Kerala CEE Mock Test

Hello I want the mock test paper for the exam of Kerala CEE so kindly provide me the test paper as I want to do preparation please???

[Arun Vats]

Here I am providing require information for which you r looking here

Eligibility Criteria for the exam of CEE by Kerala.

Contenders who wish to apply should be an Indian citizen.

Persons of Indian Origin (PIO)/Overseas Citizen of India (OCI) Card Holders
will be treated on par with Indian citizens for the purpose of admission only.



As you are asking for the mock test paper for the Kerala CEE so here I posting the paper below.

1. Bohr's theory of hydrogen atom did not explain fully
A. diameter of H atom B. emission spectra
C. ionisation energy D. the fine structure of even hydrogen spectrum
2. A current loop placed in a non-uniform magnetic field experiences :
A. a force of repulsion B. a force of attraction
C. a torque but not force D. a force and a torque
3. For a heavily doped n-type semi-conductor, Fermi-level lies
A. a little below the conduction band B. a little above the valence band
C. a little inside the valence band D. at the centre of the band gap
4. Which of the following indicates that the galaxies are receding from us ?
A. Neutron Star B. White dwarf C. Black hole D. Red shift
5. What does it represents?
A. AND B. NAND
C. OR D. NOR
6. In a transistor, the relation between α and β is
A. β = α /(1 - α ) B. β = 1/(1 - α ) C. β = α /(1 + α ) D. β = 1 - α
7. In a transistor
A. there is 1 p-n junction B. there are 2 p-n junctions
C. there are 3 p-n junctions D. none of these
8. Germanium is doped with arsenic, what will be the result ?
A. p-type semi-conductor B. n-type semi-conductor
C. intrinsic semi-conductor D. none of these
9. An electron is moving in 1st orbit. The factor nh/2π is
A. It's Angular
momentum B. Energy C. Linear momentum D. None of these
10. The energy of an electron is
A. hc/λ B. hλ/c C. hv/c D. none of these
11. According to Bohr's Theory, electron moves around in those orbits only in which nh/2π is its
A. Impulse B. Angular momentum C. Force D. Kinetic Energy
12. Which of the following waves can produce photo-electric effect?
A. Ultra-sound B. Infra-red C. Radio-waves D. X-rays
13. A glass prism of µ = 1.5 is immersed in water as shown

in the figure. A beam of light incident normally on the face
ab is internally reflected from the face ad so as to incident
normally on face bd. Given that refractive index of glass is
3/2 and that of water is 4/3. What is the value of θ ?
A. θ > sin-1 (8/9) B. θ > sin-1 (2/3)
C. θ < sin-1 (2/3) D. none of these
14. If two lenses are kept coaxial together, then what will be their power?
A. R1 + R2 B. (R1 R2)/ (R1 + R2) C. (R1 + R2)/(R1 R2) D. none of these
15. The angular fringe-width does not depend upon
A. wavelength (λ ) B. distance between slits (d)
C. distance between slits and screen (D) D. ratio (λ /d)
16. In a double slit experiment, the distance between slits is increased ten times whereas their
distance from screen is halved, then what is the fringe-width?
A. remains same B. becomes 1/10 C. becomes 1/20 D. becomes 1/40
17. Which of the following electro-magnetic rays has maximum wavelength?
A. Radio waves B. X-rays C. Infra-red rays D. Ultra-violet rays
18. The resonant frequency is proportional to
A. R/LC B. 1/√ LC C. √ LC D. none of
these
19. The wave with wavelength of 10 cm lies in region of
A. Radio waves B. Micro-waves C. X-rays D. Infra-red rays
20. If L = 100µ H, current changes by 1 A in 0.1 second. What is the emf produced?
A. 1 mV B. 100 mV C. 10 mV D. 0.1 V
21. A magnetic needle is placed in a non -uniform magnetic field; which one is correct?
A. both force and torque act B. force but no torque
C. torque but no force D. none of these
22. In a circular coil of radius r the magnetic field at the centre is proportional to:
A. r2 B. r C. 1/r D. 1/r2
23. If two electron beams travel in the same direction, they will
A. attract each other B. repel each other C. nothing will happen D. none of these
24. One charge is moving along a circle in a
magnetic field B, mass = 105 kg, velocity = 1m/s,
magnetic field = 10-2 T, Q = 107 coulomb. What is
the radius of its circular tank?
