected across same source. The
power consumed by the combination if they are connected in series is
(A) P1  P2
(B) P1P2
(C)
6.
P1P2
P1  P2
(D)
2P1P2
P1  P2
Two identical heaters produce heat H1 in time t when connected in parallel across the main
supply. They produce heat H 2 in time t when connected in series. Then H1 / H 2 is
7.
(A) 1/ 4
(B) 4
(C) 1/ 2
(D) 2
When a battery sends current through a resistance R 1 and for time t, the heat produced in
the resistance is Q. When the same battery sends current through another resistance R 2 for
time t, the heat produced in R 2 is again Q. The internal resistance of the battery is
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8.
9.
10.
11.
12.
13.
14.
15.
16.
(A)
R1  R 2
2
(C)
R1R 2
R1  R 2
2
R1R 2
(D)
2
(B)
A constant voltage is applied between the two ends of a uniform metallic wire. Some heat is
developed in it. The heat developed is doubled if
(A) both the length and radius of the wire are halved
(B) both the length and radius of the wire are doubled
(C) the radius of the wire is doubled
(D) the length of the wire is doubled
If the current in an electric bulb drops by 1% , the power decreases by
(A) 1%
(B) 2%
(C) 4%
(D) 0.5 %
An 800 W, 220 V kettle and three 100 W , 220 V bulb are connected in parallel across 220 V
source. The current drawn from the source is
(A) 0.15 A
(B) 5.0 A
(C) 5.5 A
(D) 6.9 A
Water boils in an electric kettle in 15 minutes. If the length of the heating coil is reduced to
2/3 of its initial value, then the same amount of water will boil in
(A) 15 Min
(B) 12 Min
(C) 10 Min
(D) 8 Min
What is immaterial for an electric fuse wire ?
(A) its specific resistance
(B) its radius
(C) its length
(D) current flowing through it
The thermo-emf of a thermo-couple is 40 V per degree. The smallest temperature
difference that can be detected with this couple and a galvanometer of 100  resistance
capable of measuring the minimum current of 1A is .
(A) 10 C
(B) 1.50 C
(C) 20 C
(D) 2.50 C
Which is independent of the temperature of the cold junction
(A) inversion temperature
(B) neutral temperature
(C) both inversion and neutral temperatures
(D) neither inversion nor neutral temperature.
The amount of energy absorbed or evolved at a junction when a current of 1 ampere flows
through it for 1 second is called
(A) Seeback coefficient
(B) Thomson coefficient
(C) Peltier coefficient
(D) None of these
1
2
The emf developed in a thermocouple is given by V  T  T 2 , where T is the
temperature of the hot junction, the cold junction being at 00 C . The thermo electric power of
this couple is
(A)   T
(C)  / 
17.

T
2
(D) 2 / 
(B)  
One junction of a thermocouple is at 00 C and the other is at T 0C . The thermo-emf (in volts)
is given by V  20 106 T  0.02 106 T2 . The maximum value of V is
(A) 5mV
(B) 1mV
(C) 10mV
(D) Zero
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18.
The cold junction of a thermocouple is at 00 C and the thermo-emf (in volts) as a function of
 1 
6 2
 10 t . The neutral
40
 
