CUSAT CAT 2021 Question Paper B.Tech Shift III

101 – TEST FOR B TECH / 5 YR INTEGRATED MSC
(SHIFT III)

PHYSICS

1. A certain screw gauge has a pitch of 0.5 mm. If there are 50 divisions on the head
scale, the dimension of the object can then be determined to an accuracy of
(A) 0.05 cm
(B) 0.01 cm
(C) 0.001 cm
(D) 0.0001 cm

2. The refractive index of glass measured by a given method by four independent
measurements is found to have values of 1.54, 1.58, 1.52 and 1.56 respectively. The
mean value of refractive index with percentage error is
(A) 1.55 ± 1.29 %
(B) 1.55 ± 0 %
(C) 1.56 ± 6 %
(D) 1.56 ± 0 %

3. A particle moves for 20 seconds with velocity 3 m/s and then with velocity 4 m/s for
another 20 seconds and finally moves with velocity 5 m/s for next 20 seconds. Then
the average velocity of the particle is

(A) 3 m/s
(B) 4 m/s
(C) 5 m/s
(D) Zero

4. An athlete completes one round of a circular track of radius R in 40 s. What will be
his displacement at the end of 2 min 40 seconds?

(A) 8R
(B) 8𝜋R
(C) 2R
(D) Zero

5. A wheel having 1 m diameter makes 60 revolutions per minute. The linear speed of a
point on its circumference is

(A) /2 m/s
(B)  m/s
(C) 2 m/s
(D) 60 m/s

6. A car starts from rest to cover a distance s. The coefficient of friction between the
road and the tyres is . The maximum time in which the car can cover the distance is
proportional to

(A) 
(B) √𝜇
(C) 1/
(D) 1/√𝜇

7. A diesel engine pumps 40 kg of water in 1 second. The water comes out vertically
upwards with a velocity of 3 m/s. What is the power of the engine in kilo Watt?

(A) 12 kW
(B) 1.2 kW
(C) 120 kW
(D) 1200 kW

8. Which one of the following is the S.I. unit of electric field strength?
–1
(A) Am
–1
(B) Nm
–1
(C) Vm
–1 –1
(D) Coulomb s cm

9. If the distance between the two charged particles is reduced to half the original
distance, then the force between them becomes

(A) doubled
(B) one-forth
(C) one-half
(D) four times

10. A metal sheet is placed between two charges separated by a distance. Then the force
between them will

(A) increase
(B) decrease
(C) remains the same
(D) be reduced to half the initial value

11. If the separation between carbon and oxygen in CO molecule is 0.12 nm, then the
distance of the center of mass from the carbon atom is

(A) 0.03 nm
(B) 0.068 nm
(C) 0.05 nm
(D) 0.06 nm

12. A hole is drilled along the earth’s diameter and a stone is dropped into it. When the
stone is at the center of the earth, it has

(A) mass
(B) weight
(C) potential energy
(D) zero mass

13. Two wires of the same radius and material have lengths in the ratio 1:2. If these are
stretched by the same force, the strain produced in the two cases will be in the ratio

(A) 1:2
(B) 2:1
(C) 1:1
(D) 4:1

14. The phase difference between the displacement and velocity of a particle executing
SHM is

(A) /2
(B) 
(C) /4
(D) 0

15. Standing waves are produced in a 10 m long stretched string. If the string vibrates in 5
segments and the wave velocity is 20 m/sec, the frequency is

(A) 2 Hz
(B) 4 Hz
(C) 5 Hz
(D) 10 Hz

16. A parallel plate condenser is charged and isolated. When a sheet of glass is interposed
between the plates

(A) the charges on the plates will be reduced
(B) the potential difference between the plates will be reduced
(C) the potential difference between the plates will be increased
(D) the charges on the plates will be increased

17. If a capacitor of Capacitance 10 micro Farad (µF) is charged to a potential difference
of 100 V, the energy stored in it is

(A) 0.5 J
(B) 0.05 ergs
(C) 10 J
(D) 0.05 J

18. With increase in altitude, the conductivity of the atmosphere

(A) first increases and then decreases
(B) increases
(C) decreases
(D) remains constant

19. An electric iron box has a heater coil of resistance 50 Ω. If it is connected to 230 V
AC mains, the current flowing through the heater coil will be

(A) 4.6 mA
(B) 5A
(C) 4.6 A
(D) 15 A

20. Glass has a resistivity of the order of
–8
(A) 10 Ω m
–5
(B) 10 Ω m
8
(C) 10 Ω m
12
(D) 10 Ω m

21. A long solenoid of n turns has a self inductance L and area of cross section a. When a
current flows through the solenoid, it produces a magnetic field B. The current
flowing through the solenoid is

(A) Ban/L
(B) BanL
(C) Bn / aL
(D) B / anL

22. A conductor of length r moves in a uniform magnetic field of induction B with a
velocity v. The emf induced across the conductor is

(A) (v × B) . r
(B) v. (r × B)
(C) B . (r × v)
(D) r × (v × B)

23. The penetrating powers of ,  and  radiation, in decreasing order are

(A) , , 
(B) , , 
(C)  , , 
(D) , , 

24. A half-wave rectifier is being used to rectify an alternating voltage of frequency
50 Hz. The number of pulses of rectified current obtained in one second is