A. 1m B. 0.1m C. 10m D. none of
these
25. If two resistors of resistances 2R and 3R are connected in parallel, then the heat produced in
them will be in the ratio
A. 3 : 2 B. 2 : 1 C. 1 : 4 D. 4 : 1
26. A graph is drawn with force along Y-axis & time along X-axis. The area under the graph
represents
A. momentum B. couple C. moment of the force D. impulse of the force
27. When a substance was heated, its conductivity increased. What should it be out of the
following?
A. Metal B. Insulator C. Semi-conductor D. Semi-metal
28. A mass is revolving in a circle which is in a plane of paper. The direction of tangential
acceleration is
A. upward to radius B. towards the radius
C. tangential D. at right angle to angular velocity
29. What is the potential at the center c ?
A. 0 B. Kq/a√2
C. √2 (Kq/a) D. none
30. Electric field lines are parallel to the plane face of a hemisphere, what is the total flux passing
through it
A. E.π r2/2 B. E.π r2/2E0
C. E.2π r2 D. 0
31. At Boyle's temperature,
A. Joules effect is positive B. b of Vander Waal's equation is zero
C. Gas obeys Boyle's law D. None of these
32. At 0 K which is true?
A. b of Vander Waal's equation becomes very
small B. all gases get liquified
C. metal become solidified D. the motion of gas molecules becomes zero
33. Calculate the work done if temperature is changed from 0°C to 200°C at 1 atmosphere (R = 2
cal K-1)
A. 100 calories B. 200 calories C. 400 calories D. 800 calories
34. If a Carnot's Engine functions at source
temperature 127°C and at a sink temperature 87°C,
what is its efficiency?
A. 10% B. 25% C. 40% D. 50%
35. Which is an intensive property?
A. Volume B. Mass C. Refractive index D. Weight
36. If a particle is travelling with a speed of 0.9 of the speed of sound and is emitting radiations
of frequency 1 kHz and moving towrads the observer, what is its apparent frequency?
A. 1.1 B. 0.8 C. 0.4 D. 10 kilohertz
37. In case of a transverse wave, frequency is proportional to:
A. √ T B. 1/T C. 1/√ T D. T
38. A string is tied on a sonometer. Second end is hanging downward through a pulley with
tension T. The velocity of the transverse wave produced is proportional to
A. 1/√ T B. √ T C. T D. 1/T
39. If the frequency of oscillations of a particle doing SHM is n, the frequency of K.E. is
A. 2n B. n C. n/2 D. none of these
40. The ratio of the terminal velocities of two drops
of radii R and R/2 is
A. 2 B. 1 C. 1/2 D. 4
41. If a mercury drop is divided into 8 equal parts, it's total energy
A. remains same B. becomes twice C. becomes half D. becomes 4 times
42. Strain energy per unit volume in a stretched string is
A. 1/2 (stress x strain) B. stress x strain C. (stress x strain)2 D. stress/strain
43. A satellite is revolving around earth. If it's height is increased to 4 times the height of geostationary
satellite, what will become its time period?