the temperature t of the hot junction is given by V  10 106 t  
temperature and the maximum value of the emf are
(A) 2000 C,2mV
(B) 4000 C,2mV
19.
20.
(C) 1000 C,1mV
(D) 2000 C,1mV
The chemical equivalents of copper and silver are 32 and 108 respectively. When copper
and silver voltmeters are connected in series and electric current is passed through them for
some time, 1.6 g of copper is deposited. The amount of silver deposited is
(A) 0.47 g
(B) 5.4 g
(C) 1.6 g
(D) 2.7 g
If N is the Avogardro’s number and e is the electronic charge , tehn the Faraday constant F
is equal to
(A) Ne
(B) N 2e
(C) Ne2
21.
22.
23.
24.
25.
26.
27.
(D)
1
Ne
In a copper voltmeter, the mass deposited in 30 s in m grams . If the current-time graph is as
shown in the figure, the electrochemical equivalent of copper, in g/C, is
(A) 0.1 m
(B) 0.6 m
(C) m/2
(D) m
A copper voltameter has a resistance of 1 . It is connected is series with a 2 V battery and
a resistor of 2 . The mass of Cu deposited in 1 hour is ( ece of Cu = 0.00033 g/C)
(A) 0.2 g
(B) 0.4 g
(C) 0.6 g
(D) 0.8 g
For a given temperature difference, which of the following pairs will generate maximum
thermo-emf ?
(A) antimony-bismuth
(B) Silver-gold
(C) iron-copper
(D) lead-nickle
Which of the following statements is correct ?
(A) Both Peltier and Joule effects are reversible
(B) Both Peltier and Joule effects are irreversible
(C) Joule effect is reversible, whereas Peltier effect is irreversible
(D) Joule effect is irreversible, whereas Peltier effect is reversible
A thermocouple is made from copper and iron. At the hot junction, current
(A) flows from copper towards iron
(B) flows from iron towards copper
(C) flow decreases
(D) flow increases
If a wire of resistance 20 is covered with ice and a voltage of 210 V is applied across the
wire, then the rate of melting of ice is
(A) 0.97 gm/s
(B) 2 gm/s
(C) 6.7 gm/s
(D) None of these
A battery of e.m.f 10 V and internal resistance 0.5 is connected across a variable
resistance R. The value of R for which the power delivered in it is maximum is given by
(A) 0.2
(B) 0.25
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28.
(C) 1.0
(D) 0.5
When 2 equal resistances are connected in parallel to the poles of a cell of negligible internal
resistance , the power developed is P, when the same resistances are connected in series
across the same cell, the power developed is
(A) P
(C)
29.
30.
31.
32.
(B)
P
4
(D) 4P
As the temperature of hot junction increases , the thermo-emf
(A) always increases
(B) always decreases
(C) may increases or decrease
(D) always remains constant
Two ends of a conductor are at different temperatures. The electromotive force generated
between two ends is
(A) Seebeck electromotive force (emf)
(B) Pletier electromotive force (emf)
(C) Thormson electromotive force (emf)
(D) None of the above
A electron is moving in a circle of radius r in a uniform magnetic field B. Suddenly the field is
reduced to B/2. The radius of the circle now becomes
(A) r / 2
(B) r / 4
(C) 2r
(D) 4r
Two particles X and Y having equal charge, after being accelerated through the same
potential diffence, enter a region of uniform magnetic field and describe circular paths of radii
R 1 and R 2 respectively. The ratio of the mass of X to that of Y is
(A)  R1 / R 2 
1/ 2
(C)  R1 / R 2 
33.
34.
35.
36.
1
4
(C) 2
38.
2
(B) R 2 / R1
(D) R1 / R 2
An electric current is flowing in a long straight wire. The magnetic field due to this current at
a distance of 5 cm from the wire is 10 gauss. The magnetic field at a distance of 10 cm from
the wire is
(A)2.5 gauss
(B) 5 gauss
(C) 20 gauss
(D) 40 gauss
The current sensitivity of a moving coil galvanometer independent of
(A) the number of turns in the coil
(B) moment of inertia of the coil
(C) strength of the magnetic field
(D) torsional constant of the suspension fibre
Two concentric coils carry the same current in opposite directions. He diameter of the inner
coil is half that of the outer coil. If the magnetic field produced by the outer coil at the
common centre is 1 tesla, the net field at the centre is
(A) 1 T
(B) 2T
(C) 3 T
(D) 4T
A circular loop has radius R and a current I flows through it. Another circular loop has radius
2R and a current 2 I flows through it. Ratio of the magnetic fields at their centres is
(A)
37.
P
2
(B) 1
(D) 4
The path executed by a charged particle whose motion is perpendicular to a magnetic field is
(A) straight line
(B) curcular
(C) elliptic
(D) parabolic
Magnetic field inside a solenoid is
(A) directly proportional to current
(B) inversely proportional to current
(C) directly proportional to its length
(D) inversely proportional to the total number of turns
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39.
40.
A current of 0.1 A circulates around a coil of 100 turns and having a radius equal to 5 cm.
The magnetic field set up at the centre of the coil is
(A) 4105 T
(B) 8105 T ’
(C) 4 105 T
(D) 2 105 T
A charge q coulomb is circulating in an orbit of radius r metres making n revolutions per
second. The magnetic field produced at the centre of the orbit , in N/Am , is
2q
107
nr
2nq
(C)
107
r
(A)
41.
42.
Two parallel long straight conductors are placed at right angles to a metre scale at the 2 cm
and 6 cm marks. They carry currents I and 3 I respectively in the same direction. The
resultant magnetic field due to them is zero
(A) at the 3 cm mark
(B) at the 4 cm mark
(C) at the 5 cm mark
(D) nowhere
Two long straight wires , carrying currents I1 and I 2 are placed perpendicular to each other.
The line of shortest distance between them, PQ has length r. The magnitude of the magnetic
field at the centre O of PQ is
0
 I0  I 2 
r
1/ 2

