Questions 21 to 26 are single correct answer type

Transcription

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PHYSICS
1.
2.
Two particles, each of mass m carrying charge Q, are separated by some distance. If they are
in equilibrium under mutual gravitational and electrostatic forces then Q/m (in C/kg) is of the
order of
(A) 10–5
(B) 10–10
–15
(C) 10
(D) 10–20
R
The value of R for which 20 % of the main current passes
through galvanometer of resistance 80  is
(
m
a
in
c
u
r
r
e
n
t)
(A) 10 
(B) 20 
G
I
(C) 30 
(D) 40 
3.
Charge Q is divided into two parts which are then kept some distance apart. The force
between them will be maximum if eth two parts are
(A) Q/2 each
(B) Q/4 and 3Q/4
(C) Q/3 and 2Q/3
(D) e and (Q – e), where e = electronic charge
4.
If switch S is closed at t = 0 then the time at which power supplied
by battery is equal to rate of energy storage in capacitor is
(A) t = 0
(B) t = 4RC
(C) t = 5RC
(D) It never happens (except t  ) because resistor always
consume energy
5.
6.
7.
R
C

S
A point charge Q is moved along a circular path around another fixed point charge. The work
done is zero
(A) only if Q returns to its starting point
(B) only if the two charges have the same magnitude
(C) only if the two charges have the same magnitude and opposite signs
(D) in all cases
4
6
A
Potential difference between point A and B is
(A) 122 volt
4

(B) 60 volt
A
B
3

3

(C) 100 volt
(D) none of these
Which of the following is not true for a region with a uniform electric field ?
(A) it can have free charges
(B) it may have uniformly distributed charge
(C) it may contain dipoles
(D) none of the above
8.
9.
10.
1
B 6V
Potential of point B is
(A) 6 volt
(C) 4 volt
(B) 5 volt
(D) 3 volt
3
2
A positive point charge, which is free to move, is placed inside a hollow conducting sphere
with negative charge, away from its centre. It will
(A) move towards the centre
(B) move towards the nearer wall of the conductor
(C) remain stationary
(D) oscillate between the centre and the nearer wall
C2
Charge on the capacitor having capacitance C2 in steady state
is
R
(A) Zero
(B) (C1 + C2)V
R
(C) C2V
(D) C1V
C1
V
11.
A spherical conductor A or radius r is placed concentrically inside a conducting shell B of
radius R (R > r). A charge Q is given to A, and then A is joined to B by a metal wire. The
charge flowing from A to B will be
 R 
 r 
(A) Q 
(B) Q 


Rr
Rr
(C) Q
(D) zero
12.
The capacitor shown in the figure is in steady state. The energy stored in the capacitor is
R
IR
2
2
(A) CI R
(C) 4CI2R2
R
C
(B) 2CI2R2
(D) None of the above
13.
A simple pendulum of time period T is suspended above a large horizontal metal sheet with
uniformly distributed positive charge. If the bob is given some negative charge, its time
period of oscillation will be
(A) > T
(B) < T
(C) T
(D) proportional to its amplitude
14.
Figure shows a portion of circuit the potential of point
D is.
(A) – 5 V
(B) 5 V
(C) – 10 V
(D) 10 V
10V
1
4
1
10V
1
10V
2 6A
D
15.
16.
C
In the circuit shown, the equivalent capacitance between the
points A and B is
(A) C/5
(B) C/3
(C) C/2
(D) C
C
C
A
In the figure shown, if Galvanometer shows no deflection
then the value of x is
(A) 4 
(B) 3 
(C) 2 
(D) 8 
C
B
C
2

4
4
G
8
x
17.
In a parallel–plate capacitor, the region between the plates is filled by a dielectric slab. The
capacitor is connected to a cell and the slab is taken out
(A) some charge is drawn from the cell
(B) some charge is returned to the cell
(C) the potential difference across the capacitor is reduced
(D) no work is done by an external agent in taking the slab out
18.
When the switch is closed, the initial current through the 1
 resistor is
(A) 12 A
(B) 4 A
10
(C) 3 A
(D)
A
7
1 
6 
12 V
3 
S
19.
The drift velocity of electrons in a metallic conductor carrying in current is usually of the
order of
(A) 1 cm/s
(B) 10 m/s
(C) 104 m/s
(D) 108 m/s
20.
For what value of R, power developed across 6 
resistor is equal to the power developed across 24 
resistor?
(A) 12 
(B) 6 
(C) 24 
(D) 8 
R
i
i
6 
24 
21.
The resistance of a metallic conductor increases with temperature due to
(A) change in carrier density
(B) change in dimensions of the conductor
(C) increase in the number of collisions among the carriers
(D) increase in the rate of collisions between the carriers and the vibrating atoms of the
conductor
22.
A parallel combination of two resistors of 1 each, is connected in series with a 1.5
resistor, and two uncharged capacitances of 1.5F and 3F , also in series. The combination
is connected to a 10 V battery. The initial current flowing in the circuit is (assume that the
capacitors are initially uncharged)
(A) 5 A
(B) 0 A
(C) 0.3 A
(D) 0.4 A.
23.
2V
A source of internal resistance 4 is connected in a circuit as shown
in the figure:
The maximum energy that can be dissipated in R occurs when
(A) R  1
(B) R  7
(C) R 
12

