resonance test series
TRANSCRIPT
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PART-A
SECTION - I
Straight Objective Type
This section contains 28 multiple choice
questions. Each question has 4 choices (1), (2),
(3) and (4) for its answer, out of which ONLY ONE
is correct.
1. Two bodies with masses m1 and m
2 (m
2 > m
1)
connected by an ideal string lie on a smooth
horizontal table. When constant force F is
applied on m2 towards right then tension is
string is T1, Now when F is applied on m
1
towards left then tension in string is T2 then .
m1
m2
T1
F
m1
m2
T2F
(1) T1 > T
2
(2) T1 < T
2
(3) T1 = T
2
(4) T1 and T
2 cannot be compared form given
data
2. A block of mass 1kg initially at rest is droppedfrom a height h on the a spring of force constantk = 50N/m. The maximum compression in thespring is x =1m then height h of the block is :
(1) 3 m (2)3
2m
(3)5
2m (4) 5 m
3. An ideal string and three ideal pulley are
arranged in such a way so that pulley P1 and
P2 are fixed on ground and third pulley is
movable. A vertical constant force F is
applied on P3 so that string remains tight and
the string forms an equilateral triangle. Then
tension in string is. [Assume pulley to be very
small]
F
P1
P2
P3
(1)F
2 (2) 0
(3)F
3 (4) F
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4. A stone is projected with a velocity of 10 m/s
at angle of 37º with horizontal. Its average
velocity till it reaches the highest position is :
(Assume horizontal direction as x-axis and
vertically upward direction as +y-axis)
(1) ˆ ˆ4i 3 j!
(2) ˆ ˆ8i 6 j!
(3) ˆ ˆ8i 3 j!
(4) ˆ8i
5. It is raining with a velocity of 5 2 m/s at an
angle of 45° with vertical. To a man driving
with constant velocity ‘v’ down the inclined
plane the rain appears to move vertically
upwards with a velocity of 5 m/s. If " is the
angle of the incline plane with the horizontal,
then v and " are :
(1) 5 m/s , tan –1 5
(2) 5 5 m/s, tan –1 5
(3) 5 5 m/s, tan –11
2
(4) 5 5 m/s, tan –1 2
6. A body dropped from top of a tower, covers a
distance 7h in last second of it’s motion,
where h is distance covered in first second,
then total time of flight will be.
(1) 2s
(2) 3s
(3) 4s
(4) 8s
7. For the equilibrium condition shown, the cords
are strong enough to withstand a maximum
tension 100 N. What is the largest value of W
(in newton) that can be suspended :
W
A
53°
53°
(1) 100 N
(2) 35 N
(3) 80N
(4) 55 N
8. A ship is sailing due north with speed 9 m/s
in sea. Wind is blowing with speed 2 m/s
from S –W direction. A person holding a flag
in his hand running on the deck of ship with
speed 3 m/s due east relative to ship.
Direction in which flag will flutter is :
(1) tan –1(2) W of N
(2) tan –1(2) S of E
(3) tan –1(2) N of W
(4) none of these
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9. Power delivered to a body varies as P = 3 t2.
Find out the change in kinetic energy of the
body from t = 2 to t = 4 sec.
(1) 16 J
(2) 64 J
(3) 56 J
(4) 48 J
10. Particles A and B are moving with constant
velocity in two perpendicular directions as
shown in diagram at t = 0, then the velocity of
separation between A and B at t = 1 second is :
(1) 5 2 m/s
(2)7
2m/s
(3) 7 2 m/s
(4)5
2m/s
11. Force-time graph of a particle moving in a
straight line is shown in figure. Mass of
particle is 4 kg and the particle starts from
rest. Work done by all the forces acting on
the particle between time interval t = 0 to
t = 6 s is
(1) 400 J
(2) 200 J
(3) 800 J(4) 80 J
12. A perfect smooth sphere A of mass 2kg is in
contact with a rectangular block B of mass
4kg and vertical wall as shown in the figure.