(C) 0 I12  I 22
r
(A)

43.
44.

0
 I0  I 2 
r

(D) 0 I12  I 22
2r
(B)


1/ 2
A proton and an  - particle enter a magnetic field normally. If the force experienced by the
proton is double of that experienced by the  -particle, the ratio of their speeds is
(A) 0.5
(B) 1
(C) 2
(D) 4
A metal rod of mass 10 g and length 10 cm is placed on a smooth 600 incline. A uniform
magnetic field B is applied in the region vertically downwards. If a current of 3 A is passed
through the rod then the value of B for which the rod remains stationary on the inclined plane
is
(A) 3 T
(C)
45.
2q
107
r
2rn
(D)
107
q
(B)
3T
1
T
3
1
(D)
T
3
(B)
A charged particle having kinetic energy E enters normally a region of uniform magnetic field
between two planes P1 and P2 as shown in the figure. If the particle just misses hitting the
plate P2 , then the magnetic field B in the region between the plates is
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(A)
(C)
46.
47.
48.
50.
mE
2qd
(B)
2mE
qd
(D)
2mE
qd
The time period of oscillation of a freely suspended magnet is 4 s. If it is broken in length into
two equal parts and one part is suspended in the same way, its time period will be
(A) 4 s
(B) 2s
(C) 0.5 s
(D) 0.25 s
A compass needle of magnetic moment 60A  m2 , pointing geographic north at a place
where the horizontal component of earth’s magnetic field is 40Wb / m2 experiences a
torque if 1.2 103 N  m . The declination of the place is
(A) 150
(B) 300
(C) 450
(D) None of the above
A magnetic needle lying parallel to a magnetic field requires W units of work to turn it
through 600 . The torque required to maintain the needle in this position is
(A)
49.
mE
2qd
3W
3
W
2
(D) 2W
(B)
(C) W
All the magnetic materials lose their magnetic properties when
(A) dipped in water
(B) dipped in oil
(C) broght near a piece of iron
(D) strongly heated
Two small magnets, each of magnetic moment 10A  m2 , are placed in end-on position 0.1
m apart from their centres. The force acting between them is
(A) 0.6 107 N
(B) 0.06 107 N
(C) 0.6N
(D) 0.06N
CHEMISTRY
51.
52.
53.
Which one of the following will be most basic ?
(A) Aniline
(B) p-Methoxyaniline
(C) p-Nitroaniline
(D) Benzylamine
Which of the following reagent can be used to convert benzenediazonium chloride into
benzene ?
(A) CH3OH
(B) H3PO2 / H2O
(C) Br2  H2O
(D) LiAlH 4
Benzenediazoium chloride on reaction with phenol in weakly basic medium gives
(A) Diphenyl ether
(B) p-Hydroxybenzene
(C) Chlorobenzene
(D) Benzene
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CH 3
54.
(CH3CO)2O
H+/H2O
Br2/CH3COOH
A
B
X, the product ‘X’
is
NH 2
(A)
CH 3
(B)
CH3
Br
Br
(C)
NH 2
CH 3
(D)
NH2
CH 3
CO CH 3
CO CH 3
NH 2
55.
NH 2
The major product (70% to 80%) of the reaction between m-dinitrobenzene with NH 4HS is
(A)
NO 2
NO 2
(C)
NO 2
(B)
NO 2
HS
NH 2
NH 2
(D)
NO 2
NH 2
HS
56.
The Product ‘D’ of the reaction
KCN
H / H2O
NH3