7
4
R
(D) R  0 .
3
24.
A piece of copper and another of germanium are cooled from room temperature to 80 K. The
resistance of
(A) each of them increases
(B) each of them decreases
(C) copper increases and that of germanium decreases
(D) copper decreases and that of germanium increases
25.
A cell of emf 2V is connected across a resistance 5 . The potential difference between the
terminals of the cell is found to be 1.25 V. The internal resistance is
15

8
10
(C)

3
(A)
26.
(B) 3
(D) none of these.
The net resistance between point P and Q in
shown in the figure is
R
(A)
(B)
2
3R
(C)
(D)
5
R
the circuit
R
R
Q
P
2R
5
R
3
R
27.
Current flows through a metallic conductor whose area of cross–section increases in the
direction of the current. If we move in this direction,
(A) the current will change
(B) the carrier density will change
(C) the drift velocity will increase
(D) the drift velocity will decrease
28.
The current passing through 4 resistance is zero. Then the emf
E is
(A) 8V
(B) 12V
(C) 6V
(D) none of these

12V
2
E
29.
A cell of internal resistance r drives a current through an external resistance R. The power
delivered by the cell to the external resistance is maximum when
(A) R = r
(B) R >> r
(C) R << r
(D) R = 2r
30.
In a potentiometer experiment, two cells connected in series get balanced at 9 cm length on
the wire. Now the connections of terminals of the cell of lower emf are reversed then the
balancing length is obtained at 3 cm. The ratio of emf’s of two cells will be
(A) 1 : 3
(B) 2 : 1
(C) 1 : 4
(D) 4 : 1.
31.
In the given figure R1 > R2. We will get a better ammeter if
(A) only K1 is closed
(B) only K2 is closed
(C) both K1 and K2 is closed
(D) both K1 and K2 are open
G
K
1
R
1
K
2
R
2
32.
33.
34.
When a 500 W electric bulb and a 500 W heater operate at their rated voltages, the filament
of the bulb reaches a much higher temperature than the filament of the heater. The most
important reason for this is that
(A) their resistances are not equal
(B) they are made of different materials
(C) their dimensions are very different
(D) they radiate different powers at different temperatures
A galvanometer may be converted into ammeter or voltmeter. In which of the following cases
the resistance of the device will be the largest ?
(Assume maximum range of galvanometer = 1 mA)
(A) an ammeter of range 10 A
(B) a voltmeter of range 5 V
(C) an ammeter of range 5 A
(D) a voltmeter of range 10 V.
A capacitor of capacitance C is charged by an ideal battery of emf V.
Then, heat generated during the charging of capacitor is,
(A) zero
(B) CV2
CV 2
1
(C) CV 2
(D)
.
4
2
C
V
35.
All charge on a conductor must reside only on its outer surface. This statement is true
(A) in all cases
(B) for spherical conductors only (both solid and hollow)
(C) for hollow spherical conductor only
(D) for conductors which do not have nay sharp points or corners
36.
A point charge Q is placed outside a hollow spherical conductor of radius R, at a distance r (r
> R) from its centre C. The field at C due to the induced charges on the conductor is
Q
(A) zero
(B) k
(r  R) 2
Q
Q
(C) k 2 , directed towards Q
(D) k 2 , directed away from Q
r
r
37.
A spherical equipotential surface is not possible
(A) for a point charge
(B) for a dipole
(C) inside a uniformly charge sphere
(D) inside a spherical capacitor
38.
In an isolated parallel–plate capacitor of capacitance C, the four surface
have charges Q1, Q2, Q3 and Q4, as shown. The potential difference
between the plates is
Q  Q 2  Q3  Q 4
Q  Q3
(A) 1
(B) 2
2C
2C
Q 2  Q3
Q1  Q 4
(C)
(D)
2C
2C
39.
In the arrangement shown, all plates have equal area. The amount of
spacing between plates is mentioned. Find the equivalent capacitance
A
of the system between A and B if C  0
L
5
C
7
1
(C) C
7
(A)
(B)
3
C
7
2L
L
L
L
2L
(D) None of these
Q1
Q3
