EXAM:- KEAM MODEL (TEST 1)

DATE:-20- 04-2024
NUMBER OF QUESTIONS :-150
MARKS OUT OF:-600
TIME:- 3 Hrs

Attempt all questions

PHYSICS 8. In a moving coil galvanometer, the deflection of

1. Four equal resistances each of 20 ohm form four the coil  is related to the electric current i by
sides of a square. The resistance between two the relation
opposite corners is a) i  tan  b) i c) i2
a) 50 ohm b) 10 ohm c) 15 ohm
d) i  e) i3/2
d) 20 ohm e) 40 ohm
9. Two magnets of same mass and same linear
2. A beam of light strikes a piece of glass at an
dimensions but of moments m1 and m2 make 30
angle of incidence 60o. It is found that reflected
oscillations/mt and 40 oscillations/mt at a place.
rays is completely plane polarized. The
Then the ratio of the magnetic moments is
refractive index of glass is
a) 1:1 b) 2:3 c) 3:2
a) 1.414 b) 1.5 c) 1.62
d) 9:4 e) 9:16
d) 1.732 e) 2.1
10. Effective resistance when R and R/4 are in
3. A double convex air bubble in water will act as
parallel is
a
a) R b) R/2 c) R/3
a) convex lens b) concave lens
d) R/4 e) R/5
c) plane slab d) concave mirror
11. The shortest wave length in Lyman series is
e) any of these
a) 31m Ao b) 912 Ao c) 1215 Ao
4. A parallel plate air capacitor has a capacity of 4
d) 6563 Ao e) 216 Ao
f. If a dielectric of dielectric constant 4 is
12. The length of the second hand in a watch is 1
filled between the plates the new capacity is
cm. The change in velocity of its tip in 30
1
a) f b) 1f c) 4f seconds is
4
 
d) 16f e) 64 f a) zero b) cm / s c) cm / s
15 30
5. Two positive charges 20 C and 80 C are
 
placed at a distance of 0.6 m from each other. d) 2 cm / s e) 2 cm / s
30 60
The distance/s from 20 C where electric field 13. Two projectiles are thrown with same velocity
intensities are equal is but at angles 30o and 60o with the horizontal.
a) 0.3 m b) 0.4 m c) 0.2 m The ratio of their maximum height is
d) 0.6 m e) 0.1 m
a) 1:3 b) 3:1 c) 1: 3
6. In series CR circuit current leads the voltage by
an angle 45o. The ratio of capacitive reactance d) 3 : 1 e) 1:9
to resistance is 14. A car travels 6 km/h northwards in 1 hour and
a) 1:1 b) 1:2 c) 4: turns left and travels with a speed 8 km/h for
d) :1 e) 1 :4 next one hour. Then the average velocity for
the whole journey is
7. The two coils, primary and secondary in an
a)10 Km/h east wards
ideal transformer have the following constant or b) 5 km/h east wards
same c) 5 km/h 37o north of west
d) 5 km/h 53o north of west
a) power b) frequency
e) none of these
c) flux per turn d) all of these 15. A body starts from rest and has an acceleration
e) none of these 1m/s2. After travelling for some distance it
experience a retardation of 2m/s2. If the total

1 LEARNERS ACADEMY MANJERI & KOTTAKKAL

 time taken for the whole journey is 3 second, 24. Two waves having amplitude in the ratio 1:8
the total distance covered is produce interference. The ratio of maximum to
a) 3m b) 9m c) 12m minimum intensity is equal to
d) 15m e) 18m a) 81:7 b) 81:1 c) 49:1
16. If the velocity of light c, the constant of d) 1:49 e) 81:49
gravitation G and Plank’s constant h be chosen 25. For the circuit shown in figure, the maximum
as fundamental units, the dimensions of energy and minimum values of zener diode current is
is 
k