CH3Cl 
 A 
 B 
 C 
 D is
(A) CH3CH2 NH2
(B) CH3CN
(C) HCONH2
(D) CH3CONH 2
57.
The reaction of chloroform with alcoholic KOH and p-toluidine forms
(A)
(B)
H3C
CN
H3C
NHCHCl 2
(C)
58.
H3 C
N2Cl
H3C
NC
(D)
‘Z’ in the following sequence of reactions is
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C 6 H6
HNO3/H2SO4
Zn/HCl
W
NaNO2
X
Y
HCl
59.
60.
H2O/H3PO2
Z
(A)
COOH
(B)
(C)
OH
(D)
Cl
Aniline is reacted with bromine water and the resulting product is treated with an aqeous
solution of sodium nitrite in presence of dilute HCl. The compound so formed is converted
into tetrafluoroborate which is subsequently heated dry. The final product is
(A) p-Bromofluorobenzene
(B) p-Bromoaniline
(C) 2,4,6- tribromofluorobenzene
(D) 1,3,5-Tribromobenzene
Which of the following sequence of reactions will give m-bromo aniline ?
(A)
1. Br2/FeBr3
H2/Pt
2. HNO3/H2SO4
(B)
COOH
(C)
Br2
(1) SOCl2
Br2
FeCl3
(2) NH3
NaOH
1.HNO3/H2SO4
Br2/H2O
2. Sn+HCl
(D)
+
N2 Cl
-
CuBr/HBr
61.
Which of the following reagents will be useful to distinguish between
H3C
NH 2 and
CH 2NH 2
?
(A) Dilute HCl
(B) C6H5SO2Cl and OH / H 2O
(C) HONO then  -naphthol
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(D)
62.
AgNO3 in H 2O
Which of the following is the strongest base ?
NH 2
(A)
(C)
NH 2
(B)
(D)
NH
NO 2
NH
63.
Which of the following gives propylamine upon hydrolysis ?
(A) CH3CH2C  N
(B)
 CH3CH2CH2 2 NH
(C)
O
CH 3
(D)
C
NH CH 2 CH 2 CH 3
CH3CH2  CH  NH
CH3Br
64.
CH 2CN
In the reaction
CH 3
(A)
CH
(C)
65.
66.
NaNH2,NH3-80 °C
the products obtained are
(B)
C
CH 2 NH 2
N
(D) None
CH 2 OH
Which of the following statement is correct ?
(A) Ammonia is more basic than methylamine
(B) Methyl amine is more basic than ammonia
(C) Dimethylamine is less basic than methylamine
(D) Dimthylamine is less basic than trimethylamine
The product (C) of the following series of reactions is
NH 2
Cl
NaNO2,HCl
H2O, 0°C
(A)
O
C
CH 3
Cl
(1) CH3MgBr
CuCN
(B)
(A)
(B)
COOCH3
Cl
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(2) H2O,H+
(C)
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(C)
OH
CH 3
CH
CH 2 CN
(D)
Cl
67.
Cl
Which of the following is the strongest base ?
(A)
(B)
NHCH 3
NH 2
CH 3
(C)
(D)
NH 2
68.
CH 2NH 2
Formation of polyethylene from calcium carbide takes place as follows
CaC2  2H2O 
 Ca  OH 2  C2H2
C2H2  H2 
 C2 H 4
nC2H4 
  CH2  CH2  n
69.
70.
The amount of polyethylene obtained from 64 kg of CaC2 is
(A)7 kg
(B) 14 kg
(C) 21 kg
(D) 28 kg
Violet colour is obtained when dilute CuSO4 is added in alkaline solution of protein. This
test is known as
(A) Biuret
(B) Xanthoproteic test
(C) Hopkins–cole
(D) Millon’s test
Which one of the following monomers gives the polymer neoprene on polymerization ?
(A)
CCl2  CCl2
Cl
(B)
CH2
71.
72.
(C)
CF2  CF2
Plexiglas (PMMA) is a polymer of
(A) Acrylic acid
(C) Methyl methacrylate
(D)
C
CH
CH2
CH2  CHCl
(B) Methyl acrylate
(D) Acrylonitrile
Which compound/set of compounds is used in the manufacture of nylon-66 ?
(A)
HOOC  CH2 4 COOH  H2 N  CH 2 6 NH 2
(B)
(C)
CH2  CH2
(D)
CH2  CH  C  CH   CH2
HOOC
COOH
+ HOCH  CH OH
2
2
73.
74.
Polymer obtained by condensation polymerization is
(A)Polythene
(B) Teflon
(C) Phenol-formaldehyde
(D) Nitrile rubber
Natural rubber is a polymer of
(A) Butadiene
(B) Ethylene
(C) Styrene
(D) Isoprene
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75.
76.
77.
78.
79.
80.
81.
82.
83.
84.
85.
86.
87.
88.
89.
Glucose molecule reacts with X number of molecules of phenylhydrazene to yield osazone.
The value of X is
(A) Three
(B) Two
(C) One
(D) Four
Which of the following does not reduce Benedict’s solution ?
(A) Glucose
(B) Fructose