Q2
Q4
A
B
40.
41.
Potential within a hypothetical charged sphere varies with the distance of a point from centre
as V  a.r where a is a vector of constant magnitude parallel to r and r is position vector
of point under consideration taking centre of sphere as origin. Then the total charge stored
within a sphere of radius R is.
(A) R2 0a
(B) 2R2 0a
(C) 3R2 0a
(D) 4R2 0a
y-axis
What is the direction of electric field at point O as shown in figure ?
+ + – ––
(A) positive x-axis
(B) negative x-axis
+
––
+
–
+
(C) positive y-axis
(D) negative y-axis
O
–
– x-axis
+
+
++
+ –
–
––
–
–
42.
In a parallel plate capacitor of plate area A, plate separation d and charge Q, the force of
attraction between the plates is F, then
1
(A) F  Q2
(B) F  2
A
1
(C) F  d
(D) F 
d
43.
An arrangement of three metallic conductors is shown. What is the
magnitude of charge appearing on the left face of the conductor B?
(A has a total charge Q1 and C has a total charge Q2)
(A) zero
(B) Q1
Q  Q1
(C) Q2
(D) 2
2
Q1
Q2
B
A
C
44.
Uniform electric field lines pass inward through the flat surface of a hemisphere of radius r ,
making angle of 60º with the normal to the plane of the surface. The strength of the field is
E0 . There is no charge anywhere. The net outward flux through the curved surface is  . Then
(A)   E0  r 2 cos60º
(B)   E0  r 2 sin 60º
(C)   0
(D)   E0 r 2 cos2 60º .
45.
A, B, C, D are identical, parallel, conducting plates arranged as
shown, with equal separations between consecutive plates. A and D
are connected to a cell. If B is now connected to C, which of the
following will occur ?
(A) only that some charge will flow through the cell.
(B) only that some charge will flow from B to C.
(C) only that there will be no electric field between B and C.
(D) more than one of the above.
A
46.
A B C D
E
A particle of charge q and mass m is projected from a large distance towards another identical
charged particle at rest with velocity v0. The distance of closest approach will be
q2
q2
(A)
(B)
20 mv02
0 mv02
(C)
2q 2
0 mv02
(D)
q2
40 mv02
47.
48.
A point of charged q is placed at a distance 2r from the centre O
of a conducting uncharged sphere of radius r. Potential of
O
+q
induced charges at point P(lying in a line joining the point charge P
2r
and centre of sphere) is
Kq
Kq
(A)
(B)
2r
3r
Kq
(C)
(D) None of these
6r
Four charges of 6C, 2C, 12C and 4C are placed at the circumference of a circle. The
circle is in x-y plane and its centre at its origin. Locus of the points where electric potential is
zero is
(A) x = y, z = 0
(B) x = 0 = z
(C) x = 0 = y
(D) x = z, y = z
49.
A large metallic plate is given a charge Q. Area of one face of the plate is A. Electric field at
a point near the metallic plate is
Q
Q
(A)
(B)
Aε 0
2Aε 0
Q
(C)
(D) None of the above
4Aε 0
50.
In the circuit shown below, the galvanometer G will show zero
deflection
(A) in all cases
(B) only if S is open
(C) only if S is closed
(D) none of the above
6
4
+
4
6
G
S
CHEMISTRY
51.
The general molecular formula, which represents the homologous series of alkanols is :
(A) CnH2n+1O
(B) CnH2n+2O
(C) CnH2nO2
(D) CnH2nO
52.
Reaction of t-butyl bromide with sodium methoxide produces :
(A) isobutane
(B) isobutylene
(C) sodium t-butoxide
(D) t-butyl methyl ether
53.
The best reagent to convert pent-3-en-2-ol into pent-3-en-2-one is :
(A) acidic KMnO4
(B) alkaline K2Cr2O7
(C) Chromium anhydride in glacial acetic acid
(D) pyridinium chlorochromate
54.
Ethylene oxide when, treated with Grignard reagent yields :
(A) cyclopropyl alcohol
(B) primary alcohol
(C) secondary alcohol
(D) tertiary alcohol
55.
Reaction of
H2C
CH2
O
with RMgX followed with hydrolysis produces :
(A) RCHOHR
(B) RCH2CH2OH
(C) RCHOHCH3
(D) RCH = CHOH
56.
The major organic product in the reaction,
CH3  O  CH  CH3 2  HI 
 Product is :
(A) CH3O C (CH3)2