A. 8 days B. 4 days C. 2 days D. 16 days
44. When a body is lifted from surface of earth to a height equal to radius of earth, then the
change in its P.E. is
A. mgR B. 2 mgR C. 1/2 mgR D. 4 mgR
45. A body is projected from earth's surface to become its satellite, its time period of revolution
will not depend upon
A. mass of earth B. its own mass C. gravitational
constant D. radius of orbit
46. Moment of inertia depends upon
A. Axis of
rotation
B. Torque
applied
C. Angular
speed
D. Angular
momentum
47. What is not conserved in the case of celestial bodies revolving around sun?
A. Kinetic energy B. Mass C. Angular momentum D. Linear momentum
48. If a force acts on a body, whose action line does not pass through its centre of gravity, then
the body will experience
A. Angular acceleration B. Linear acceleration
C. No acceleration D. None of these
49. If a neutron collides with an alpha-particle, with velocity V, what is its resultant velocity?
A. 1/5 V B. 2/5 V C. 3/5 V D. 4/5 V
50. Momentum is closely related to
A. Force B. Impulse C. Velocity D. Kinetic Energy
51. In case of a uniform circular motion, velocity and acceleration are
A. Perpendicular B. Same direction C. Opposite direction D. Not related to each
other
52. An engine of power 7500W makes a train move
on a horizontal surface with constant velocity of 20
ms-1. The force involved in the problem is
A.375 N B.400 N C.500 N D.600 N
53. A person moves towards east for 5 km, then towards north for 12 km and then moves
vertically up by 13 km. What is his distance now from the origin?