(A) 50
(B) 25
(C) 100
(D) 6

25. The voltage V and the current I flowing through an A.C circuit are given by
V = 2 cos 100 πt and I = 4 sin 100 πt, where t represents time. The power
dissipated in the circuit is

(A) zero Watt
(B) 8 Watt
(C) 4 Watt
(D) 2 Watt

26. An alternating e.m.f. is given by V = 100 sin 314 t. Its frequency is

(A) 100 Hz
(B) 50 Hz
(C) 314 Hz
(D) 60 Hz

27. In a purely inductive circuit, the current

(A) is in phase with voltage
(B) is out of phase with voltage
(C) leads the voltage by 90°
(D) lags behind the voltage by 90°

 
28. The current and voltage in an A.C. circuit are given by I  I o sin  t   and
 2
E = Eo sin ωt. Then the average power consumption P in the circuit is

E I
(A) P o o
2
EI
(B) P 
2
E I
(C) P  o o
2
(D) zero

29. Two electric bulbs whose resistances are in the ratio 1:2, are connected in parallel to a
constant voltage source. The power dissipated in them is in the ratio

(A) 1:2
(B) 2:1
(C) 1:1
(D) 1:4

30. The neutral temperature for a thermocouple is 270°C. If the temperature of the cold
junction is 15°C, then the inversion temperature is

(A) 255°C
(B) 285°C
(C) 570°C
(D) 525°C

31. A source emits a sound of frequency 400 Hz but the listener hears it to be 390 Hz.
Then

(A) the listener is moving towards the source
(B) the source is moving toward the listener
(C) the listener is moving away from the source
(D) the listener has a defective ear

32. The binding energy of the electron in a hydrogen atom is 13.6 eV, the energy required
++
to remove the electron from the first excited state of Li is

(A) 122.4 eV
(B) 30.6 eV
(C) 13.6 eV
(D) 3.4 eV

33. Which of the following nuclei has lowest value of the binding energy per nucleon?
4
(A) 2He
52
(B) 24Cr
152
(C) 62Sm
100
(D) 80Hg

235
34. The average number of neutrons emitted during the fission of U is

(A) 3
(B) 2
(C) 1.5
(D) 2.5

35. The radioactive decay of uranium into thorium is represented by the equation
238 234
92U → 90Th + X, then X is

(A) an electron
(B) a neutron
(C) a proton
(D) an alpha particle

36. The same radioactive nucleus may emit

(A) all the three α, β and γ simultaneously
(B) either α or β or γ at a time
(C) all the three α, β and γ at a time
(D) only α and β

37. The radius of a nucleus of mass number A is proportional to

(A) A
(B) A½
(C) A⅓
(D) A3

38. Which one of the statements about nuclear forces is INCORRECT?

(A) Nuclear forces are short range forces
(B) Nuclear forces are charge independent forces
(C) Nuclear forces are exchange forces
(D) Nuclear forces are central forces

39. Which one of the statements about neutron is INCORRECT?

(A) Neutron is a fundamental particle
(B) Neutron has no charge
(C) Nuclei of all elements in nature contain neutron
(D) Neutron has a spin

40. The ground state energy of the hydrogen atom is

(A) 13.6 eV
(B) 0 eV
(C) –3.4 eV
(D) –13.6 eV

41. Which one of the statements about matter waves is INCORRECT?

(A) Matter waves are not electromagnetic waves
(B) Matter waves are also called probability waves
(C) de Broglie waves are pilot waves i.e., these waves guide the particle
(D) The phase velocity of the matter waves in vacuum is independent of
wavelength

42. Kinetic energy of the cathode rays (electrons) depend on

(A) voltage applied to the electrode
(B) depend on work function
(C) depend on both (A) and (B)
(D) does not depend on any physical quantity

43. A man cannot see objects clearly at a distance greater than 2 m. He is then suffering
from

(A) short sight
(B) long sight
(C) astigmatism
(D) presbyopia

44. The magnifying power of a simple microscope can be increased by if we use eyepiece
of

(A) higher focal length
(B) smaller focal length
(C) higher diameter
(D) smaller diameter

45. If the focal length of the objective and eyepiece lens of an astronomical telescope are
f o and f e respectively, then its magnifying power is

fo
(A)
fe
fe
(B)
fo
2 fo
(C)
fe
(D) 2 fe

46. If f r and f v stand for focal length of the lens for red colour and violet colour
respectively, then the longitudinal chromatic aberration of the lens for parallel rays is
given by

(A) f r  fv
(B) fv  f r
(C) f r fv
(D) fv  f r

47. The deviation produced by a flint glass prism for violet and red light rays are 3.25°
and 3.10° respectively. Then the angular dispersion is

(A) 6.35°
(B) 3.175°
(C) 0.15°
(D) 6.35 radians

48. Total internal reflection is NOT possible in the case when light travels from

(A) glass to air
(B) glass to water
(C) water to glass
(D) water to air

49. When the angle of incidence on a certain material is 60°, the reflected light is
completely polarized. The angle of refraction is then

(A) 60°
(B) 90°
(C) 30°
(D) 45°

50. A sugar solution of length 15 cm has specific rotation of 65° and produces a optical
rotation of 7°. Then the concentration of the solution is

(A) 0.7 g/cc
(B) 13.9 g/cc
(C) 0.0717 g/cc
(D) 0.01g/cc

51. To observe diffraction, the size of an obstacle

(A) should be of the order of wavelength
(B) should be much larger than the wavelength
(C) has no relation to wavelength
(D) should be exactly λ/2.