(C) Sucrose
(D) Aldehyde
Hydrolysis of sucrose gives
(A) Two molecules of glucose
(B) Two molecules of fructose
(C) One molecule each of glucose and fructose
(D) One molecule each of glucose and manose
The term invert sugar refers to an equimolar mixture of
(A) D-glucose and D-galactose
(B) D-glucose and D-fructose
(C) D-glucose and D-mannose
(D) D-glucose and D-ribose
Cellulose is a polymer of
(A) glucose
(B) fructose
(C) ribose
(D) sucrose
Which amino acid is achiral ?
(A) alanine
(B) valine
(C) proline
(D) Glycine
Peptides on hydrolysis give
(A) Amines
(B) Amino acids
(C) Ammonia
(D) Alcohols
The helical structure of proteins is stabilized by
(A) H-bonding
(B) van der Waals forces
(C) ionic bond
(D) peptide bond
The enzyme which converts glucose and fructose into ethyl alcohol is
(A) Diastase
(B) Invertase
(C) Sucrose
(D) Zymase
  D    - glucose and   D    -glucose are
(A) enantiomers
(B) geometrical isomers
(C) epimers
(D) anomers
The rapid interconversion of   D -glucose and   D -glucose in solution is known as
(A) Racemization
(B) Asymmetric induction
(C) Fluxional isomerism
(D) Mutarotaiton
In an amino acid, the carboxyl group ionizes at pK a1  2.34 and ammonium ion at pK a 2  9.60 .
The isoelectric point of the amino acid is at pH
(A)5.97
(B)2.34
(C) 9.60
(D) 6.97
If one strand of DNA has the sequence ATGCTTGA, the sequence in the complimentary
strand would be
(A) TACGAACT
(B) TCCGAACT
(C) TACGTACT
(D)TACGTAGT
RNA is different from DNA because RNA contains
(A) ribose sugar and thymine
(B) ribose sugar and uracil
(C) deoxyribose sugar and thymine
(D)deoxyribose sugar and uracil
Which of the following is a example of co-polymer ?
(A) Buna-S
(B) PAN
(C) Polythene
(D) PTFE
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90.
91.
Luminal, a barbiturate drug is used as a/an
(A) antihistamine
(B) sedative
(C) antiseptic
(D) antimalarial
The correct structure of the drug paracetamol is
(A)
OH
(C)
CONH 2
Cl
(B)
(D)
NHCOCH 3
Cl
COCH 3
CONH 2
92.
OH
Which of the following amine will not respond to carbylamines reaction ?
(A) Ethylamine
(B)  CH3 2 NH
(C)
93.
94.
(D)Phenylamine
CH3 NH2
How many isomeric forms of C7 H9 N contain a bezene ring ?
(A) 4
(B) 5
(C) 6
(D) 7
Which of the following can be prepaired by Gabriel phthalimide reaction
C6 H5  NH  CH3
(A)
(C)
(B) CH3  CH2  NH2
(D) CH3
CH3
N
NH
CH3
95.
The reactivity of diazonium salt for coupling with the following compound is in the order
O
-
I
96.
CH3
CH3
OH
NH 2
+ NH 3
II
III
IV
(A) IV<II<III<I
(C) II <IV<I<III
The strongest base among the following is
(A)
(B) IV>III<II<I
(D) I<II<III<IV
(B)
N
H
N
(C)
(D)
NH 2
N
H
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97.
98.
99.
100.
Glyptal is a polymer of
(A) ethylene glycol
(B) ethylene glycol and phthalic acid
(C) ethylene glycol and adipic acid
(D) carprolactum
Caprolactum polymerises to give
(A) Terylene
(B) Teflon
(C) Gluptal
(D) Nylon-6
Alizarin belongs to the class of
(A) Vat dyes
(B) Mordant dyes
(C) Basic dyes
(D) Reactive dyes
Which of the following is a broad spectrum antibiotic
(A) Paracetamol
(B) Penicillin
(C) Aspirin
(D) Chloramphenicol
MATHEMATICS
101.
102.
The value of cos100  sin100 is
(A) Positive
(B) Negative
(C) 0
(D) 1
2
4
Given A  sin   cos  , then for all real 
3
 A 1
4
3
13
(D)  A 
4
16
(A) 1  A  2
(C)
103.
(B)
13
 A 1
16
The equation a sin x  bcos x  c , where c  a 2  b2 has
(A) a unique soln
(C) no soln
104.
Suppose that sin 3 x sin 3x 
(B) Infinite no. of Solns
(D) None of these
n
c
m 0
m
cos mx is an identity in x , where c1,c2 ,c3....,cn are
constants and cn  0 . Then the value of n is
(A) 4
(B) 5
(C) 6
(D) 8
105.