(B) CH3I + (CH3)2CHOH
|
I
(C) CH3OH + (CH3)2CHI
(D) ICH2OCH(CH3)2
57.
HBr reacts with CH2 = CH – OCH3 under anhydrous conditions at room temperature to give
(A) CH3CHO and CH3Br
(B) BrCH2CHO and CH3OH
(C) BrCH2 – CH2 – OCH3
(D) H3C – CHBr – OCH3
58.
An industrial method of preparation of methanol is :
(A) catalytic reduction of carbon monoxide in presence of ZnO – Cr2O3
(B) by reacting methane with steam at 900°C with a nickel catalyst
(C) by reacting formaldehyde with lithium aluminium hydride
(D) by reacting formaldehyde with aqueous sodium hydroxide solution
59.
Which will not form a yellow precipitate on heating with an alkaline solution of iodine?
(A) CH3CHOHCH3
(B) CH3CH2CHOHCH3
(C) CH3OH
(D) CH3CH2OH
60.
1-phenyl ethanol can be prepared from banzaldehyde by the action of :
(A) CH3Br
(B) CH3Br and AlBr3
(C) CH3I, Mg and HOH
(D) C2H5I and Mg
61.
HBr reacts fastest with :
(A) 2-methylpropan-2-ol
(C) propan-2-ol
(B) propan-1-ol
(D) 2-methylpropan-1-ol
62.
Dehydration of alcohols to alkene by heating with conc. H2SO4 the initiation step is . . . . .
followed with . . . . . mechanism,
(A) elimination of water, free radical
(B) formation of an ester, free radical
(C) protonation of alcohol, carbocation
(D) protonation of alcohol, carbanion
63.
A carbonyl compound reacts with hydrogen cyanide to form cyanohydrin which on
hydrolysis form a racemic mixture of -hydroxy acid. The carbonyl compound is :
(A) diethyl ketone
(B) formaldehyde
(C) acetaldehyde
(D) acetone
64.
The increasing order of the rate of HCN addition to compounds A – D is :
(i) HCHO
(ii) CH3COCH3
(iii)PhCOCH3
(iv) PhCOPh
(A) (i) < (ii) < (iii) < (iv)
(B) (iv) < (ii) < (iii) < (i)
(C) (iv) < (iii) < (ii) < (i)
(D) (iii) < (iv) < (ii) < (i)
65.
Nucleophilic addition reaction will be most favoured in :
(A) CH3CH2CHO
(B) CH3CHO
(C) CH3  CH2  CH2COCH3
(D) (CH3)2C = O
66.
Which one of the following aldehydes will not form an aldol when treated with dil. NaOH?
(A) CH3CHO
(B) CH3CH2CHO
(C) (CH3)3CCHO
(D) C6H5CH2CHO
67.
Ketones can be obtained in one step by :
(A) hydrolysis of ester
(C) reaction of acid halide with alcohols
68.
69.
70.
(B) oxidation of primary alcohols
(D) oxidation of secondary alcohol
 CH3 2 C  CHCOCH3 can be oxidized to  CH3 2 C  CHCOOH by :
(A) Cu at 300°C
(C) chromic acid
(B) KMnO4
(D) NaOI
Acetaldehyde reacts with :
(A) only nucleophiles
(C) only electrophiles
(B) both electrophiles and nucleophiles
(D) only free radicals
CH3COCH3 can be obtained by :
(A) heating acetaldehyde with methanol
(C) oxidation of isopropyl alcohol
(B) oxidation of propyl alcohol
(D) reduction of propionic acid
71.
The reagent which can be used to distinguish acetophenone from benzophenone is :
(A) 2, 4-dinitrophenyl hydrazine
(B) aqueous NaHSO3
(C) benedict’s solution
(D) I2 and Na2CO3
72.
Pd/H
CH3COCl 
 X. Here X is :
BaSO
2
4
(A) acetaldehyde
(C) acetone
(B) propionaldehyde
(D) acetic anhydride
73.
Which of the following compounds will undergo self aldol condensation in presence of cold
dilute alkali?
(A) C6H5CHO
(B) CH2 = CH – CHO
(C) CH3CH2CHO
(D) none of these
74.
Which can be oxidized to the corresponding carbonyl compound?
(A) Propan-2-ol
(B) Ortho-nitro-phenol
(C) Phenol
(D) 2-methylpropan-2-ol
75.
Which can be reduced to corresponding hydrocarbon by Zn / HCl?
(A) Butan-2-one
(B) Acetic acid
(C) Acetamide
(D) Ethyl acetate
76.
Which of the following will react with acetone to give a product containing
C=N–
(A) C6H5NH2
(B) (CH3)3N
(C) C6H5NHC6H5
(D) C6H5NHNH2
77.
78.
dil.NaOH
 how many distinct products (saturated) are
In the reaction HO – CH2 – CHO 
possible ?
(A) 1
(B) 2
(C) 3
(D) 4
In which of the following substrates, rate of Benzoin condensation will be maximum?
79.
(a)
(A)
O2N
(C)
(c)
HO
(B)
(b)
CHO
H3C
CHO
(D) NH2
CHO
CHO
Mg/Hg
2CH3  C  CH3 
 Product. Product in the reaction is