All surfaces are smooth. The normal reaction
by vertical wall on sphere A is : (g = 10 m/s2)
(1) 45 N
(2) 40 N
(3) 50 N
(4) 42 N
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13. A block of mass m is placed on a rough
horizontal surface. The coefficient of static
friction and kinetic friction are given to be #s
and #k respectively. A constant horizontal
force F0 is applied to the block. The distance
travelled by the block in t0 seconds is :
(Given : m = 2kg, #s = 0.3, #k = 0.2,
F0 = 10N, t0 = 4 sec)
(1) 16 m
(2) 24 m
(3) zero
(4) None of these
14. A particle of mass 2 kg is subjected to a
force which varies with distance as shown in
figure. If it starts its journey from rest at x = 0,
its velocity at x = 15 m is
(1) 10 m/s
(2) 0 m/s
(3) 20 2 m/s
(4) 20 3 m/s
15. A small frictionless block slides with velocity
0.5 gr on the horizontal surface as shown
in the Figure. The block leaves the surface at
point C. The angle " in the Figure is :
(1) cos$1 (4/9)
(2) cos$1(3/4)
(3) cos$1(1/2)
(4) none of the above
16. A is highest point on the path of a projectile.
If the average velocity of the projectile
between O and A is ˆ ˆ8i 3 j! then tan % is :
O CBx
y
Au
%
(1) 3/8
(2) 1
(3) 3/4
(4) data is not sufficient
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17. A point mass m is suspended from a light
thread of length !, fixed at O, is whirled in a
horizontal circle at constant speed as
shown, the forces on the mass are
m
l
O
(1)
T
F
W
(2)
T
W
(3)
T
F
W
(4)
T
F
W
F
18. In the system shown in figure acceleration of
the two blocks is :
30º
4 kg
8 kg
(1) 4/3 m/s2
(2) 2/3 m/s2
(3) 20/3 m/s2
(4) 10/3 m/s2
19. In the figure a block slides along a track
from one level to a higher level, by moving
through an intermediate valley. The track is
frictionless until the block reaches the
higher level. There a frictional force stops
the block in a distance d. The block’s initial
speed v0 is 6m/s, the height difference h is
1.1 m and the coefficient of kinetic friction µ
is 0.6. The value of d is :
(1) 1.17 m (2) 1.71 m
(3) 7.11 m (4) 11.7 m
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20. Initially the block is at rest acceleration of the
block is :
(1) 2 m/s2 (2) 0 m/s2
(3) 1 m/s2 (4) 0.5 m/s2
21. A body of mass 2 kg is kept stationary by
pressing it against a vertical wall by a force
of 100 N. The coefficient of friction between
wall and body is 0.3. Then the frictional force
is equal to
(1) 100 N
(2) 20 N
(3) 30 N
(4) 10 N
22. Block A of mass 4 kg and block B of mass
6 kg are resting on a horizontal surface as
shown in the figure. There is no friction
between the block B and the horizontal
surface. The coefficient of friction between
the blocks is 0.2. If the value of g = 10 ms –2
,
the maximum horizontal foce F that can be
applied on block B without any relative
motion between A and B is
(1) 20 N
(2) 40 N
(3) 60 N
(4) 100 N
23. Contact force between the blocks is :
(1) 8 N
(2) 12 N
(3) 16 N
(4) None of these
24. Two blocks m1 = 4kg and m
2 = 2kg,
connected by a weightless rod on a plane
having inclination of 370. The coefficients of
dynamic friction of m1 and m
2 with the
inclined plane are # = 0.25. Then the
common acceleration of the two blocks and
the tension in the rod are :
(1) 2 m/s2, T = 5 N
(2) 10 m/s2 ,T = 0 N
(3) 15 m/s2, T = 9N
(4) 4 m/s
2
, T = 0
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25. The blocks A and B are released as shown
in the figure. Friction is absent everywhere.
Find the ratio of magnitude of acceleration of
block A and acceleration of block B
(1) 3/4
(2) 4/3
(3) 1
(4) zero
26. Two masses of 10 kg and 20 kg respectively
are connected by a massless spring as shown
in figure. A force of 200 N acts on the 20 kg
mass at the instant when the 10 kg mass has
an acceleration of 12 ms –2 towards right, the
acceleration of the 20 kg mass is :
20kg
200 N
10kg
(1) 2 ms –2
(2) 4ms –2
(3) 10ms –2
(4) 20ms –2
27. The blocks A and B are arranged as shown
in the figure. The pulley is frictionless. The
mass of A is 10 kg. The coefficient of friction
between block A and horizontal surface is
0.20. The minimum mass of B to start the
motion will be-
A
B
P
(1) 2 kg
(2) 0.2 kg
(3) 5 kg
(4) 10 kg
28. A heavy particle of mass 1kg is suspended
from a massless string attached to a roof. A
horizontal force F is applied to the particle
such that in the equilibrium position the string
makes an angle 60° with the vertical. The
magnitude of the force F equals
60°
(1) 10 N
(2) 10 3 N
(3) 5 N
(4)10
3 N
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SECTION - II
Reasoning Type
This section contains 2 reasoning type questions.