The maximum value of 5cos   3cos    
(A) 5
(C) 11
106.
107.
108.

  3 is
3
(B) 10
(D) -11
The value of 3 cosec200  sec200 is equal to
(A) 2
(B) 1
(C) 4
(D) -4
2
2
If sin x  sin x  1 , then value of cos x  cos 4 x is
(A) 1
(B) 2
(C) 1.5
(D) None of these
    5   7 
 sin   sin   is
 18   18   18 
The value of sin 
1
1
(B)
2
4
1
1
(C)
(D)
8
16
If cos x  tan y,cos y  tan z,cos z  tan x , then the value of sin x is
(A)
109.
(A) 2cos180
(B) cos180
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(C) sin180
(D) 2sin180
110.
The value of tan90  tan 270  tan 630  tan810 is
(A) 2
(B) 3
(C) 4
(D) None of these
111.
If 0  A 
112.
113.
114.
7

A
and sin A  cos A 
, then tan 
6
2
2
7 2
7 2
(A)
(B)
3
3
7
(C)
(D) None of these
3
3
A
5A
If cos A  , then the value of sin sin
is
4
2
2
11
1
(A)
(B)
8
32
11
11
(C)
(D)
16
32
The general value of  satisfying the equation
2sin 2   3sin   2  0 is
n 
n 
(A) n   1 , n  I
(B) n   1 , n  I
6
2
n 5
n 7
(C) n   1
(D) n   1
,n I
,n I
6
6
The most general value of  , satisfying the two equations cos   
5
,n I
4
5
(C) n 
,n I
4
(A) 2n 
115.
The general solution of tan3x  1 is
116.
is
(A) 2
(C) 6
117.

,n I
4

(D)  2n  1   , n  I
4
(B) 2n 
n 
 ,n I
3 12

(C) n,n  I
(D) n  , n  I
4
The number of pairs  x, y  satisfying the equations sin x  sin y  sin  x  y  and x  y  1
(A) n 

,n I
4
1
, tan   1 is
2
(B)
(B) 4
(D) infinite
tan  cos1 x  is equal to
(A)
1 x2
x
(B)
(C)
1 x2
x
(D)
x
1 x2
1 x2
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118.
119.
120.
121.
122.
123.
124.
1
1
is equal to
4 tan 1  tan 1
5
239
(A) 
(B)  / 2
(C)  / 3
(D)  / 4
2
If sin 1 x  sin 1 y 
, then cos1 x  cos1 y 
3
2