||
H
O
CH3
CH3
|
|
(B) CH3  C O  C CH3
(A) H3C  C  C  CH3
|
|
OH
OH
(C) CH3  CH CH  CH3
|
||
||
O
O
(D) none of these
|
OH OH
80.
What is A in the following reaction?
O
Cl
O
t  BuOK

A
t  BuOH

O
H5 C 2
O
O
H3C
O
(A)
(B)
C 2 H5
C 2H5
O
O
(C)
O
O
81.
OH
(D)
C 2 H5
O
CH3
is the final product obtained when one of the following is reacted with base.
O
O
O
(A)
(B)
H3C
H3C
CH3
O
(C)
O
CH3
O
O
(D)
H3C
H3C
CH3
82.
O
CH3
End product of the following sequence of reactions is
CH3MgBr
CO2 /H3O
HgSO4 /H2SO4
Ag2O
CH  CH 
 
 
 


O
(A)
O
H3C
OH
O
(B)
HO
O
OH
O
(C)
O
H3C
(D)
H
O
83.
O
OH
H / Pt
2
—CH=CH—CHO 
A
NaBH 4
B 

A and B are:
(A)
—CH CH CHO,
2
2
—CH=CH—CH2OH
(B)
—CH2CH2CH2CHOH,
(C)
—CH=CH—CH2OH in both cases
(D)
—CH2CH2CH2OH in both cases
—CH=CH—CH2OH
84.
Dipole moment of CH3CH2CH3(I), CH3CH2OH (II) and CH3CH2F(III) is in order
(A) I  II  III
(B) I  II  III
(C) I  III  II
(D) III  I  II
85.
The strongest acid among the following aromatic compounds is
(A) p-chlorophenol
(B) p-nitrophenol
(C) m-nitrophenol
(D) o-nitrophenol
86.
The boiling points of isomeric alcohols follow the order
(A) primary  secondary tertiary
(B) tertiary  secondary  primary
(C) secondary  tertiary  primary
(D) does not follow any order
87.
Phenol can be distinguished from alcohol with
(A) Tollens reagent
(B) Schiff's base
(C) Neutral FeCl3
(D) HCl
88.
Which compound is formed when CH3OH reacts with CH3 – Mg - X
(A) Acetone
(B) Alcohol
(C) Methane
(D) Ethane
89.
Methyl alcohol can be distinguished from ethyl alcohol using
(A) Fehling solution
(B) Schiff’s reagent
(C) Sodium hydroxide and iodine
(D) Phthalein fusion test
90.
The reagent which easily reacts with ethanol and propanol is
(A) Fehling solution
(B) Grignard reagent
(C) Schiff’s reagent
(D) Tollen’s reagent
91.
An aromatic amine (A) was treated with alcoholic potash and another compound (Y) when
foul smelling gas was formed with formula C6H5NC. Y was formed by reacting a compound
(Z) with Cl2 in the presence of slaked lime. The compound (Z) is
(A) C6H5NH2
(B) C2H5OH
(C) CH3OCH3
(D) CHCl3
92.
The reaction of C2H5OH with H2SO4 does not yield
(A) Ethylene
(B) Diethyl ether
(C) Acetylene
(D) Ethyl hydrogen sulphate
93.
Which of the following are isomers
(A) Methyl alcohol and dimethyl ether
(C) Acetone and acetaldehyde
(B) Ethyl alcohol and dimethyl ether
(D) Propionic acid and propanone
94.
An alcohol on oxidation is found to give CH3COOH and CH3CH2COOH. The structure of the
alcohol is
(A) CH3CH2CH2OH
(B) (CH3)2C(OH)CH2CH3
(C) CH3CH2CHOHCH3
(D) CH3CH(OH)CH2CH2CH3
95.
Dehydration of cyclopentyl carbinol with conc. H2SO4 forms
(A) Cyclopentene
(B) Cyclohexene
(C) Cyclohexane
(D) None of these
96.
Phenol does not react with NaHCO3 because
(A) phenol is a weaker acid than carbonic acid
(B) phenol is a stronger acid than carbonic acid
(C) phenol is as strong as carbonic acid
(D) phenol is insoluble in water.
97.
The acidic character of 1°, 2°, 3° alcohols, H2O and RCCH is in the order
(A) H2O  1°  2°  3° RCCH
(B) RCCH  3°  2°  1°  H2O
(C) 1°  2°  3°  H2O  RCCH
(D) 3°  2°  1°  H2O  RCCH
98.
The major product P in the following reaction is