a) h1/2 b) h-1/2 c1/2 G1/2

1/2 5/2 -1/2
c) h c G d) h1/2 c5/2 G1/2 V 
k
V
e)h C G
17. If the KE of a body is increased by 200%. Its a) 2mA & 9mA b) 9 mA & 9 mA
momentum will increases by c) 9 mA & 1m A
a) 50% b) 44.4% c) 73.2% d) 14mA & 5mA e) 6mA & 1mA
d) 100 % e) 200 % 26. The transverse displacement of a string fixed at
18. The weight of a body at the centre of the earth is
 2x 
a) zero b) infinite both ends is given by y=0.06 Sin   cos
 3 
c) slightly less than at the poles
d) slightly less than that at the equator (120t) where x and y are in metres and t is in
e) none of these seconds. The length of the string is 1.5 m and
19. The moment of inertia of a straight thin rod its mass is 30g. the tension in the string is
about an axis perpendicular to its length and a) 516 b) 648N c) 712 N
passing through the centre is 200 gm – cm2. d) 13 N e) 916 N
Then its moment of inertia about an axis 27. A ball of mass m moving with a velocity v hits
perpendicular to its length and passing through another ball of mass 2m at rest. Assuming the
one end is collision to the elastic the fraction of loss of KE
a) 200 gm – cm2 b) 600 gm-cm2 for mass m is
c) 800 gm – cm2 d) 1200 gm – cm2 1 8 2
a) b) c) 1 d) e)0
e) 1500 gm-cm2 9 9 9
20. The dimensional formula for stressstrain is 28. A vertical wire carries a current in upward
a) MLT-2 b) ML2 T-2 c) ML-1T-2 direction. An electron beam sent horizontally
d) M2 L-2 T-2 e) ML2 T-1 towards the wire will be deflected
21. If one mole of monoatomic gas (r = 5/3) is a) towards right b) towards left
mixed with one mole of diatomic gas c) upwards d) downwards
(r =7/5), the value of Cp is given by e) none of these
a) R b) 2R c) 3R 29. An alternating current is given by
d) 4R e) 5 R i = i1coswt + i2sin wt. The rms current is given
22. Water falls from a height 42 m. assuming that by
all the energy is used in heating the water, the i1  i 2 | i1  i 2 | i12  i 22
a) b) c)
rise in temperature of water will be 2 2 2
a) 0.1oC b) 0.01oC c) 0.2oC
i12  i 2
d) 1oC e) 10oC d) e) none of these
2
23. The equation of motion for a body executing
30. Planck’s constant has the dimension of
SHM is given by y = 1.5 sin(100t + 5). The
a) force  time b)force  distance
frequency is given by
c) distance  time
a) 0 b) 25 Hz c) 50 Hz
d) force  distance  time
d) 100 Hz e) 200 Hz
e) power  time
2 LEARNERS ACADEMY MANJERI & KOTTAKKAL
31. The minimum orbital angular momentum of the capillary tube, the potential energy of this mass
electron in a hydrogen atom is of the liquid in the tube is
a) mgh b) mgh/2 c) mgh/4
a) h b) 2h
d) mgh/8 e) mgh/6
c) h/2 39. Two rods of different materials having
h coefficient of linear expansion 1 and 2 and
d) h/2 e)
4 Young’s modulii Y1 and Y2 are fixed between
32. The ratio of dimensional formula of energy and two rigid massive walls. The rods are heated to
moment of inertia is the same temperature. If there is no bending of
a) MLT-2 b) T-2 c) M-1L2T2 the rods. The thermal stress developed in them
d) T2 e) L-2 are equal provided
 