(A)
(B)
3
3

(C)
(D) 
6
7 

The value of cos 1  cos
 is
6 

7
5
(A)
(B)
6
3
5
13
(B)
(D)
6
6
4
2

The value of tan  cos 1  tan 1  is
5
3

7
6
(A)
(B)
16
17
17
(C)
(D) None of these
6
If   x  2 , then cos1  cos x  is equal to
(A) x
(B) x
(C) 2  x
(D) 2  x
1
1
If 4sin x  cos x   , then x equals
1
3
(A)
(B)
2
2
1
(C) 
(D) None of these
2
The number of real solutions of tan 1 x  x  1  sin 1 x 2  x  1   / 2 is
(A) zero
(C) two
125.
(B) One
(D) infinite
In a ABC , if
cos A cos B cos C


and the side a  2 , then area of the triangle is
a
b
c
(A) 1
126.
(B) 2
(C) 3 / 2
(D) 3
The perimeter of a ABC is 6 times the arithmetic mean of the sines of its angles . If the
side a is 1, then the angle A is

6

(C)
2
(A)
127.
(B)

3
(D) 
In a triangle ABC , a  4,b  3, A  600 . Then c is the root of the equation
(A) c2  3c  7  0
(B) c2  3c  7  0
(C) c2  3c  7  0
(D) c2  3c  7  0
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128.
129.
130.
In a triangle ABC, if a  13,b  14,c  15 , then its inradius is equal to
(A) 4
(B) 8
(C) 2
(D) 6
The ex-radii of a triangle r1 , r2 , r3 are in harmonic progression, then the sides a,b,c are
(A) in H.P
(B) in A.P
(C) in G.P
(D) None of these
If in a triangle ABC,   a 2   b  c  , then tan A 
2
(A) 15/16
(C) 8/17
131.
(B) 8/15
(D) 1/ 2
If in a triangle ABC, 3a  b  c then the value of cot
(B) 3
(D) None of these
(A) 1
(C) 2
132.
In a triangle ABC, if r, r1, r2 , r3 have their usual meanings, the value of
(C)
134.
135.
136.
(B)
1
r
a cos A  bcos B  ccos C
is equal to
a bc
r
R
(A)
(B)
R
r
2r
R
(C)
(D)
R
2r
2
2
2
2
If in a triangle ABC, 8R  a  b  c , then the triangle ABC is
In a triangle ABC,
(A) right angled
(B) isosceles
(C) equilateral
(D) None of these
The angle of elevation of the top of the tower observed from each of the three points A,B,C
on the ground, forming a triangle is the same angle  . If R is the circum-radius of the
triangle ABC, then the height of the tower is
(A) R sin 
(B) R cos
(C) R cot 
(D) R tan 
The top of a hill observed from the top and bottom of a building of height h is at angles of
elevation p and q respectively. The height of the hill is
h cot q
cot q  cot p
h tan p
(C)
tan p  tan q
(A)
137.
(B)
h cot p
cot p  cot q
(D) None of these
A tree is broken by wind, its upper part touches the ground at a point 10 metres from the foot
of the tree and makes an angle of 450 with the ground. The entire length of the tree is
(A) 15 metres
(B) 20 metres


(C) 10 1  2 metres
138.
1 1 1
  is
r1 r2 r3
2
r
3
(D)
r
(A) 1
133.
B
C
cot is
2
2

(D) 10 1 


3
 metres
2 
An aeroplane flying at a height of 300 metres above the ground passes vertically above
another plane at an instant when the angles of elevation of the two planes from the same
point on the ground are 600 and 450 respectively. The height of the lower plane from the
ground (in metres ) is
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139.
140.
(B)
(C) 50
(D) 150