H
(CH3 )3 COH  C2 H5OH 
P
(A) (CH3)3COC(CH3)3
(C) C2H5OC2H5
(B) (CH3)3COC2H5
(D) (CH3)2C = CH2
OD
99.
D
i) CO2
NaOH

[ ] 
 P.
ii)D
Here P is
OH
(A)
D
O
OD
(C)
100.
OD
OD
(B)
OD
D
O
OH
D
O
(D) Reaction not possible
The product (B) in the following sequence of reaction is:
C6 H5CO3H
HCl

 A 
B
CH2
OH
O
(A)
(B)
Cl
O
Cl
(C)
(D)
OH
OH
MATHEMATICS
101.
x
3
 x  1 dx
If
= Ax3 + Bx2 + Cx – ln (x + 1) + k then A + B + C is equal to
1
6
2
(C)
3
2
6
5
(D)
6
(A)
102.

x 2f (x 3 )
dx is equal to
f (x 3 )
I
(A)
f (x 3 )  c
3
2x
f (x 3 )
(D) 2 f (x 3 )  c
(2x  3)
is equal to
x 1
(A) 2ex x  1 + C
ex
(C)
+ C
x 1
e
x
1
104.
(B)
2
f (x 3 ) dx
3
(C)
103.
(B)
The value of

dx
x1/3  1
(A) (9/40) (8.22/3 - 9)
(C) (9/40) (8.21/3 - 9)
3
(B) ex x  1 + C
(D) none of these
is equal to
0
(B) (40/9) (8.22/3 - 9)
(D) none of these
4
105.
 {x  0.4}dx equals ({x} is a fractional part of x)
1
(A) 1.3
(C) 1.5
106.
(B) 6.3
(D) 7.5
1
log(x  1  x 2 )
1
x  log(x  1  x 2 )

(A) 0
(C) 2f(x)
(f (x)  f (x)) dx is equal to
(B) 2
1
log(x  1  x 2 )
x  log(x  1  x 2 )
(D) none of these
0
(f (x)  f (x))dx
1
107.
| x  x
2
| dx   | x 2  3x  2 |dx 
2
0
1
1
(A)
2
1
(C)
4
108.
109.
1
3
1
(D)
8
(B)
 tan–1 . tanx d equals
(A) tan–1. secx + c
1
(C) tanx { tan–1 –
log (1 + 2)} + c
2
x
2
dx
is equal to
(1  x 4 )  / 4
 (1  x 4 )1/ 4
c
x
 (1  x 4 )3 / 4
c
(C)
x
(A)
110.
111.
(B)
(1  x 4 )1/ 4
c
x
(D) none of these


2x 
1

 e  tan x  1  x2 2  dx is equal to
 

1 

(A) e x  tan 1 x 
C
1  x2 

1 

(C) e x  cot 1 x 
C
1  x2 

x
The value of the
x
2
11
5 2
10  C
x

2
x


11
11
6
(C)  x  110  C
7
x
dx
1 x3

x x
(A)
112.
(B) tan–1.. log(secx) + c
1
(D) tan {x tan–1 x – log (1 + x2)} + c
2
8
1 

(B) e x  tan 1 x 
C
1  x2 

2 

(D) e x  tan 1 x 
C
1  x2 


1
 2 x 9 10
dx is
11
5
 x  110  C
6
10
11 2
(D)
x

2
x

11  C
5
(B)
dx 
(A)
1
1  x3 1
log
c
3
1 x3 1
(B)
1
1 x2 1
log
c
3
1  x 2 1
(C)
1
1
log
c
3
1 x3
(D)
1
log 1  x 3  c
3
1
113.
If   e  x sin  x  k   0 (for some ,   R),   0, then the value of k can belong to
2
0
  5 
(A)  , 
 3 12 
 