33. If a & b and two nonzero coplanar vectors Y  Y  1 Y12
  a) 1  1 b) 1  2 c) 
ab Y2  2 Y2  1  2 Y22
is
ab sin  12 Y1
a) is always a unit vector d)  e) independent of 1& 2
 22 Y2
b) is some times a unit vector
40. A source of heat supplies heat a constant rate to
c) will never be a unit vector
a solid cube. The variation of the temperature of
d) is a pseudo scalar e) none of these
the cube with heat supplied is shown in figure.
34. A person throws a stone so as to have maximum
Slope of the curve AB represents
range. Maximum height attained during that
flight is 25m. The greatest height to which he F
can thrown the stone is D
a) 12.5 m b) 25m c) 50m Temp E
d) 100m e) can not be calculated B
 C
35. A force F  3î  4 ˆj  5k̂ newton applied on the
body gives an acceleration of 1 m/s2. The mass A Heat
a
of the body is a) specific heat capacity t
a) 5kg b) 2.5 kg c) 5 2 kg b) heat capacity H
c) latent
heat
d) 10 kg e) 3 kg d) reciprocal of heat capacity
36. Two discs of moments of inertia I1 and I2 about e) none of these
their respective axes, rotating with angular 41. During an adiabatic compression of 5 moles of
frequencies w1 and w2 respectively are brought gas, 250J of work was done. The change in
into contact face to face with their axes of internal energy is
rotation coincident. The angular frequencies of a) 0 b) 50J c) 100J
composite disc will be d) 250J e) 1250J
I1 w1  I 2 w2 I w I w 42. The electric potential V in volt varies with x (in
a) b) 1 1 2 2
I1  I 2 I1  I 2
metre) according to the relation V = 5+4x2.The
I 2 w1  I1 w2 I w I w
c) d) 2 2 1 1 force experienced by a negative charge of 210-
I1  I 2 I 2  I1
6
e) none of these C located at x = 0.5 m is
B2 a) 110-6N b) 210-6N c) 410-6N
37. The dimension of is
0
-2 2 -2 2 -3
d) 610-6N e) 810-6N
a) MLT b) ML T c) ML T
-1 -2
d) ML T e) M L T 2 -2 +2 43. To obtain a P type semiconductor, it must be
38. When a capillary tube of radius r is immersed in doped with
a liquid of density , the liquid rises to a height a) arsenic b) antimony c) indium
h in it. If m is the mass of the liquid in the
3 LEARNERS ACADEMY MANJERI & KOTTAKKAL
 d) phosphorus e) all of these e) O 2 and O 2
44. The energy of the electron of hydrogen orbiting 54. According to VSEPR theory, the shape of IF4 is
on a stationary orbit of radius rn is proportional expected to be
to a) octahedral b) square-planar
a) rn b) 1/rn c) rn2 c) sea-saw shaped
d) 1 / rn2 e) rn 1 / 2 d) square pyramidal
e) tetrahedral
45. Monochromatic light is refracted from air into
55. RCHO + NaHSO3  RCH(OH)SO3Na is an
glass of refractive index . The ratio of
example for
wavelength of the incident and refracted wave is
a) electrophilic addition
a) 1:1 b) 1: c) :1
b) free radical addition
d)  :1
2
e) 1: 2
c) nucleophilic addition
CHEMISTRY
d) coupling reaction
46. The element whose atom has a mass of 6.6410-
27 e) condensation reaction
kg is
56. IUPAC name of CH3COOCOC6H5 is
a) C b) Ca c) O
a) acetic benzoic anhydride
d) He e) S
b) acetyl benzoate
47. The volume of water to be added to convert 600
c) ethanoic benzoic anhydride
mL of 0.2 M H2SO4 into 0.3 N H2SO4 is
d) benzoyl acetate
a) 400 mL b) 200 mL c) 800 mL
e) benzoic ethanoic anhydride
d) 300 mL e) 500 mL
48. By Bohr theory results, the velocity of electron in 57. ‘Acetal’ form of glucose corresponds to the
the K-shell of H-atom is about  times the compound/structure
velocity of light a) ring form of glucose
a) 7.310-1 b) 7.310-2 c) 7.3103 b) monomethyl glucoside
d) 7.310-4 e) 7.310-3 c) glucose pentaacetate
49. Li+ is isoelectronic with d) glucofuranose
a) H 2 b) H c) H 2 e) mannose
d) Be+ e) both (b) and (d) 58. The d and p orbitals involved in the dsp2
50. The group to which rhenium belongs is hybridization are
a) 4 b) 5 c) 6
d) 7 e) 8 a) d z 2 , p x and py b)dxy , px and py
51. A reaction of the type, c) d x 2  y 2 , px and pz d) d x 2  y 2 , px and py
CH3Br + AgF  CH3F+AgBr, is known as
e) dxy, py and pz
a) Finkelstein reaction
b) Swarts reaction 59. Tollen’s reagent is reduced to metallic silver by
c) Schmidt reaction
a) glucose b) fructose
d) Balz-Schiemann reaction
e) Wurtz reaction c) formic acid d) all these
52. The ratio of kinetic energy and total energy of e) only (a) and (c)
electron in a Bohr orbit of hydrogen atom is 60. Reduction of nitrobenzene with zinc and alkali
1
a) b) 1 gives
2
c) zero a) hydrazobenzene
3
d) 1 e) b) azobenzene c) azoxybenzene
2 d) phenylhydroxylamine
53. The number of unpaired electrons is the same in
e) p-aminophenol
the pair
61. In the disproportionation reaction
a) O2 and N2 b) O 2 and F2
c) O 22 and N 2 d) O 22 and O 2
4 LEARNERS ACADEMY MANJERI & KOTTAKKAL
 3HClO3  HClO4 + Cl2 + 2O2 + H2O, the c) 625 104 Sm2 mol1
equivalent mass of the oxidising agent is (molar d) 62.5 Sm2 mol1 e) 0.625
mass of HClO3 = 84.45) 69. The outer electrons configurations of Gd (At
a) 16.89 b) 32.22 no.64) is
c) 84.45 d) 28.15 a) 4f3 5d5 6s2 b) 4f8 5d0 6s2
e) 29.7 c) 4f4 5d4 6s2 d) 4f7 5d1 6s2
62. Which transition in the hydrogen atomic
spectrum will have the same wavelength as the e ) 4f8 5d1 6s2
transition, n = 4 to n= 2 of He2+ spectrum? 70. The primary and secondary valencies of
a) n = 4 to n =3 b) n = 3 to n = 2 chromium is the complex ion,
c) n= 4 to n = 2 d) n = 3 to n = 1 dichlorodioxalatochromium (III), are
e) n = 2 to n = 1 respectively
63. Which of the following sets of quantum a) 3,4 b) 4, 3
numbers represents the highest energy of an c) 3, 6 d) 6,3 e) 4, 4
atom? 71. In the chemical reactions
a) n  3, .l  1, m  1, s  1 / 2
b) n= 3, l = 2 , m = 1, s = + 1/2
c) n = 4, l = 0, m = 0 s = + 1/2
d) n = 3, l = 0, m = 0, s = +1/2 the compound, ‘A’ and ‘B’ respectively are
e) n = 3, l = 1, m = 0, s = +1/2 a) nitrobenzene and fluorobenzene
64. Four moles of PCl5 are heated in a closed 4dm3 b) phenol and benzene
container to reach equilibrium at 400K. At c) benzene diazonium chloride and
equilibrium 50% of PCl5 is dissociated. What is fluorobenzene
the value of Kc for the dissociation of PCl5 into d) nitrobenzene and chlorobenzene
PCl3 and Cl2 at 400 K? e) Nitro benzene and phenol
a) 0.50 b) 1.00 c) 0.25 72. In the reaction
d) 0.05 e) 0. 25
65. A weak monobasic acid is 1% ionised in 0.1M
solution at 250C. The percentage of ionization in HBr