52. If the distance between the screen and the slit is doubled in Young’s double slit
experiment, the fringe width will become

(A) four times
(B) two times
(C) one-half
(D) one-fourth

53. When light waves suffer reflection at the interface between air and glass, the change
of phase of the reflected wave is

(A) zero
(B) π
(C) 2π
(D) π/2

54. If a string of string constant k is stretched by a length x under tension T, the energy
stored is

2k
(A)
T2
2T 2
(B)
k2
T2
(C)
2k
2T
(D)
k2

55. The Young’s modulus of a perfectly rigid body is

(A) zero
(B) unity
(C) infinite
(D) may be any finite non-zero value

56. A wire elongates by l mm when a load W is hanged at from it. If the wire goes over a
pulley and the two weights W each are hung at the two ends, the elongation of the
wire (in mm) will be

(A) l/2
(B) l
(C) 2l
(D) zero

57. If two liquids of same masses but densities 1 and  2 respectively are mixed, then
the density of the mixture is

(A) 1   2
1  2
(B)
2
1 2
(C)
1   2
2 1 2
(D)
1   2

58. A boy carries on his head an airtight box containing a bird resting on the floor of the
box. When the bird starts flying inside the box, he will feel that the box is now

(A) lighter
(B) heavier
(C) same in weight as before
(D) lighter in the beginning and heavier later

59. A cork ball is floating on the surface of water in a beaker. The beaker is covered with
a bell jar and the air is evacuated. What will happen to the ball?

(A) Sink a little
(B) Rise a little
(C) Remain unchanged
(D) Sink completely

60. The thermometer used as a reference standard is

(A) mercury thermometer
(B) platinum resistance thermometer
(C) gas thermometer
(D) thermocouple thermometer

61. If α is coefficient of linear expansion, β is coefficient of superficial expansion and γ is
the coefficient of cubical expansion, then for the same rise in temperature, the
percentage changes in α, β and γ are in the ratio

(A) 1:2:3
(B) 3:2:1
(C) 1:1:1
(D) 1:2:4

62. If K and σ respectively are the thermal and electrical conductivities of a metal at
absolute temperature T, then

K
(A) = constant
T
K
(B) = constant

K
(C) = constant
T

(D) = constant
KT

63. The velocity V of thermal radiation is (C = velocity of light in vacuum)

(A) V<C
(B) V>C
(C) V=C
(D) dependent on the medium

64. Which one of the following statements about electromagnetic waves is
INCORRECT?

(A) They do not require material medium for propagation
(B) They are not deflected in electric an magnetic fields
(C) The waves are transverse in nature
(D) They cannot be diffracted

65. If E and B represent electric and magnetic field vectors of the electromagnetic
waves, then the direction of propagation of the waves will be along

(A) B E
(B) E
(C) B
(D) EB

66. The area of B-H hysteresis loop in a ferromagnetic material is a measure of the

(A) net energy dissipated per unit volume per cycle of magnetization of the
material
(B) permeability of the material
(C) susceptibility of the material
(D) retentivity of the material

–10
67. The unit cubic cell of Al has an edge length equal to 4.5 × 10 m. The number of
–6 3
unit cells in an aluminium foil of volume 91 × 10 m is
24
(A) 10
–24
(B) 10
8
(C) 10
23
(D) 10

68. The gate with the Boolean expression Y = A  B for its output is

(A) AND
(B) NAND
(C) XOR
(D) XNOR

69. The Boolean expression for NOR gate is

(A) Y=A+B
(B) Y= A+B
(C) Y=A+B
(D) Y=A+B

70. What gate has the truth table given below?

A B Y
0 0 0
0 1 0
1 0 0
1 1 1

(A) NOT
(B) AND
(C) NAND
(D) NOR

71. A transistor amplifier is operated in common emitter configuration at constant
collector voltage of VC = 1.5 V, such that the change in the base current from 100 μA
to 150 μA produces a change in the collector current from 5 mA to 10 mA. The
current gain β of the circuit is then

(A) 50
(B) 67
(C) 75
(D) 100

72. A two stage transistor amplifier has a gain of 10 for the first stage and a gain of 20 for
the second stage. The overall gain of the cascade amplifier will be

(A) 30
(B) 10
(C) 200
(D) 2

73. Long range radio transmission is possible when the radio waves are reflected from the
ionosphere. For this to happen, the frequency of the radio waves must be in the range

(A) 80-150 MHz
(B) 8-25 MHz
(C) 1-3 MHz
(D) 150-1500 kHz

74. The colour of a star is dependent on its

(A) radius
(B) distance from the earth
(C) temperature
(D) structure

75. Hubble constant H has the dimensions of

(A) mass
(B) length
–1
(C) (time)
(D) temperature

CHEMISTRY
–1
76. Given the latent heat of vapouration of water as 40.7 kJ mol at 373 K, ∆S for one
mole of water converted to steam at 373 K is
–1 –1
(A) 109.1 JK mol
–1
(B) 40.7 kJ mol
–1
(C) 81.4 kJ mol
–1 –1
(D) 218.2 JK mol

77. For a non-linear triatomic gas the value of the ratio of Cp and Cv at laboratory
temperature is (assuming no vibrational contribution)