Each question has 4 choices (1), (2), (3) and (4),
out of which ONLY ONE is correct.
29 . STATEMENT-1 : A man standing in a lift
which is moving upward, will feel his weight
to be greater than when the lift was at rest.
STATEMENT-2 : If the acceleration of the lift
is ‘a’ upward, then the man of mass m shall
feel his weight to be equal to normal reaction
(N) exerted by the lift given by N = m(g+a)
(where g is acceleration due to gravity)
(1) Statement-1 is True, Statement-2 is True;
Statement-2 is a correct explanation for
Statement-1.
(2) Statement-1 is True, Statement-2 is True;
Statement-2 is NOT a correct explanation for
Statement-1
(3) Statement-1 is True, Statement-2 is False
(4) Statement-1 is False, Statement-2 is True
30. STATEMENT-1 : While drawing a l ine on
a paper, friction force acts on paper in
the same direction along which l ine is
drawn on the paper.
STATEMENT-2 : Friction always opposes
motion.
(1) Statement-1 is True, Statement-2 is True;
Statement-2 is a correct explanation for
Statement-1.
(2) Statement-1 is True, Statement-2 is True;
Statement-2 is NOT a correct explanation for
Statement-1
(3) Statement-1 is True, Statement-2 is False
(4) Statement-1 is False, Statement-2 is True
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PART – B
Atomic masses : [H = 1, D = 2, Li = 7, C = 12,
N = 14, O = 16, F = 19, Na = 23, Mg = 24, Al = 27,
Si = 28, P = 31, S = 32, Cl = 35.5, K = 39, Ca = 40,
Cr = 52, Mn = 55, Fe = 56, Cu = 63.5, Zn = 65,
As = 75, Br = 80, Ag = 108, I = 127, Ba = 137,Hg = 200, Pb = 207]
SECTION - I
Straight Objective Type
This section contains 30 multiple choice
questions. Each question has 4 choices (1),
(2), (3) and (4) for its answer, out of which
ONLY ONE is correct.
31. Use the data given in the following table to
calculate the molar mass of naturally
occurring argon isotopes:
Isotope Isotopic Abundancemolar mass
36Ar 35.96755 g mol
–1 0.337%
38Ar 37.96272 g mol
–1 0.063%
40Ar 39.9624 g mol
–1 99.600%
(1) 39.948 g mol –1
(2) 37.96272 g mol –1
(3) 38.48562 g mol –1
(4) 39.9624 g mol –1
32. Which of the following relations is/are
correct:
(i) 98.6º º
(ii) 1 torr < 1 pascal < 1 cm of Hg < 1 bar < 1
atm
(iii) 1 cm3 = 1 mL < 1 dm
3 = 1 L < 1 m
3
(iv) 106 J = 1 MJ = 10
–3 KJ
(1) (i), (ii) & (iii) only
(2) (iii) only
(3) (i) & (iii) only
(4) (i), (ii), (iii) & (iv) all
33. What is the number of photons of light with a
wavelength of 4000 pm that provide 1J of
energy?
(1) 2.01216
photons
(2) 2.01210
photons
(3) 2.01223
photons
(4) 20.1216
photons
34. The energy of second Bohr's orbit in H-atom
is -328 kJ mol-1
, hence the energy of fourth
Bohr orbit would be :
(1) -82 kJ mol-1
(2) -41 kJ mol-1
(3) -1312 kJ mol-1
(4) -164 kJ mol-1
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35. Light of wavelength ! falls on a metal having
work function 2hc/ !1. Photoelectric effect will
take place only if:
(1) ! " !1
(2) ! " 2!1
(3) ! # !1
(4) ! # !1 / 2
36. Let the total number of orbitals in ath shell be
16 and value of azimuthal quantum number
for the unpaired electron in vanadium atom
(Z = 23) be 'b', then find the sum (a + b).