 the products are,
its 0.025 M solution is
a) 1 b) 2 c) 3
d) 4 e) 5
66. Arrange the carbanions ,
CH 3 3 C, CCl3 , CH 3 2 CH, C6H5 CH2 , in order of
their decreasing stability
a) C6 H5 CH2  CCl 3  (CH 3 ) 2 C  CH 3 2 CH
b) CH 3 2 CH  CCl 3  C6 H5CH 2  CH 3 3 C e) None of these
c) CCl 3  C6 H5CH 2  CH 3 2 CH  CH 3 3 C 73. Which of the following on heating with aqueous
KOH, produces acetaldehyde ?
d) CH 3 3 C  CH 3 2 CH  CH2  CCl 3
a) CH3COCl b) CH3CH2Cl
e)𝐶6 𝐻5 𝐶 𝐻2 > (𝐶𝐻3 )2 𝐶 > 𝐶 𝐶𝑙3 > (𝐶𝐻3 )2 𝐶 𝐻 c) CH2ClCH2Cl d) CH3CHCl2
67. Identify the compound that exhibits tautomerism e) CH3Cl2
a) 2-butene b) lactic acid 74. Trichloroacetaldehyde was subjected to
c) 2-pentanone d) phenol
Cannizaro’s reaction by using NaOH. The
e) 2-butyne
68. Resistance of 0.2M solution of an mixture of the products contains sodium
electrolyte is 50 .The specific trichloroacetate ion and another compound.
conductance of the solution is 1.3Sm1.If The other compound is
resistance of the 0.4M solution of the same a) 2,2,2-trichlorethanol
electrolyte is 260,its molar conductivity is b) trichloromethanol
a)6250 Sm2 mol1 c) 2,2,2-trichloropropanol
b) 6.25  104 Sm2 mol1 d) chloroform e)2,2,2- trichloromethanol