A. 13 √ 2 B. 5 C. 10 D. 20
54. What is F . ds
A. Torque B. Impulse C. Momentum D. Work
55. Which one is not a dimensional constant?
A. Acceleration due to gravity B. Surface Tension of water
C. Velocity of light D. Reynold's Numer
56. Which of the following can measure the position of a particle most accurately?
A. polarized light B. light with high wavelength
C. light with low wavelength D. none of these
57. The dimension of Angular Momentum is
A. MLT-2 B. ML2T-1 C. ML2T-2 D. ML2T
58. The dimension of 'a' in Vander Waal's gas equation is?
A. Atom litre-2 mol2 B. Atom litre2 per mol C. Atom litre-1 mol-2 D. Atom litre2 mol-2
59. The dimension of Action is
A. M2LT-3 B. MLT-1 C. MLT-2 D. ML2T-1
60. Photos get stuck on perfectly easily on reflecting surfaces because:
A. sticking area is more because of smoothness of reflecting surfaces
B. vacuum gets created between photo and reflecting surface
C. reflecting surfaces are warm surfaces
D. glue sticks nicely on reflecting surfaces
61. When oxalic acid crystals are heated with phosphorus pentaoxide, we get
A. vapours
of
phosphorus
trioxide
B. carbon
monoxide
C. carbon
dioxide and
water
vapours
D. carbon
monoxide
and carbon
dioxide
62. When very dilute nitric acid acts on magnesium, it gives rise to
A. ammonia B. nitrous oxide C. hydrogen D. nitric oxide
63. The general formula for alkene is
A. CnH2n + 2 B. CnH2n - 2 C. CnH2n D. CnHn
64. The coloured discharge tubes for advertisements contain
A. Argon B. Xenon C. Helium D. Neon
65. While preparing Cl2 from HCl, MnO2 acts as a/an
A. dehydrating agent B. reducing agent C. catalytic agent D. oxidising agent
66. When a bee bites, it injects mainly
A. formic acid B. acetic acid C. carbonic acid D. hydrochloric acid
67. Most stable valence state of Mn in its salts is
A. 2 B. 5 C. 3 D. 7
68. The polarity is maximum in
A. N-F B. C-F C. O-F D. F-F
69. Which of the following is used in radio carbon dating?
A. C12 B. C11 C. C13 D. C14
70. If one starts with 1 curie of radioactive substance (T1/2 = 12 hr), the activity left after a period
of 1week will be about
A. 1 curie B. 120 microcurie C. 60 microcurie D. 8 millicurie
71. The number of d-electrons in [Cr (H2O6)]3+ ion (Atomic no. of Cr = 24) is
A. 2 B. 3 C. 4 D. 5
72. The pyrites are heated with hydrochloric acid. The solution so obtained will give blood red
colour with
A. K4Fe(CN)6 B. KCN C. K3Fe(CN)6 D. KSNC
73. Which of the following structures is most likely for XeOF4?
A. Tetrahedral B. Square pyramidal C. Square planar D. Octahedral
74. The harmonic connected with growth of animal is
A. Pepsin B. Ptylin C. Thyroxine D. Renin
75. The correct order of increasing oxidising power is
A. F2 < Cl2
< Br2 < I2
B. F2 < Br2 <
Cl2 < I2
C. Cl2 < Br2
< F2 < I2
D. I2 < Br2 <
Cl2 < F2
76. Nitrates of all metals are
A. unstable B. stable C. coloured D. soluble
77. Bromination of aniline will give
A. 2, 3, 4 trinitrophenol B. 2, 4, 6
tribromoaniline
C. 1, 3, 5-
tribromoaniline
D. 2, 3, 5-
tribromoaniline
78. Acetamide is treated separately with the following reagents. Which of them would give
methylamine?
A. PCl5 B. NaOH/Br2 C. Sodalime D. Hot conc. H2SO4
79. Acetic acid exists as a dimmer in benzene due to
A. condensation reaction B. hydrogen bonding
C. presence of carbonyl group D. presence of H-atom and α -carbon atom
80. There is no s-s bond in
A. S2O4
2 - B. S2O5
2 - C. S2O5
2 - D. S2O6
2 -
81. Which one of the following statements shows the
difference between ketone and ether?
A. Ether
contains N,
P but ketone
does not
contain N, P
B. Ether
reacts with
phenylhydrazine
but ketone
does not
C. Ketone
does not
give
acetylation
but ether
does
D. None of
these
82. Dry distillation of calcium acetate yields
A. acetaldehyde B. formaldehyde C. acetone D. ethane
83. Phenol under vigorous nitration condition, i.e., treating with conc. HNO3 and conc. H2SO4
will give
A. 1, 2, 3-trinitrophenol B. Diethylbenzene C. Aniline D. 2, 4, 6-trinitrophenol
84. The reaction of C2H5MgCl with acetaldehyde on acidification yields
A. an aldehyde B. a ketone C. a primary alcohol D. a secondary alcohol
85. For an exothermic reaction, temperature increases by 10oC; then how will the equilibrium be
attained faster?
A. 2 times B. same C. 1/2times D. 4 times
86. A catalyst increases the rate of reaction as
A. reacting substances are brought into higher
specific relation with each other
B. energy is added to the system
C. molecules of the reactants are speeded up so that
random encounters are more
D. product of the reaction are removed
simultaneously
87. What weight of K2Cr2O7 would be required to produce 100 ml of 0.1 N K2Cr2O7 solution?
(Eq. Wt. of K2Cr2O7 = 49)