(B)  , 
3 2
  
(D)   ,  
 2 3
   
(C)  , 
4 6
114.
The value of
x cot x cosec x
  x  cot x 
2
dx is equal to
(A)
1
C
 x tan x  1
(B)
1
C
 x sin x  cos x 
(C)
1
C
 x  cot x 
(D)
1
C
115.
Area bounded by the curve y = (x – 1) (x – 2) (x – 3) and x-axis lying between the ordinate x
= 0 and x = 3 is equal to
9
11
(A)
(B)
4
4
11
(C)
(D) none of these
2
116.
The area bounded by the curve y = 2x – x2 and the straight line y = – x is
9
43
(A)
(B)
2
6
35
(C)
(D) none of these
6
117.
The area of the region bounded by the curve y =
ordinates x = /6 and x = /3 is;
(A) /4
(C) /8
1
1  (tan x)
Area enclosed by the curve y = x3 and y = x1/3 is
(A) 1 sq. unit
(B) 2 sq. unit
(C) there is no area enclosed
(D) none of these
119.
 | ln x | dx equals (0 < x < 1)
1
120.
| x  x
(B) x |lnx| – x + c
(D) x + x |lnx| + c
2
2
| dx   | x 2  3x  2 |dx 
0
121.
and the x-axis between the
(B) /2
(D) none of these
118.
(A) x (|lnx| – (x – 1)) + c
(C) x (|lnx| + (x – 1)) + c
2
1
(A)
1
2
(B)
1
3
(C)
1
4
(D)
1
8
The value of
x cot x cosec x
  x  cot x 
2
dx is equal to
1
C
 x tan x  1
1
C
(C)
 x  cot x 
(A)
1
C
1
C
(D)
(B)
122.
The area bounded by the curve y = 2x – x2 and the straight line y = – x is
9
43
(A)
(B)
2
6
35
(C)
(D) none of these
6
123.
The area of the region bounded by the curve y =
ordinates x = /6 and x = /3 is;
(A) /4
(C) /8
124.
x
c
y
x
(C) x 2 y 2  2In  c
y
126.
(B) xy  2In
x
c
y
(D) none of these
The degree and order of differential equation of family of circle touching a parabola
y2 = 4x (R) at its vertex is
(A) degree = 2, order = 1
(B) degree = 1, order = 2
(C) degree = 1, order = 0
(D) none of these
Let y   A  Bx  e3x is a solution of the differential equation
then (m, n) is
(A) (-6, 9)
(C) (9, 6)
127.
(B) /12
(D) none of these
The solution of the differential equation 1  x 2 y2  y dx   x 2 y2  1 x dy  0 is
(A) xy  In
125.
1
and the x-axis between the
1  (tan x)1/2
d2 y
dy
 m  ny  0, m n  I,
2
dx
dx
(B) (-6, 8)
(D) (-9-, -6)
The area bounded by the parabola y = x2 – 7x + 10 and x-axis equals
1
(A) 5/2 sq. units
(B)
sq. units
6
5
9
(C) sq. units
(D)
sq. units
6
2
2
128.
129.
 dy  dy
A solutions of the differential equation    (e x  e x )  1  0 are given by
 dx  dx
–x
(A) y + e = C
(B) y – e–x = C
x
(C) y + e = C
(D) none of these

2
1
2
1
1

cos ec101  x   dx is
x
x

(A) 1
(C) 2
130.
131.
132.

/ 2
(B) 3
(D) 0
2cos x
1  2x
(A) 1
(C) 3
 / 2
3
dx is
(B) 2
(D) 0

sin 6x
dx is
sin x
(A) 0
(C) 4
(B) 6
(D) 3
The area bounded by y = 3x and y = x2
(A) 5/2
(C) 3
(B) 7/2
(D) 9/2

0
133.
The area bounded by x = 4 – y2 and the y-axis
(A) 16/3
(B) 4/3
(C) 4/3
(D) 8/3
134.
The area in square units of the region bounded by the curve x2 = 4y the line x = 2 and the xaxis is
(A) 1
(B) 5/3
(C) 2/3
(D) 7/6
135.
The area bounded by y = x3, y = x2 and x = 1, x = 2
(A) 13/12
(B) 17/12
(C) 5/12
(D) none of these
136.
137.
 d2 y 
The order and degree of  2 
 dx 
(A) (2, 2)
(C) 1,2
2/3
 43
  dy 2 
The order and degree of 1    
  dx  
(A) (1, 2)
(C) (3, 4)
3/2
dy
0
dx
(B) (3, 2)
(D) (3, 4)
d3 y
 K 3 is
dx
(B) (3, 2)
(D) (2, 2)
 /4
138.
In In =
 tan
n
d, then I8 + I6 equals
0
(A) 1/4
(C) 1/6
 /2
139.