(A) 7/5
(B) 9/7
(C) 8/3
(D) 4/3

78. 6 moles of SO2 and 6 moles of O2 are allowed to form SO3 in a closed vessel. At the
equilibrium stage, 60% of SO2 is used up. The total number moles of the mixture at
equilibrium is

(A) 10.2
(B) 9.8
(C) 7.2
(D) 11.2

79. pH of a solution obtained by mixing equal volumes of the solutions
with pH 3 and pH 5 is

(A) 4.0
(B) 3.5
(C) 3.3
(D) 2.0

–10
80. The Ksp of AgCl is 1 × 10 , its solubility in pure water in 0.01 M NaCl is

(A) 2 × 10–10
(B) 1 × 10–8
(C) 2 × 10–8
(D) 1 × 10–10
81. The edge length of fcc unit cell is 508 pm. The radius of the atom is …………… pm.

(A) 180
(B) 200
(C) 618
(D) 288

82. Crystalline solids having the least enthalpy of fusion is

(A) Molecular solid
(B) Metallic solid
(C) Ionic solid
(D) Covalent solid

83. Vapour pressure of water at 298 K is 19.8 mm of Hg. 0.1 mole of glucose is dissolved
in 172.8 g of water. The vapour pressure of the solution is

(A) 19.6 mm
(B) 16.9 mm
(C) 19.0 mm
(D) 18.9 mm

84. Osmotic pressure of blood is 8.21 atm at 37°C. Amount of glucose that should be
used per litre of intravenous injection that is at the same osmotic pressure of blood is

(A) 58.4 g
(B) 29.2 g
(C) 5.84 g
(D) 2.92 g

2 –1
85. The equitant conductance of 1 M benzoic acid is 12.8 Scm eq and if the limiting
+ 2 –1
equivalent conductance of benzoate ion and H ion are 42 and 288.42 Scm eq ,
respectively, its degree of dissociation is

(A) 39%
(B) 3.9%
(C) 0.35%
(D) 0.039%

86. Two half-cells of electrode potentials of E1 and E2 are combined to form a cell of
potential E3, (n1, n2 and n3 are number of electrons involved in first electrode, second
electrode and the cell) E3 is

(A) E3 = E2 – E1
(B) E3 = (E1n1 + E2n2)/n3
(C) E3 = (E1n1 – E2n2)/n32
(D) E3 = E1 + E2

87. The potential of half-cell consisting of zinc electrode in 0.01 M ZnSO4 solution at
25°C is (E° = –0.763 V)

(A) –0.8221 V
(B) –0.704 V
(C) –0.881 V
(D) –0.645 V

88. A dilute aqueous solution of CuSO4 is electrolyzed using Pt electrodes. The products
at the anode and cathode are

(A) O2, H2
(B) H2, O2
(C) O2, Cu
2–
(D) S2O8 , H2

14
89. The half-life for radioactive decay of C is 5730 years. An archaeological
14
artefact containing wood had only 80% of the C found in living tree. The age
of the sample is

(A) 1845 years
(B) 2865 years
(C) 4584 years
(D) 1146 years

90. If the volume of the reaction vessel is halved, for the reaction,
2SO2(g) + O2(g)  2SO3(g), then the rate is
th
(A) 1/6 of its initial value
th
(B) 1/4 of its initial value
(C) 8 times of its initial value
(D) 4 times of its initial value

0
91. The rate equation for a reaction: A → B is r = k[A] . If the initial concentration of the
–3
reactant is ‘a’ mol dm , then half-life period of reaction is

(A) a/k
(B) 2a/k
(C) a/2k
(D) k/a

92. The number of unit cells present in 39 g of potassium that crystallizes as body
centered cubic structure is (NA = Avogadro number)

(A) NA
(B) 0.25 NA
(C) 0.5 NA
(D) 0.75 NA

93. Which one of the following is not correctly matched?
2− 2
(A) [Ni(CN)4] – dsp hybridization, dia-magnetic
2+ 3
(B) [Cu(NH3)4] – sp hybridization, para-magnetic
2− 3
(C) [NiCl4] – sp hybridization, tetrahedral
2− 3
(D) [CuCl4] – sp hybridization, para-magnetic

94. Which one of the following statements is not true according to Werner’s theory of
coordination compounds?

(A) Both primary and secondary valencies can be satisfied by anions
(B) Secondary valency is non-directional
(C) Primary valency is ionic valency
(D) Metal ions exhibit two types of valencies

95. Which one of the following is true regarding the energies of d-orbitals of tetragonally
distorted octahedral geometry?

(A) dyz > dxz > dxy
(B) d x 2  y2  d z2
(C) dxz > dyz
(D) d z2  d x 2  y2

96. In the estimation of Ca(II) ions, in the presence of ammonia-ammonium chloride
buffer solution, EDTA acts as a …………… ligand.