A. 0.049 gm B. 4.9 gm C. 0.49 gm D. 0.0049 gm
88. Molecular O2 contains two unpaired electrons. They are
A. π * and σ B. σ * and π C. σ * and π * D. π * and π *
89. In the addition of HBr to propene in the absence of peroxides, the first step involves the
addition of
A. H+ B. Br – C. Ho D. Bro
90. The number of sigma bond in toluene is
A. 12 B. 18 C. 15 D. 9
91. It is possible to distinguish between optical isomers by
A. infra-red spectroscopy B. mass spectrometry
C. melting point determination D. polarimetry
92. Organic Compounds of carbon and hydrogen
and with a general formula CnH2n are called
A. alkanes B. alkenes C. alkynes D. olefines
93. Electrolysis of CH3COOK will give
A. methane B. ethene C. ethane D. manganese
94. Coinage metals are present in
A. s-block B. d-block C. p-block D. f-block
95. The most commonly used silver salt in photography is
A. AgNO3 B. AgCl C. AgBr D. Ag2O3
96. Besides iron, essential component of steel is
A. cobalt B. chromium C. copper D. manganese
97. An important mineral for magnesium is
A. malachite B. cassiterite C. carnalite D. galena
98. If a reaction takes place like H3BO3 + NaOH → X + H2O, then X will be
A. Na2BO3 B. NaBO2 C. Na3BO3 D. none of these
99. Which of the following nitrate evolves laughing gas on heating?
A. KNO3 B. Pb(NO3)2 C. NH4NO3 D. AgNO3
100. Nitrogen (I) oxide is produced by
A. thermal decomposition of ammonium nitrate B. disproportion of ammonium N2O4
C. thermal decomposition of ammonium nitrite D. interaction of hydroxylamine with nitrous
acid
101. Inertness of N2 gas is due to
A. no vacant d orbital B. high dissociation
energy
C. high
electronegativity D. none of these
102. In reaction of H2O2 and alkaline K3Fe(CN)6, H2O2 acts as a/an
A. acid B. base C. oxidant D. reductant
103. Which of these contains only an electron and a proton?
A. Helium B. Deuterium C. Hydrogen D. Tritium
104. For reaction N2 (g) + O2 (g) → 2NO (g), ∆ H = + 1812, then
A. ∆ E = ∆ H B. ∆ E > ∆ H C. ∆ E < ∆ H D. none of these
105. What will be the IUPAC name of CH2 = CHCH2Cl?
A. 1-
chlorotripropene
B. 3-
chloro-1-
propene
C.
Methylchloroethene
D. 1-chloro-
2-
methylethene
106. Which of the following statements is/are wrong?
A.All hydrocarbons
containing 6 carbon
atoms are aromatic
B. There is no organic
compound except
bromine which contains
6 C atoms and is known
as aromatic compound
C. Hydrocarbon
contains C, H, N, P,
etc.