5 LEARNERS ACADEMY MANJERI & KOTTAKKAL

75. The strongest acid amongst the following 13
d) e) none of these
compounds is 36
a) CH3COOH b)HCOOH 84. The area bounded by the curves y = 2x – x2 and y
c) CH3CH2CH(Cl)CO2H = x is
9 
d) ClCH2CH2CH2COOH a) 9 b) c)
e) ClCH2CH2COOH 2 2
1
d) e) 0
2
MATHEMATICS
85. If z = cos  + i sin, then  z 2  2   z 2  2  =
1 1
 1 1 1 
76. Lt    .......  =  z  z 
n 
 4n  1 3n 
2 2 2 2
4n  2 a) 1 b) cos 2  + i sin 2 
a) 0 b) 1 c) /3 c) 2 cos 4  d) 4 cos 4 
d) /6 e) 2/3 e) 2 i sin 4 
77. The chance of throwing a total of 3 or 5 or 11 86. For the AP. a1, a2, a3, -----a40,
with two dice is a1 + a5 + a15 + a26 + a36 + a40 = 105. the sum of the
5 1 2 AP is
a) b) c)
36 9 9 a) 700 b) 1400 c) 630
19 d) 740 e) none of these
d) e) none of these 1
36
2 x 1 e x 1
2x 87. Lt =
78. Lt   = x 0 1
x   1 x  ex 1
e 2 a) 1 b) +1 c) 0
a) e b) e2 c) d)  e) does not exist
2
1
3e
d) e) none of these    x
2 88. Lt  tan  x  =
79. The fundamental period of the function
x 0
 4 
1
1 a) e b) e2 c) e 2
f(x) = 2 sin (x) is
3 1
a) 6  b) 4  c) 2  d)
e2
e) none of these
d)  e) none of these 89. 10 men and 10 women are to sit around a table so
2 d2y that men and women sit alternatively. The
80. If x = at , y = 2at, then 2 =
dt number of ways of seating is
1 1 a) (10!)2 b) (9!)2 c) 10!  9!
a)  3 b) 3 c) 0
2at t d) 10!  8! e) none of these
d) 2a e) none of these 90. If y = a cos (log x) + b sin (logx), then
10
d2y dy
81.  x  [x] dx =
0
x2
dx 2
+ x
dx
+y=

a) 10 b) 5 c) 0 a) 0 b) 1 c) 2
5 d) x e) none of these
d) e) none of these dy y
2 91. If xy = (x+y)n and  , then n =
2 dx x
x sin 100 x
82.  sin 100 x  cos100 x
dx  a) 1 b) 2 c) 3
0 d) 4 e) none of these
  92. If f(x) = log |x-1|, x 1, then f1(½) =
a) b) c) 2
4 2 a) 1 b) 2 c) 1
2 d) 2 e) none of these
d) e) none of these
4 93. log tan 1 + log tan 20 + log tan 30 + ------+ log
0