(A) flexidentate
(B) pi-donor
(C) hexadentate
(D) tetradentate

97. How much amount of oxalic acid dihydrate crystals are required to prepare 1 L of a
decinormal solution of it?

(A) 6.3 g
(B) 12.6 g
(C) 3.15 g
(D) 9g

98. What is correct order of increasing acidic strength of oxides of nitrogen?

(A) NO < N2O3 < N2O4 < N2O5
(B) NO = N2O3 < N2O4 = N2O5
(C) NO > N2O3 < N2O4 > N2O5
(D) NO > N2O3 > N2O4 > N2O5

99. Regarding compounds of sulfur, which one of the following statements in not true?

(A) SF6 does not undergo hydrolysis
(B) SF4 undergoes hydrolysis
(C) SF6 is thermally stable and chemically inert
(D) SF4 acts as Lewis acid

100. Fluorine does not act as the central atom in interhalogen compounds, because

(A) it is highly electronegative
(B) of absence of d-orbitals
(C) of its small size
(D) of its gaseous nature

101. A hydrometallurgical process involves the following steps.

Ag2S + 4 NaCN → 2 Na[Ag(CN)2] + Na2S

2 Na[Ag(CN)2] + Zn → Na2[Zn(CN)4] + 2 Ag↓

Which one of the following statements is true?

(A) In the second step Zn(II) is reduced to Zn(0)
(B) Dicyanoargentum(I) complex is insoluble in water
(C) In the first step Ag(I) is reduced to Ag(0)
(D) Tetracyanozinc(II) complex is soluble in water

102. Transition metals exhibit variable oxidation states. This is because

(A) the outermost shell is empty
(B) they are all metals
(C) the energies of (n – 1)d and ns orbitals are almost equal
(D) the ionization energy to remove electron from ns orbital is very low

103. The general electronic configuration of inner-transition elements is
1–14 0, 1
(A) (n – 2)f (n – 1)d
1–14 0–1 2
(B) (n – 2)f (n – 1)d ns
1–14 0–1 2
(C) (n – 1)f (n – 1)d ns
1–14 2
(D) (n – 2)f ns

104. Which of the following species would be diamagnetic?
3+
(A) Cr
3+
(B) Co
(C) Br
2+
(D) Zn

105. Which orbital is designated by the quantum numbers: n = 5, l =1, ml = 0?

(A) 5s
(B) 5p
(C) 5d
(D) 5f

106. If travelling at equal speeds, which of the following matter waves have the longest
wavelength?

(A) Electron
(B) Proton
(C) Neutron
(D)  particle

107. Number of angular nodes for 4d orbital is

(A) 4
(B) 3
(C) 2
(D) 1

108. Which of the following will not show deflection from the path on passing through
electric field?

(A) Electron
(B) Neutron
(C) Cathode rays
(D) Proton

109. Complete the following nuclear equation:
59
27 Co  0n  25Mn  ?
1 56

(A) 4 11H
(B) 4 11n
4
(C) 2 He
(D) 2 11H

110. Which among the following sequence is best suited for selective transformation
on 2-methylbutane to 2-methylbutan-2-ol?

(A) Treatment with Cl2 in the presence of UV light followed by hydrolysis with
potassium hydroxide in water
(B) Treatment with Cl2 in the presence of UV light followed by hydrolysis with
potassium hydroxide in ethanol
(C) Treatment with Br2 in the presence of UV light followed by hydrolysis with
potassium hydroxide in water
(D) Treatment with I2 in the presence of UV light followed by hydrolysis with
potassium hydroxide in a 1:1 mixture of water and ethanol

111. Ozone depletion in Antartica is due to

(A) sulphur containing gases
(B) peroxy acetyl nitrate
(C) chlorine nitrate
(D) fluorine

112. When an organic compound ‘A’ was treated sequentially with ammonia and
Br2/KOH, methanamine was obtained. Then ‘A’ is an

(A) ethanol
(B) ethyl acetate
(C) acetonitrile
(D) acetic acid

113. How many structural isomers are possible for C3H9N?

(A) 3
(B) 4
(C) 5
(D) 6

114. Which is a non-reducing sugar?

(A) Glucose
(B) Sucrose
(C) Maltose
(D) Fructose

115. 0.200 g of an organic compound contains 71% carbon. What is the mass of CO2
produced when it is subjected to complete combustion?

(A) 0.142
(B) 0.039
(C) 0.521
(D) 0.733

116. Consider the following compounds:
(i) hydrazine
(ii) paracetamol
(iii) chlorophyll
(iv) saccharin
How many among them will test negative for nitrogen in Lassaigne’s test ?

(A) 1
(B) 2
(C) 3
(D) 4

117. Which among the following is more reactive towards nitration
using nitrating mixture?

(A) tertiary-Butylbenzene
(B) Toluene
(C) Benzene
(D) Chlorobenzene

118. Which among the following is antiaromatic?

(A)

(B)

(C)
-

(D)
+

119. Hydrogenation of acetyl chloride in the presence of Pd-BaSO4 as catalyst to obtain
ethanal is

(A) Clemmensen reduction
(B) Rosenmund reduction
(C) Schmidt reaction
(D) Dakin reaction

120. Which among the following compounds will selectively give the same addition
product with HBr under both Markonikkoff’s and anti-Markonikkoff’s addition
conditions?