D. All of the above
107. Which of the following is the hardest substance?
A. Steel B. Graphite C. Silicon D. Diamond
108. Hydrogen gas has
A. covalent bonding B. ionic bonding C. metallic bonding D. Vander Wall’s force
109. The momentum associated with a photon of frequency v is
A. hv/c B. hc/v C. uc/h D. h/uc
110. Slag is an easily fusible material formed by
the reaction between
A. ore and the flux B. ore and reducing
agent
C. impurities present
and the flux D. none of these
111. (C6H5NH2 + COCl2 + [A] → C6H5NH.CO.NHC6H5). The compound [A] is
A. (C6H5)2NH B. C6H5NH2 C. (CH3)3N D. (C6H5)3N
112. In which molecule, the distance between the two adjacent carbon a1kanes is largest?
A. Ethane B. Ethene C. Ethyne D. Benzene
113. Baeyer's reagent is
A. alkaline permanganate solution B. acidified permanganate solution
C. neutral permanganate solution D. aqueous bromine solution
114. The hybridisation of carbon atom in C-C single bond of HC ≡ C – CH = CH2 is
A. sp3-sp3 B. sp2-sp3 C. sp-sp2 D. sp3-sp
115. Iron is in + 2 oxidation state in
A. K4[Fe(CN)6] B. K3[Fe(CN)6] C. Na2[Fe(NO)2CN)5] D. [Fe(OH)2]+
116. Transition metals
A. exhibit dia
magnetism B. do not form alloys
C. undergo inert pair
effect
D. show variable
oxidation state
117. Ozone can be easily detected by the use of
A. silver B. silver chloride C. mercury D. hydrogen peroxide
118. Oxygen molecule exhibits
A. paramagnetism B. bleaching powder C. potassium
permanganate D. sodium peroxide
119. Which of the following phosphorus oxyacids is reducing in character?
A. H3PO3 B. H3PO4 C. H4P2O6 D. H4P2O7
120. Which one of the following is dibasic acid?
A. Phosphorous acid B. Hypophosphorous
acid C. Phosphoric acid D. Hypophosphoric
acid
121. If in a triangle ABC, angle C is 45o, then (1
+ cot A)(1 + cot B) equals
A. 1 B. -1 C. 2 D. 1/√2
122. If the cube roots of unity are 1, ω, ω2, then the roots of the equation (x - 2)3 + 27 = 0 are
A. -1, 2 - 3ω, 2 - 3ω2 B. -1, 2 + 3ω, 2 + 3ω2 C. -1, - ω, - ω2 D. -1, -1, -1
123. If A, B, and C are any three sets, then A - (B ∩ C) is equal to
A. (A - B) ∩ C B. (A - B) ∪ C C. (A - B) ∩ (A - C) D. (A - B) ∪ (A - C)
124. The angle of elevation of the top of a tower at horizontal distance equal to the height of the
tower from the base of the tower is
A. 30o B. 45o C. 60o D. none of the above
125. If α is a complex number such that α2 + α + 1 = 0, then α31 is
A. 1 B. 0 C. α2 D. α
126. If z is a complex number, then
A. | z2 | < | z |2 B. | z2 | ≥ | z |2 C. | z2 | = | z |2 D. | z2 | > | z |2