(1) 4
(2) 5
(3) 6
(4) 3
37. Calcium carbonate reacts with aqueous HCl
to give CaCl2 and CO2 according to the
reaction,
CaCO3 (s) + 2 HCl (aq) $ CaCl2 (aq) +
CO2(g) + H2O(l).
What mass of CaCO3 is required to react
completely with 25mL of 0.75 M HCl?
(1) 0.938 g
(2) 2.938 g
(3) 10 g
(4) 9.38 g
38. NH3 is formed in the following steps :
I : Ca + C %%$ CaC2 50% yield
II : CaC2 + N2 %%$CaCN2 + C 100% yield
III : CaCN2 + H2O %%$NH3 + CaCO3
100% yield
To obtain 2 mol NH3, calcium required is :
(1) 1 mol
(2) 2 mol
(3) 3 mol
(4) 4 mol
39. Which of the following graphs is correct?
(1)
PV
T(at constant amount of gas)
(2)
(3)
(4)
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40. What will be the pressure exerted by a
mixture of 3.2 g of methane and 4.4 g of
carbon dioxide contained in a 9 dm3 flask at
27° . lit. atm. –1
.mol –1
)
(1) 0.821 atm.
(2) 8.21atm
(3) 0.0821atm
(4) 82.21atm
41. Identify the correct statement(s)
I - Average translational kinetic energy is
independent of the amount of the gas.
II - If a gas expands at constant temperature,
it indicates that pressure of the gas
increases :
III- If temperature of gas is increased from T
K to 2T K then pressure of gas increases to
double value in a constant volume container.
(1) I, II and III
(2) I and III
(3) II and III
(4) & and &&
42. Distribution of molecules with velocity is
represented by the curve as shown.
Velocity at point A is :
(1)3RT
M
(2)2RT
M
(3)8RT
M'
(4)RT
M
43. Two chemically non-reactive gases are
contained separately in two bulbs of same
capacity at pressure P1 and P2 under similar
conditions respectively. If the two bulbs are
connected, the pressure of gaseous mixture
after some time would be :
(1) equal to (P1 + P2)
(2) greater than (P1 + P2)
(3) less than (P1 + P2)
(4) Cannot be predicted
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44. Two glass bulbs A (of 100 mL capacity), and
B (of 150 mL capacity) containing same gas
are connected by a small tube of negligible
volume. At particular temperature the
pressure in A was found to be 20 times more
than that in bulb B. The stopcock is opened
without changing the temperature. The
pressure in A will
(1) drop by 75%
(2) drop by 57%
(3) drop by 25%
(4) will remain same
45. A vessel initially contains two gases A and B
in the mass ratio 2 : 1 respectively. If the
above gas mixture is allowed to effuse
through a hole, the molar composition of the
mixture coming initially out of the hole
is 1 : 4.
Find the ratio of the moles of gases A and B
present in the vessel in the beginning
respectively :
(1) 1 : 2
(2) 8 : 1
(3) 2 : 1
(4) 1 : 8
46. The IUPAC name of the compound
is :
(1) 3,3-dimethyl-1-hydroxy cyclohexane
(2) 1, 1 – dimethyl –3 –hydroxy cyclohexane
(3) 3,3-dimethyl-1-cyclohexanol
(4) 1,1-dimethyl-3-cyclohexanol
47. The correct IUPAC name of the compound
is-
3
3 2 2 3
3 2 2 2 2 3
CH|
CH – –|
CH CH – –
(
(1) 5,6-diethyl-8-methyldec-6-ene
(2) 5,6-diethyl-3-methyldec-4-ene
(3) 6-butyl-5-ethyl-3-methyl-oct-4-ene
(4) 2,4,5-triethyl-3-ene
48. Which of the following pairs of structures do
not represent isomers –
(1) and
(2) and
(3) and
(4) and
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49. Which of the following pairs of compounds
are ring-chain isomers ?
(1) Propene and cyclopropene
(2) 1-Propanol and methoxyethane
(3) 1-Propanol and epoxypropane
(4) Propene and cyclopropane
50. Which one of the following has the regular
tetrahedral structure?