(A) CH3-CH=CH-CH2-CH3
(B) CH3-CH=CH-C(CH3)2
(C) CH3-CH=CH-CH(CH3)2
(D) C6H5-CH=CH2

121. Among the following, the organic compound that gives propyne on treatment with
sodamide with minimal side products is

(A) CH3CH2CHCl2
(B) CH3CCl=CH2
(C) CH3CCl=CH2Cl
(D) CH3CCl2-CH3

122. Which among the following tests is useful to differentiate between styrene and
phenol?

(A) Lucas test
(B) Test with bromine water
(C) Test with bromine in dry chloroform
(D) Test with KMnO4

123. Identify the incorrect statement about natural rubber.

(A) Double bonds are located between C2 and C3 of each isoprene unit
(B) Has mostly trans double bonds
(C) Intermolecular forces are quite weak
(D) Has a randomly coiled structure

124. The monomer unit/units in cellulose is/are

(A) α-D-glucose
(B) β-D-glucose
(C) Alternating -D-glucose and D-fructose units
(D) Alternating β-D-fructose and D-fructose units

125. Which among the following vitamins is the most efficient antioxidant?

(A) Vitamin D
(B) Vitamin C
(C) Vitamin B
(D) Vitamin A

MATHEMATICS

1  cos A
126. Suppose  2. Then tan A 
1  cos A

(A) tan A  1
(B) tan A  2
(C) tan A  1
(D) tan A  

127. Let a and b be non zero real numbers such that a 2  b2  1. Then

(A) a  b 1
(B) a b  2
(C) a b  2
(D) a b  2

128. Let tan 2 x  2 tan 2 y  1. Then sin 2 y 

(A) sin 2x
(B)  cos 2x
(C) cos 2x
(D)  sin 2x

x x 1
129. Let tan   and tan   . Then    
x 1 x


(A)
3

(B)
6

(C)
2

(D)
4

130. Let a  sin x, b  cosec x and a  b  3. Then a 2  b2 

(A) 3
(B) 5
(C) 7
(D) 9

1  sin 2
131. Suppose  cot 2 ( x   ), then x is equal to
1  sin 2


(A)
4

(B)
3
2
(C)
3
3
(D)
4

x x
132. The maximum value of 5sin 2 x  4 cos 2 x  sin  cos is
2 2

(A) 5 2 2
(B) 52 2
(C) 5 2
(D) 5 2

133. The chances to fail in Mathematics is 20% and the chances to fail in Chemistry is
25%. The chance to fail in at least one subject is

11
(A)
13
14
(B)
15
2
(C)
5
11
(D)
12

134. An urn contains 4 red and 6 blue balls. The probability that two balls are drawn in
which second ball drawn is blue without replacements, is

3
(A)
5
4
(B)
5
2
(C)
5
7
(D)
15

135. The third moment about the mean for normal distribution is

(A) 5
(B) 3 2
(C) 7 2
(D) 0

136. A box contains 24 identical balls of which 12 are white and remaining black. The
balls are drawn at random from the box one at a time with replacement. The
th th
probability that a white ball is drawn for the 4 time on the 7 draw is

6
(A)
32
5
(B)
32
7
(C)
32
1
(D)
2

137. 5 gentlemen and 5 ladies take seats at random round a table. The probability that they
are sitting alternatively is

3
(A)
126
1
(B)
252
1
(C)
126
3
(D)
252

138. Let A and B be two non-empty subsets of a set X such that A is not a subset of B. Then
(A) A and B are disjoint
(B) B  A
(C) A is the complement of B
(D) A and B may be disjoint

139. Let f : R  R be defined by f ( x)  cos 2 x. Then f is

(A) a one-to-one function
(B) an onto function
(C) both one-to-one and onto function
(D) neither one-to-one nor onto function

 1 1
140. Let f  z    z 2  2 for all real z  R \{0}. Then f ( z ) 
 z z

(A) z2
(B) z2 1
(C) z 2  2 for all z  2
(D) z 2  2 for all z  2

141. Define f ( x)  x 1 for all real numbers x. Then

f  x2    f ( x)  for all x
2
(A)
(B) f ( x  y )  f ( x)  f ( y ) for all x, y
(C) f  x   f ( x) for all x
(D) All (A) to (C) above are not true

 1 i 
142. The sum    2k 1  is equal to
i 1 i !  k 1 

(A) e2  e
(B) e2  e
(C) e2  1 e
(D) e 1 e

 (log x) 2 n
143. If S   , then S 
n 0 (2n)!

(A) x  x1
(B) x  x1
x  x 1
(C)
2
(D) 0

22 32
144. The sum of the series   ...   is
2! 3!

(A) 2e
(B) 2e 2
(C) e2
(D) e 2

 x 6 x9 
145. If y    x3    ...   
 2 3 
 

(A) x  1 e y
(B) x  1 e y
(C) x3  1  e y
(D) x3  1  e  y

2 4 6
146. Sum of the series    ...  
1! 3! 5!

(A) e
(B) e 2
(C) e
(D) e2

cos 2  cos  sin  sin 
147. The value of f ( )  cos  sin  sin 2   cos 
sin   cos  0

(A) 0
(B) 1
(C) 1
(D) 2

148. If A is a skew-symmetric matrix of order n, then the trace of A is

(A) n 2
(B) n
(C) 0
(D) 1

y 1 0 7
149. Suppose A  y 2  1 y  1 8  ay 3  by 2  cy  d . Then
2y 3y 0

(A) c  17, d  0
(B) b  38, d  0
(C) a  21, b  38
(D) a  21, d  0

4 x  7 2 2 
150. Let A   4x  7 2  . One of the root of the equation A  0 is
 2
 2 2 4 x  7 

(A) 34
(B) 3 4
(C) 43
(D) 4 3

 2 0 0
151. 
Let A be the matrix  0 2 0  . Then the value of adj A is equal to
 0 0 2 