0
(B) 1/5
(D) 1/7
2sin x
dx is
2sin x  2cos x
(A) 2
(C) /4
(B) 
(D) /2
140.
The area common to the parabola y = 2x2 and y = x2 + 4 is
(A) 2/3 sq. units
(B) 3/2 sq. units
(C) 32/3 sq. units
(D) 3/32 sq. units
141.
The area bounded by y = 1 + 8/x2 and the ordinates x = 2 and x = 4 is
(A) 2
(B) 4
(C) log 2
(D) log 4
2/3
142.
143.
144.
 d3 y 
d2 y
dy
The degree of the differential equation  3   4  3 2  5
= 0 is
dx
dx
 dx 
(A) 1
(B) 2
(C) 3
(D) none of these
The solutions of (x + y + 1) dy = dx is
(A) x + y + 2 = Cey
(C) log (x + y + 2) = Cy
The solution of the equation dy/dx =
(A) y siny = x2 logx + x2/2 + c
(C) ycosy = x2 log x + x2/2 + c
145.
146.
(B) x + y + 4 = C logy
(D) log (x + y + 2) = C - y
x(2log x  1)
is
sin y  y cos y
(B) y cosy = x2 (logx + 1) + c
(D) y siny = x2 log x + c
dy
= y (logy - logx + 1) then the solution of the equation is
dx
y
x
(A) log  cy
(B) log  cy
x
y
x
(C) log  cx
(D) none of these
y
If x
 dy 
The solution of the equation log   = ax + by is
 dx 
by
ax
e
e
e by eax
(A)
(B)

c

c
b
a
b
a
e by eax

c
(C)
(D) none of these
a
b
3
147.
The solution of y dx - x dy + 3x2 y2 e x dx = 0 is
3
3
x
x
(A)  e x  C
(B)  e x = 0
y
y
3
x
(C)   e x = C
(D) none of these
y
148.
Solution of differential equation dy - sinx siny dx = 0 is
(A) ecosx. tan y/2 = c
(B) ecosx . tany = c
(C) cosx. tany = c
(D) cosx. siny = c
149.
The order of the differential equation whose solution is y = acosx + bsinx + Ce-x is
(A) 3
(B) 2
(C) 1
(D) none of these
5
150.
If f(x) denotes the greatest integer less than or equal to x, then the value of
 | x  3 | dx
1
(A) 1
(C) 4
(B) 2
(D) 8
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.
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.
(B)
(B)
(A)
(D)
(D)
(A)
(D)
(B)
(C)
(A)
(C)
(B)
(B)
(A)
(D)
(D)
(B)
(B)
(A)
(C)
(D)
(A)
(B)
(D)
(B)
(B)
(D)
(B)
(A)
(B)
(C)
(C)
(D)
(C)
(A)
(C)
(B)
(C)
(B)
(D)
(A)
(A)
(D)
(A)
(D)
(B)
(C)
(C)
(A)
(C)
MATHEMATICS
CHEMISTRY
51.
52.
53.
54.
55.
56.
57.
(B)
(B)
(D)
(B)
(B)
(B)
(D)
(A)
(C)
(C)
(A)
(C)
(C)
(C)
(B)
(C)
(D)
(D)
(B)
(C)
(D)
(A)
(C)
(A)
(A)
(C)
(D)
(D)
(A)
(C)
(A)
(B)
(B)
(A)
(B)
(A)
(C)
(C)
(C)
(B)
(B)
(C)
(B)
(D)
(D)
(A)
(A)
(B)
(C)
(C)
101.
102.
103.
104.
105.
106.
107.
108.
109.
110.
111.
112.
113.
114.
115.
116.
(D)
(C)
(A)
(A)
(C)
(A)
(B)
(C)
(A)
(A)
(A)
(A)
(C)
(B)
(B)
(A)
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.
(D)
(A)
(D)
(B)
(B)
(A)
(B)
(C)
(D)
(A)
(D)
(A)
(D)
(B)
(A)
(D)
(B)
(C)
(B)
(A)
(B)
(D)
(C)
(C)
(B)
(B)
(A)
(D)
(D)
(B)
(A)
(A)
(A)
(B)
is

Questions 21 to 26 are single correct answer type

Transcription

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