83. The probability of getting multiple of 2 on one tan 890 is

and multiple of 3 on the other in a single throw of a) 1 b)
1
c) 0
two dice is 2
a)
12
b)
11
c)
1 d) 1 e) none of these
36 36 36
6 LEARNERS ACADEMY MANJERI & KOTTAKKAL
 b a) (4,1) b) (1,2) c) (1,2)
94. If tan x = , then the value of
a d) (4,1) e) none of these
a cos 2x + b sin 2x is 106. The orthocentre of the triangle whose vertices
a) a b) ab c) a+b are (5,2), (1,2) and (1,4) is
a)  ,  b)  ,  c)  , 
d) b e) none of these 1 14 14 1 1 1
95. The value of sin (8700) is 5 5   5 5 5 5
1 1 d) (1,4) e) none of these
a) b) c) 1
2 2 107. The radius of the circle passing through the
1 point P(6,2), two of whose diameters are x+y=6
d)  e) none of these and x+2y = 4 is
2
96. If x = sin6 + cos6, then x belongs to the interval a) 10 b) 2 5 c) 6
for all real  is d) 4 e) none of these
108. If the line 2x y+k = 0 is a diameter of the
a)  ,  b)  ,  c)  ,1
3 5 1 3 1
4 4 2 4 4  circle x2 + y2 + 6x  6y + 5 = 0, then k =
97. The sum of n terms of two AP’s are in the ratio of a) 6 b) 9 c) 12
(7n+1): (4n+27). The ratio of their 11th terms is d) 6 e) 9
a) 2:3 b) 4:3 c) 5:4 109. If sinx +sin2x = 1, then the value of cos4x +
d) 5:6 e) none of these cos2x is
98. If n+2C8 : n  2P4 = 57: 16, then n = a) 1 b) 1 c) 0
a) 19 b) 18 c) 16 d) 2 e) none of these
d) 17 e) none of these 110. In a right angled triangle ABC,
dy cos2A + cos2B + cos2C =
99. If y = sin1x + sin1 1  x 2 , then =
dx a) 2 b) 3 c) 3
a) 0 b) x c) 1 x2 d) 1 e) none of these
2  sin 2x 2
d) e) none of these   e x , x  0
111. If the function f(x) =  x 2 is
1 x2
K ,x 0
100. If x sin  = y cos , then 
x y continous, then K is
 =
sec  cos ec 2 
2 a) 2 b) 3 c) 4
a) x b) y c) xy d) 5 e) none of these
d) x+y e) 1
101. The minimum value of cos (cos x) is 112. The function f(x) = xex (x  R) attains a
a) x b) cos 1 c) cos 1 maximum value at x =
d) 1 e) none of these a) 2 b)
1
c) 1
102. The term independent of x in the expansion of e
6 d) 3 e) none of these
 3
 2x   is 3
 x 113. If sin1x + sin1y + sin1z = , then
2
a) 4320 b) 216 c) 216 9
d) 4320 e) none of these x100 + y100 + z100  =
x 101
 y101  z101
103. The coefficient of x in the expansion of
(1+3x+8x2)10 is a) 1 b) 2 c) 0
a) 10 b) 40 c) 50 d) 1 e) none of these
114. If sin  sin 1  cos1 x  = 1, then x =
d) 70 e) none of these 1
104. The point (a,0), (0,b), (1,1) are collinear if  5 
1 1 1 1 1
a)  = 1 b)  = 1 a) 0 b) 1 c)
a b a b 5
1 1 1 4
c) 1 = 0 d)  = 1 d) e) none of these
ab a b 5
e) none of these 115. If a,b,c are in AP, then (a+2bc)(2b+ca)
e) none of these (c+ab) =
105. The image of the point (2,1) with respect to the
line mirror x+y5 = 0 is
7 LEARNERS ACADEMY MANJERI & KOTTAKKAL
 a)
1
abc b) abc c) 2abc

  
r  4î  ĵ   î  2 ĵ  3k̂ 
2
d) 4abc e) none of these

  
and r  î  ĵ  2k̂   2î  4 ĵ  5k̂ is 
116. There are 10 lamps in a hall. Each one of them 5 1 6
a) b) c)
can be switched on independently. The number of 6 6 5
ways in which the hall can be illuminated is 1
d) e) none of these
a) 102 b) 1024 c) 1023 5
11
d) 2 e) none of these 127.The length of perpendicular from (1,6,3) to the
 x n  x n 
1   then f1(1) = x y 1 z2
117. If f(x) = cot line = = is
 2  1 2 3
a) log 2 b) log 2 c) n a) 3 b) 11 c) 13
d) n e) none of these d) 5 e) 7
118. If y = ax +
a2
, then
dy
at x = a is 128.If a line makes angle , ,  with X, Y and Z the
ax dx axes respectively, then cos 2  + cos
a) a b) 0 c) 1 2  + cos 2  =
d) 1 e) none of these a) 2 b) 1 c) 1
119. Let R1 = {(x,y) : x2 + y2 = 1, x,y R} then R1 is d) 2 e) 0
a) reflexive b) symmetric x2 y3 z4 x 1
129.The lines = = and =
c) transitive d) anti-symmetric 1 1 k k
e) none of these y4 z5
= are co-planar if
1 2 1
120. The expansion of is valid for
1  3x a) k = 1 or 1 b) k = 0 or +3
1 c) k = 3 or 3 d) k = 0 or 1
a) | x | > 1 b) | x | 
3 e) none of these
1 1 130.Solution of the DE y(1+ex)dy = (y+1)ex dx
c) | x | > d) | x | < is
3 3
e) none of these ey ey
a) = c(ex+1) b) = c ex
121. The number of roots of 3| x | |2 | x || = 1 is| y 1 y 1
a) 1 b) 2 c) 3 ey
d) 4 e) none of these c) ey = c(ex+1) d) = c(ex+1)
y
122. If z = 1 + i 3 and n is a natural
e) none of these
number but not a multiple of 3, then z2n+2n zn +
131.Solution of the D.E (x+y1)dy = (x+y)dx is
22n =
a) 2(y+x)  log (2x + 2y1) = c
a) 0 b) 1 c) 1
b) 2(y-x)  log (2x+y1) = c
d) 3 e) none of these c) 2(y-x)  log (2x+2y1) = c
123. If w is a complex x cube root of unity, then d) 2(y-x) + log (2x+2y1) = c
(1+w) (1+w2)(1+w4)(1w6) (1+w8) = e) none of these
a) 3 b) 3 c) 9
132.Solution of the D.E x sin  dy =
y
d) 1 e) none of these
x
124. If the mean of numbers 27 +x, 31+x, 89+x,
 y 
107+x, 156+x is 82, then the mean of 130+x,  y sin    x dx is
126+x, 68+x, 50+x, 1+x is  x 
a) 75 b) 75 + x c) 68 + x y y
a) log(cx) = cos   b) log x = sec  
d) 82 e) none of these x x
125. The plane XOZ devides the join of (1,1,5) and c) log cx = sin (y/x)
(2,3,4) in the ratio  : 1, then  = d) log (xc) = cosec (y/x) e) none of these.
a) 3 b) 
1
c) 3 dy xy  y
133.Solution of = is
3 dx xy  x
1
d) e) none of these  cx   cx 
3 a) y = x  log   b) y = x + log  
126. The shortest distance between the lines  y   y 