(A) 8
(B) 64
(C) 16
(D) 32

2
1 36 0   6 0
152. Given that the matrix    . Then the value of x is
 x 1 36   a 6 

a
(A)
108
5a
(B)
108
3a
(C)
118
a
(D)
118

n
 a  4
153. For a positive integer n, the third term in the expansion of  4 a   is 15a .
 1 
 a 
Then the value of n is

(A) 6
(B) 5
(C) 3
(D) 15

k i.k Ci
154.  kC is equal to
i 0 i 1

k (2k  1)
(A)
2
k ( k  1)
(B)
2
k (2k  1)
(C)
2
2
k (k  1)
(D)
2

155. The coefficient of x8 in the expansion of (1  x)7  (1  x)8  ...  (1  x)14 
 

(A) 15 C8
15
(B) C6
15
(C) C4
(D) 15 C5

n
7 8  x
156. Given that the coefficient of x and x in the expansion of  2   are equal. Then
 4
n=

(A) 91
(B) 8.7!
(C) 71
(D) 7.8!

    is
4 4
157. Number of terms in the expansion of y 2  y 2  1  y2  y2 1

(A) 10
(B) 8
(C) 6
(D) 5

158. There are 5 letters and 5 different envelopes. The number of ways in which all the
letters can be put in wrong envelope is
(A) 119
(B) 44
(C) 59
(D) 40

159. The number of diagonals in an octagon will be

(A) 12
(B) 16
(C) 18
(D) 20

160. The number of divisors of the form 4n  2 (n  0) of the integer 240 is equal to

(A) 3
(B) 4
(C) 12
(D) 15

161. There are three coplanar parallel lines. If any p points are taken on each of the lines,
the maximum number of triangles with vertices at these points is

(A) p 2 ( p  3)
(B) p 2 ( p  3)
(C) p2 (4 p  3)
(D) p2 (4 p  3)

162. In class of 18 students, every student has to hand shake with every other student.
The total number of handshakes was
(A) 17
(B) 18
(C) 153
(D) 306

6
163. Total number of numbers that are less than 4.10 and can be formed using
the digits 1, 2, 3 is equal to

9.38  3
(A)
2
8
9.3  2
(B)
3
8
9.3  3
(C)
3
8
9.3  3
(D)
2

164. A variable name in certain computer language must be either an alphabet or an
alphabet followed by a decimal digit. Total number of different variable names that
can exist in that language is equal to
(A) 280
(B) 286
(C) 290
(D) 296

165. Let X = {a | a is a prime number and a < 30}. The number of different rational
numbers whose numerator and denominator belong to X is
(A) 90
(B) 91
(C) 180
(D) 181

166. Let z 2  z  1  0 and z be a complex number. Then the value of z n  z n , where n is
a multiple of 3 is

(A) 2(1)n
(B) 2n
(C) (1)n1
(D) 0

167.  
Assume that (1  i )(1  2i )(1  3i )...(1  xi )    i  . Then 2.5.10... 1  x 2 is equal to

(A)  2   2
(B) 2  2
(C)   i 
(D)  .

   3  3  5 2  is equal to
2 2
168. If  is a cube root of unity, then 3  5  3 2

(A) 2
(B) 2
(C) 4
(D) 4

  x  iy  
169. cos  i log    is equal to
  x  iy 

x2  y 2
(A)
x2  y 2
xy
(B)
x2  y 2
x2  y 2
(C)
2 xy
2xy
(D)
x2  y 2

2 2
170. Let z be a complex number satisfying the relation z  36  36 z  1 .
Then z is equal to

(A) 5
(B) 6
(C) 7
(D) 8

z 1
171. If z is a complex number such that  0 is purely real. Then
z 1

(A) z is purely imaginary
(B) z is purely real
(C) z  1
(D) Re( z )  0 and Im( z )  0

3
172. The product of all values of (cos x  i sin x) 4 is

(A) (cos 4 x  i sin 4 x)
(B) (cos 4 x  i sin 4 x)
(C) (cos 3x  i sin 3x)
(D) (cos 3x  i sin 3x)

173. Let z be a complex number such that z  4  3. Then

(A) z 1  6
(B) 0  z 1  6
(C) z 1  0
(D) 3  z 1  6

1 1 1
174. Let a, b, c  0. Then a (1  b)  , b(1  c)  , c(1  a) 
4 4 4

(A) are never possible
(B) are always possible
(C) are sometimes possible
(D) cannot be discussed

2
175. The inequality  3 is true, when x belongs to
x

(A) 2 3,
(B)  , 2 3
(C) (2 3, )  (,0)
(D) (, 0)

  sin 2 
176. Let    0,  . The value of the expression x2  x  is always greater
 2 x2  x
than or equal to
(A) 1
(B) 2
(C) 2sin 
(D) 2cosec 

177. Solutions of 2 y  3  y  6 are

(A) 1, 1
(B) 1, 1
(C) 1,9
(D) 9

a2
178. If a  R and m  is real, then
1  a4

1
(A) 0m
2
(B) 0  m 1
(C) 0m2
(D) 0m

179. Let a, b, c be three distinct numbers which are in a Geometric Progression. Also the
numbers a, 2b, 3c are in an Arithmetic Progression. Then the common ratio of the
Geometric Progression is
(A) 3
(B) 1
2
(C)
3
1
(D)
3