127. The origin and the roots of the equation z2
+ pz + q = 0 form an equilateral triangle if
A. q2 = p B. q2 = 3p C. p2 = 3q D. p2 = q
128. The distance between the lines 4x + 3y = 11 and 8x + 6y = 15 is
A. 7/10 B. 7/2 C. 4 D. none of the above
129. Two circles x2 + y2 = 6 and x2 + y2 - 6x + 8 = 0 are given. Then the equation of the circle
through their points of intersection and the point (1, 1) is
A. x2 + y2 - 4y + 2 = 0 B. x2 + y2 - 6x + 4 = 0 C. x2 + y2 - 3x + 1 = 0 D. none of the above
130. In an ellipse, the distance between its foci is 6 and its minor axis is 8. Then its eccentricity
is
A. 3/5 B. 1/√2 C. 1/2 D. 4/5
131. If b and c are the length of the segments of any focal chord of a parabola y2 = 4ax, then the
length of the semi-latus rectum is
A. bc/(b + c) B. √bc C. (b + c)/2 D. 2bc/(b + c)
132. [1 + cos(π/8)] [1 + cos(3π/8)] [1 + cos(5π/8)] [1 + cos(7π/8)] is equal to
A. π/2 B. (1 + √2)/2√2 C. 1/2 D. 1/8
133. In a triangle ABC, a = 13cm, b = 12cm,
and c = 5 cm. The distance of A from BC is
A. 144/13 B. 65/12 C. 60/13 D. 25/13
134. The principal value of sin -1 (sin5π/3) is
A. 4π/3 B. -π/3 C. -5π/3 D. 5π/3
135. If sin -1 x = π/5 for some x ∈ [1, -1], then the value of cos -1 x is
A. 9π/10 B. 7π/10 C. 5π/10 D. 3π/10
136. If ω is a cube root of unity, then the value of (1 + ω - ω2) (1 - ω + ω2) is
A. 4 B. 2 C. 0 D. 1
137. tan -1 (1/5) + tan -1 (1/7) + tan -1 (1/3) + tan -1 (1/8) =
A. π/3 B. π/4 C. π/2 D. π
138. The equations x2 - ax + b = 0 and x2 + bx - a = 0 have a common root, then
A. a + b = 0 or a - b = 1 B. a - b = 0 C. a + b = 1 D. a = b
139. If α, β are the roots of x2 + px + q = 0, then
-1/α, 1/β are the roots of the equation
A. x2 - px +
q = 0
B. x2 + px
+ q = 0
C. qx2 + px
+ 1 = 0
D. qx2 - px
+ 1 = 0
140. The real roots of | x |2 - 3x2 + 3| x | - 2 = 0 are
A. ± 1 B. ± 2 C. 1, 2 D. 0, 2
141. The 20th term of the series 2 x 4 + 4 x 6 + 6 x 8 ....... is
A. 840 B. 420 C. 1680 D. 1600
142. If (a, b), (c, d), (e, f) are the vertices of a triangle such that a, c, e are in G.P. with common
ratio r and b, d, f are in G.P. with ratio s, then the area of the triangle is
A. (ab/2) (r + 1) (s + 1) (s - r) B. (ab/2) (r - 1) (s - 1) (s - r)
C. (ab/2) (r - 1) (s - 1) (s - r) D. (ab/2) (r + 1) (s + 2) (s + r)
143. If (a + b)/(1 - ab), b, (b + c)/(1 - bc) are in A.P., then a, 1/b, c are in
A. H.P. B. A.P. C. G.P. D. none of the above
144. 1/2! - 1/3! + 1/4! - 1/5! + ........ equals
A. e-1 B. log 2 C. log e D. e
145. (1/2)x2 + (2/3)x3 + (3/4)x4 + (4/5)x5 + ......