(Atomic nos. : B = 5, S = 16, Xe = 54)
(1)4BF
)
(2) SF4
(3) XeF4
(4) XeO2F4
51. Which of the following is wrong -
(1) NH3 < PH3 < AsH3 * Acidic character
(2) Li < Be < B < C * IE1
(3) Al2O3 < MgO < Na2O < K2O * Basic
character
(4) Li+ < Na+ < K+ < Cs+ * Ionic radius
52. Which of the following is correct statement ?
(1) SO2 is anhydride of sulphuric acid
(2) NO2 is anhydride of nitric acid
(3) Cl2O7 is anhydride of perchloric acid
(4) N2O is anhydride of nitrous acid
53. Which of the following statement is not
correct -
(1) 3CH+
shows sp2-hybridisation whereas
3CH
,
shows sp3-hybridisation
(2) 4NH+
has a regular tetrahedral geometry
(3) sp2-hybridised orbitals have equal s and
p character
(4) Hybridisation orbitals always form
--bonds
54. A molecule which can not exist theoretically
is:
(1) SF4
(2) OF2
(3) OF4
(4) O2F2
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55. IUPAC name of the compound
is
(1) 2-Ethanoyl oxy-3-methoxycarbonyl
cyclopropane carboxylic acid
(2) 2-Methoxycarbonyl-3-ethanoyloxy
cyclopropane carboxylic acid
(3) Methyl-2-carboxy-3-ethanoyloxy
cyclopropane carboxylate
(4) 2-Methoxycarbonyl-3-carboxy cyclopropyl
ethanoate
56. The minimum number of carbon atoms in an
alkane, alkene and alkyne with one smallest
side chain is given by the set
(1) 3, 4, 5
(2) 4, 4, 5
(3) 4, 5, 5,
(4) 4, 6, 4
57. Alkane that give only one alkyl-chloride upon
reaction with chlorine inpresence of light.
(1) (2)
(3) (4)
58. In P4, P
4O
6 and P
4O
10 have how many -
bonds respectively?
(1) 12, 6, 16
(2) 16, 6, 12
(3) 6, 12, 16
(4) 16, 16, 12
59. Correct order of bond angle in CH2F2
(1) H C H > H C F > F C F
(2) F C F > H C F > H C H
(3) H C H > F C F > H C F
(4) H C F > F C F > H C H
60. Number of S –S bond in H2SxO6
(1) x
(2) (x – 1)
(3) x – 2
(4) x + 1
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Space for Rough Work
PART – C
SECTION - I
Straight Objective Type
This section contains 30 multiple choice questions.
Each question has 4 choices (1), (2), (3) and (4) for
its answer, out of which ONLY ONE is correct.
61. Let A = {1, 2, 3, 4, 5}; B = {2, 3, 6, 7}. Then
the number of elements in (A ! (B
is
(1) 18 (2) 6
(3) 4 (4) 0
62. x a y(log a .log y. log z)
x is equal to
(1) x
(2) y
(3) z
(4) None of these
63. If p, q, r, s "R then equation
(x2 + px + 3q) ( –x
2 + r x + q) ( –x
2 + sx –2q)= 0
has
(1) 6 real roots
(2) At least two real roots
(3) 2 real and 4 imaginary roots
(4) 4 real and 2 imaginary roots
64. The roots of the equation ix2 – 4x – 4i = 0 are
(1) –2i
(2) 2i
(3) –
2i, –
2i
(4) 2i, 2i
65 . If graph of y = ax2 + bx + c is as shown
below, then which of the following options
is/are true ?