8 LEARNERS ACADEMY MANJERI & KOTTAKKAL

  cx   cx  a) 1 b) 2 c) 0 d) 1 e) 2
c) y = x2  log   d) x+y = log  
 y   y  142. The middle term in the expansion of
2n
e) none of these  2 1 
134.If A is a non-singular square matrix of order 3 x  2  is
 x 
then |adj(A3)| = 1
2n 2n 2n
a) |A|8 b) |A| 6 a) Cn b) C n x 2 n c) Cn
xn
c) |A| 9d) |A| 12
d) 2 n C n x n e) none of these
e) none of these
143. If the coefficient of x2 and x3 in the expansion of
135.The component of î  ĵ  2k̂ along 2î  ĵ  k̂ is
(3+ax)9 are the same, then the value of a is
a)
1
2

î  ĵ  2k̂ b)
1
2

2î  ĵ  k̂   a)
9
b)
7
c)
9
7 9 7
1
 1

c) î  ĵ  2k̂ d) 2î  ĵ  k̂
3 3
  d)
7
e) none of these
9
e) none of these
144. The vertices of a triangle are A(1,3) B(1,1)
136.The set B on to which the set A = {3,27} is and C(5,1). The equation of the median through
mapped by the function f(x) = log3x is A is
a) {0,3} b) {1,3} c) {1,4} a) 3x + 4y  9 = 0 b) x + 4y = 9
d) {0,1} e) none of these c) 3x  4y  9 = 0 d) x  4y  9 = 0
cot x e) none of these
137.  dx 
145. The image of the point (,) on the line
sin x
x + y = 0 is
2 2
a) C b) C a) (,) b) (,) c) (,)
sin x sin x d) (,) e) none of these
c) 2 sin x  C d)
1
C 146. An angle between the lines x  y = 0 and
2 sin x y = 0 is
e) none of these a) 30 b) 45 c) 60 d) 75 e) 90
1  x  x 2  (2x  1) 20 (3x  1) 50
138.  e tan
1
147. lim is
 dx 
x
 x  (3x  1) 70
 1 x 
2

a) 0 b) 1 c) 1 d) 2 e) none of these
 
1 1
a) e tan x
C b) x e tan C x

e x cos e x
e tan x
1
tan x 1
148.  dx 
c) C d) x2 1  x 2  C x
1 x2
e) none of these   1
a) sin e x  c b) sin e x  c
2
sin 8 x  cos8 x
139.  dx  c) 2 sin e  c d) 4 sin e x  c
x

1  2 sin 2 x cos2 x
e) none of these
sin2x + C b)sin2x+C 149. If a  b is at right angles to b and 2b  a is at
1 1
c)  sin 2x+C d)  cos 4x +C right angles to a then
2 2
a) a  2b b) a = 2b c) a = b
e) none of these
d) 2a = b e) none of these
140. The maximum value of 1  x  3x2, x  R is 150. An integrating factor of
13 1 dy y
a) 1 b) c) d) 3 e) none of these   x 3  3, x  0 is
12 3 dx x
141. If the numbers a,b,c,d,e form an A.P, then the a) x b) logx c) x
x
value of a  4b + 6c  4d + e = d) e e) none of these

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9 LEARNERS ACADEMY MANJERI & KOTTAKKAL