is
A. -x/(1 +
x) + log (1
+ x)
B. x/(1 + x)
+ log (1 +
x)
C. x/(1 - x)
+ log (1 -
x)
D. none of
the above
146. The number of ways in which n ties can be selected from a rack displaying 3n different ties
is
A. 3 x n! B. 3n!/(n! 2n!) C. 3n!/2n! D. 3n!
147. The number of ways in which 5 boys and 5 girls can sit in a row so that all the girls sit
together is
A. 12600 B. 7200 C. 86400 D. 14400
148. The coefficient of x6 in the expansion of (1 + x + x2)-3 is
A. 6 B. 5 C. 4 D. 3
149. The sum of the
series
20Cr is
A. 219 - [(1/2)(20Cr)] B. 219 + [(1/2)(20Cr)] C. 219 D. 220
150. If α is a zero of ax2 + bx + c, then one of the factors of ax2 + bx + c is
A. c - α B. a - α C. x + α D. x - α
151. If A is 3 x 4 matrix and B is a matrix such
that A'B and BA' are both defined. Then B is of
the type
A. 3 x 4 B. 4 x 4 C. 3 x 3 D. 4 x 3
152. The point (3, 2) is reflected in the y-axis and then moved a distance 5 units towards the
negative side of y-axis. The co-ordinates of the point thus obtained are
A. (3, -3) B. (-3, 3) C. (3, 3) D. (-3, -3)
153. If a, b, c are different
and
a
b
c
a2
b2
c2
a3 - 1
b3 - 1
c3 - 1
= 0, then
A. ab + bc + ca = 0 B. a + b + c = 0 C. a + b + c = 1 D. abc = 1
154.
If A
=
a
b
b
a
,
A2
=
α
β
β
α , then
A. α = 2ab,
β = a2 + b2
B. α = a2 +
b2, β = a2 -
b2
C.α = a2 +
b2, β = 2ab
D. α = a2 +
b, β = ab
155. The value of ∆
=
1
-1
0
2
3
-2
- 1
0
1
is
A. 5 B. 2 C. 1 D. 0
156. The equation of the line joining the points
(-2, 4, 2) and (7, -2, 5) are
A. (x + 2)/3 = (y - 4)/-2 B. x/-2 = y/4 = z/2
= (z - 2)/1
C. x/7 = y/-2 = z/5 D. none of the above
157. If difference of the roots of the equation x2 + px + 8 = 0 is 2, then p is equal to
A. ± 2 B. ± 4 C. ± 6 D. ± 8
158. The mean deviation of the numbers 3, 4, 5, 6, 7 is
A. 25 B. 5 C. 1.2 D. 0
159. If byx and bxy are the regression coefficients of y on x and x on y respectively, then
A. byx + bxy ≥ 2r (x, y) B. byx + bxy = 2r (x, y) C. byx + bxy < 2r (x, y) D. none of the above
160. Cards are drawn from a pack until the spade-ace turns up. Then on an average, the number
of cards dealt is
A. 57/2 B. 49/2 C. 53/2 D. none of the above
161. A number is chosen at random among the first 120 natural numbers. The probability that the
number chosen being a multiple of 5 or 15 is
A. 1/6 B. 1/5 C. 1/8 D. none of the above
162. For two events A and B, if P(A) = P(A/B)
= 1/4 and P(B/A) = 1/2, then
A. A is a subevent of B B. A and B are
mutually exclusive
C. A and B are
independent and
P(A'/B) = 3/4
D. none of the above
163. The inverse of the function y = [(10x - 10-x)/(10x + 10-x)] + 1 is
A. y = 1/2 [log10 x/(2 -
x)] B. y = [log10 x/(2 - x)] C. y = 1/2 [log10 x/(1 -
x)] D. none of the above
164. Let f : R → R be a mapping defined by f(x) = x3 + 5, then f -1(x) is equal to
A. (5 - x)1/3 B. (x + 5)1/3 C. 5 - x D. (x - 5)1/3
165. If f(x) = (1 - sinx)/(π - 2x)2 when x ≠ π/2 and f(π/2) = λ, then f(x) will be a continous
function at x = π/2 when λ is
A. 1/4 B. 1/2 C. 1/8 D. none of the above
166. Lim [loge x/(x -1)] is equal to
x → 1
A. 1/2 B. 0 C. 1 D. 2
167. If the line ax + by + c = 0 is a normal to the
curve xy = 1, then
A. a < 0, b < 0 B. a > 0, b > 0
C. a > 0, b < 0 or a < 0,
b > 0 D. none of the above
168. If f '(x) = (x - 2a)2n (x - b)2m + 1 where m, n ∈ N, then
A. x = b is a point of inflexion B. x = b is a point of minima
C. x = b is a point of maxima D. none of the above
169. ∫ | x |3 dx is equal to
A. - x3/4 B. | x |4/4 C. x4/4 D. none of the above
170. ∫ dx/(x2 + x + 1) is equal to
A. √3/2 + tan -1 [(2x + 1)/√3] + c B. 2/√3 + tan -1 [(2x + 1)/√3] + c
C. 1/√3 + tan -1 [(2x + 1)/√3] + c D. none of the above
171. dx/(1 + tanx) is equal
to
A. π/4 B. π/3 C. π/2 D. π
172. Lim φ(x) = a3, a ≠ 0, then Lim
φ(x/a) is
x →
0 x → 0
A. 1/a2 B. 1/a3 C. a3 D. a2
173. 7 men and 7 women are to sit round a table so that there is a man on either side of a woman.
The number of seating arrangement is
A. (7!)2 B. (6!)2 C. (6!) D. (7!)
174. If the position vectors of three points are a - 2b + 3c, 2a + 3b - 4c, -7b + 10c, then the three
points are
A. collinear B. coplanar C. non-collinear D. none of the above
175. The scalar A . [(B + C) x (A + B + C)] equals
A. 0 B. [ABC] + [BCA] C. [ABC] D. none of the above
176. If a variable takes the discrete values α + 4, α - 7/2, α - 5/2, α - 3, α + 1/2, α - 1/2, α + 5 (α
> 0), then the median is
A. α - 1/2 B. α + 5/4 C. α - 5/4 D. α - 2
177. The angle of the elevation of the top of a
tower any point on the ground is 30o and
moving 20 metres towards the tower, it becomes
60o. The height of the tower is
A. 10 m B. 10√3 m C. 10/√3 m D. none of
the above
178. If A, B, and C be any three sets such that then A ∪ B = A ∪ C and A ∩ B = A ∩ C, then
A. A = B = C B. A = C C. B = C D. A = B
179. The equation y2 - x2 + 2x - 1 = 0 represents
A. a pair of straight
lines B. a circle C. a parabola D. an ellipse
180. The points (-a, -b), (0, 0), (a, b) and (a2, ab) are
A. collinear B. vertices of a rectangle
C. vertices of a parallelogram D. none of the above