(1)bc
2a =
bc
2a
(2)b
2a
# =
b
2a
(3)2b 4ac
a
## =
2b 4ac
a
##
(4)2b 4ac
a
## =
2b 4ac
a
#
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Space for Rough Work
66. If both roots of x2 – 2ax + a
2 + a – 2 = 0 are
less than 2, then 'a' lies in interval -
(1) (1, 2)
(2) ( –$, 1)
(3) (2, $)
(4) [1, 2]
67. The sum of the cubes of the roots of
the equation, x3 # p x2 + qx # r = 0 is
(1) p3 + 3pq – 3r
(2) p3 + 3pq + 3r
(3) p3 – 3pq – 3 r
(4) p3 – 3pq + 3r
68. sin 36° sin ° sin ° sin °
(1) 1/4
(2) 1/16
(3) 3/4
(4) 5/16
69. If cos% + cos& = a, sin% + sin& = b and
% – & = 2' thencos3
cos
''
=
(1) a2 + b
2 – 2 (2) a
2 + b
2 – 3
(3) 3 – a2
– b2
(4) 2 – a2
– b2
70. Ifx
cos' =
y
2cos
3
() *'+, -. /
=z
2cos –
3
() *', -. /
, then
x + y + z is
(1) – 1
(2) 0
(3) 1
(4) 2
71. If tanA =3
4 and A lies in third
quadrant thensin A cos A
cotA
+ is equal to
(1)20
21
#
(2)21
20
#
(3)20
21
(4) 2120
72. The minimum value of 3 cosx + 4 sinx + 8 is
(1) 5
(2) 9
(3) 7
(4) 3
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Space for Rough Work
73. If 2 5 7 6 a 4 5 6 b is divisible by 15 then
(1) a = 6 and b = 5
(2) a = 4 and b = 0
(3) a = 4 and b = 5
(4) a = 3 and b = 0
74. Ifx88 = 4096 then x is equal to
(1) 12/5
(2) 3/4
(3) 5/4
(4) 4/3
75. Greatest integer less than the number
lo g2 15 . log1/ 62. log31/ 6 is
(1) 4
(2) 3
(3) 2
(4) 1
76. The set of real value(s) of p for which
the equation,02x + 30+02x#30=px+ 6
has more than two solutions is :
(1) {0, 4}
(2) ( – 4, 4)
(3) R –{4, – 4, 0}
(4) {0}
77. If A = 1 + ra + r
2a + r
3a +.........$ and
B = 1 + rb + r
2b + r
3b +.......$, where 0 < r < 1
thena
b is equal to
(1) logB A
(2) log1 – B(1 – A)
(3) B –
B
A 1log
A
#) *, -. /
(4) None of these
78. If x =1 3 i
2
+, then the value of the
expression x4 – x
2 + 6x – 4, equals
(1) – 1 + 2 3 i
(2) 2 – 2 3 i
(3) 2 + 2 3 i
(4) None of these
79. The solution set of
10 3 5 2
24 3 5
(x – –
x (x –
+ ++
1 0 is
(1) ( –2, –1] 2 [1/2, 3)
(2) ( –2, – 1) 2 (1/2, 3)
(3) [ –2, –1] 2 [1/2, 3] 2 { –8}
(4) ( –2, –1] 2 [1/2, 3) 2 { –8}
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Space for Rough Work
80. Number of integral solution of equation
| |x –1| + 2 | 1 4, is/are
(1) 4
(2) 5
(3) 3
(4) 6
81. Solution set of the inequality
2x – – < 2x – 3 is
(1) x "5 –
– ,2
4 *-5 -56 /
(2) x "16 7
, 102
4 7+5 85 86 9
(3) x " [3, $)
(4) x " 3
,2
4 *$ -56 /
82. In the sequence a b b b c c c c c d d d d d d d
e e............. which alphabet comes at 50 th
position :
(1) f
(2) g
(3) h
(4) j
83. Sum to infinite terms of the series
2
3 –
5
6 +
8
12 –
11
24 .............is
(1)4
9
(2)2
9
(3)1
3
(4) none of these
84. If a, b, c are positive numbers then greatest
value of
bc ac ab
b c a c a ba b c
+ ++ + +
+ + is :
(1)1
3
(2)1
2
(3)1
4
(4) tending to infinite
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Space for Rough Work
85. If 2nd
, 5th, 11
th terms of an AP are in G.P. and
10th term is three more than thrice of 2
ndterm
then the sum of square of first 11 terms of the
AP is :
(1) 24252
(2)5841
4
(3)2277
2
(4)4563
4
86. If in a G.P. Sn = 1023, Tn = 512, T3 = 4 then
n =
(1) 8
(2) 9
(3) 10
(4) 11
87. Which of the following is not an equivalence
relation in Z:
(1) a R b : a + b is an even integer
(2) a R b : a – b is an even integer
(3) a R b : a < b
(4) a R b : a = b
88. 2 2
2 2
tan 4 – tan
1 – tan tan
' '' '
is equal to
(1) cot ' cot 7 '
(2) tan7 ' tan '
(3) tan3
2
' tan2 '
(4) cot3
2
'cot
2 '
89. If relation R is defined as R =x 1 x –
,2 2
; +) *