3 1
If z 
4
 2 , then the maximum value of z is
z
(A)
5
(B)
(C)
5 1
(D) None of these
5 1
If z  3 , then the points representing the complex numbers 1  4z lie on a
(A) line
(C) parabola
141.
100
3
(A) 100 3
(B) Circle
(D) Hyperbola
If z 2  1  z  1 , then z lies on a
2
(A) circle
(C) an ellipse
(B) a parabola
(D) None of these
 1 i 
The least positive integer n for which 
 is real, is
 1 i 
n
142.
143.
(A) 2
(C) 8
The value of
1   1  2 1  3 1  4 1  5 1  6 ...1  3n  ,
imaginary cube root of unity , is
(A) 23n
(C) 2n
144.
(B) 4
(D) None of these
where  is an
(B) 22n
(D) None of these
If z  z  z  z , then the locus of z is
(A) a pair of straight lines
(B) a rectangular hyperbola
(C) a line
(D) a set of four lines
145.
If
2z1  3z 2
5z 2
is purely imaginary , then
is equal to :
2z1  3z 2
7z1
(A) 5/7
(B) 7/9
25
(C)
49
(D) None of these
146.
The locus represented by the equation z  1  z  i is
147.
(A) a circle of radius 1
(B) an ellipse with foci at 1 and –i
(C) a line through the origin
(D) a circle on the line joining 1 and –i as diameter
The inequality z  4  z  2 represents the region given by
148.
(A) Re  z   3
(B) Re  z   0
(C) Re  z   2
(D) None of these
If z1, z 2 , z3 are vertices of an equilateral triangle inscribed in the circle z  2 and if
z1  1  i 3 , then
(A) z 2  2,z3  1  i 3
(B) z 2  2,z3  1  i 3
(C) z 2  2,z3  1  i 3
(D) z 2  1  i 3,z3  1  i 3
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149.
Let z and w be two non-zero complex numbers such that z  w and arg  z   arg  w    .
Then z equals
(A) w
(C) w
150.
If z 
(A) i
(C) 1
(B) –w
(D)  w
3 i
, then z 69 equals
2
(B) i
(D) 1
ANSWERS
PHYSICS
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13
14
15
16
17
18
19
20.
21.
22
23.
24
25
26
27
28
29
30
31
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
(C)
(B)
(B)
(C)
(C)
(B)
(C)
(B)
(B)
(B)
(C)
(C)
(D)
(B)
(C)
(A)
(A)
(D)
(B)
(A)
(C)
(C)
(A)
(D)
(A)
(C)
(D)
(C)
(C)
(C)
(C)
(C)
(B)
(C)
(A)
(B)
(B)
(A)
(A)
(C)
(A)
(C)
(D)
(D)
(D)
(B)
(B)
(A)
(D)
(C)
CHEMISTRY
51.
52.
53.
54.
(D)
(B)
(B)
(B)
55.
56.
57.
58.
59.
60.
61.
62.
63.
64.
65.
66.
67.
68.
69.
70.
71.
72.
73.
74.
75.
76.
77.
78.
79.
80.
81.
82.
83.
84.
85.
86.
87.
88.
89.
90.
91.
92.
93.
94.
95.
96.
97.
98.
99.
100.
(C)
(D)
(D)
(B)
(C)
(B)
(C)
(B)
(C)
(A)
(B)
(A)
(D)
(D)
(A)
(B)
(C)
(A)
(C)
(D)
(A)
(C)
(C)
(B)
(A)
(D)
(B)
(A)
(D)
(D)
(D)
(A)
(A)
(B)
(A)
(B)
(B)
(B)
(B)
(B)
(A)
(C)
(B)
(D)
(B)
(D)
112.
113.
114.
115.
116.
117.
118.
119.
120.
121.
122.
123.
124.
125.
126.
127.
128.
129.
130.
131.
132.
133.
134.
135.
136.
137.
138.
139.
140.
141.
142.
143.
144.
145.
146.
147.
148.
149.
150.
(C)
(D)
(D)
(B)
(C)
(A)
(D)
(B)
(C)
(C)
(D)
(A)
(C)
(D)
(A)
(A)
(A)
(B)
(B)
(C)
(C)
(A)
(A)
(D)
(B)
(C)
(A)
(B)
(B)
(D)
(A)
(C)
(A)
(D)
(C)
(A)
(A)
(D)
(A)
MATHEMATICS
101.
102.
103.
104.
105.
106.
107.
108.
109.
110.
111.
(A)
(B)
(C)
(C)
(B)
(C)
(A)
(C)
(D)
(C)
(A)
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