180. Three positive real numbers x, y, z are in Arithmetic Progression and xyz = 4.
The the minimum value of y is

(A) 2
(B) 3
2
(C) 21 3
(D) 22 3

1 2
181. The maximum possible integer value of sum 15  14  13  ... is
7 7

(A) 134
(B) 136
(C) 138
(D) 140

182. Let S n denotes the sum of n terms of an Arithmetic Progression.
Then the value of Sn3  5Sn 2  7 Sn1  3Sn is

(A) 0
(B) 3
(C) 6
(D) 9

183. The sum of 10 terms of the series 3  12  48  ...

(A) S  1023 3
(B) S  1023 2
(C) S  1025 2
(D) S  1025 3

184. The harmonic mean of two numbers is 8. Also their arithmetic mean is A and
2
geometric mean is G. If G satisfies 2A + G = 90, then the numbers are

(A) 2, 2
(B) 6, 12
(C) 2,12
(D) 6,12

n r 2  r 1
185. The sum  is equal to
r 1 (r  1)!

n
(A)
(n  1)!
1
(B) 
(n  1)(n  1)!
n
(C) 1
(n  1)!
n
(D)  1
(n  1)!

186. The equation y  2  4 y  2  y  7  6 y  2  1 has

(A) no solution
(B) one solution
(C) two solutions
(D) more than two solutions

2
187. Let α and β be the roots of the equation my − ny − p = 0.
2 2
Then the root of the equation (m + px) = n x are

(A)    ,   
1 1
(B) 2
, 2
 
11
(C) , 2
2
 
(D)  2 ,  2

2 2
188. If the roots of the equation y − 2my + m + m − 3 = 0 are real and less than 3, then

(A) m = 1
(B) m  1
(C) m = 2
(D) m < 2

189. Let  ,  2 be the roots of the equation y 2  4 y  1  0.
Then  46 ,  62 are roots of the equation

(A) y2  4 y 1  0
(B) y2  4 y 1  0
(C) y 2  4 y 1  0
(D) y 2  4 y 1  0

x
7
190. The number of real solutions of the equation    13  x  x 2 is
 13 

(A) 3
(B) 2
(C) 1
(D) 0

191. Given that the sum of the squares of the roots of the equation y 2  (k  3) y  k  2  0
is 13. Then number of values of k lying in the interval [1, 4] is
(A) 0
(B) 1
(C) 2
(D) 3

2 2
192. Let 8sin x  8cos x  6. Then

2
(A) sin 2 x 
3
1
(B) sin x  
3
1
(C) cos 2 x 
2
1
(D) cos x  
2

193. The equation sin x  2cos x has

(A) infinitely many solutions
(B) finitely many solutions
(C) has no solutions in integers
(D) has no solutions

 
194. The value of x satisfying 1  cos x  cos 2 x  ...  4  2 3 in the interval  ,   is
2 

2
(A)
3

(B)
2
4
(C)
5
3
(D)
4

2 cos A cos B 2 cos C a b
195. In a triangle ABC, let     . Then b2  c2 is equal to
a b c bc ac

(A) a 2
(B) ac
(C) bc
(D) a  b

196. Let a, b, c be the sides of a ABC. Further two equation ax 2  bx  c  0 and
x 2  5 x  2  0 have a common root. Then the C 


(A)
2

(B)
4

(C)
3
2
(D)
6

197. If the sides of a triangle are proportional to the cosines of the opposite angles, then
(A) the triangle is right angled
(B) the triangle is isosceles
(C) the triangle is equilateral
(D) one of the angle is obtuse

A
198. Let a  7, b  4, c  9 a in a ABC. Then the values of sin and cos A are equal to
2
respectively

4 9
(A) and
13 13
5 8
(B) and
13 13
7 6
(C) and
13 13
6 7
(D) and
13 13

199. Given that the lengths of the sides p, q, r of a PQR are in an Arithmetic
q
Progression. Then the ration lies in the interval
r

1 2
(A)  , 
3 3
2 
(B)  ,2
3 
2 
(C)  ,1
3 
1 4
(D)  , 
3 3

200. The two adjacent sides AB and BC of a cyclic quadrilateral ABCD are 2 and 5 units
respectively and the angle between them is 60°. Then the area of circle circumscribing
the quadrilateral ABCD is

9
(A)
2
19
(B)
2
9
(C)
3
19
(D)
3

201. In a ABC , 2a2  9b2  c2  6ab  2ac, then cosC is equal to

(A) 12
(B) 13
(C) 14
(D) 16

 A B
202. In the ABC , (a  b  c)  tan  tan  is equal to
 2 2

C
(A) 2c cot
2
A
(B) 2a cot
2
B
(C) 2b cot
2
C
(D) tan
2

  1 
203. sin   sin 1     is equal to
6  2 

(A) 0
(B) 
(C) 1
(D) 1

204. If sin A  cos B  a and sin B  cos A  b, sin( A  B ) is equal to

a 2  b2  2
(A)
2
2
a  b2  2
(B)
2
2
a  b2  2
(C)
2
2
a  b2  2
(D)
2

205. The first and last terms of an Arithmetic Progression are 1 and 56.
If the sum of its terms is 290, then the number of terms will be
(A) 4
(B) 6
(C) 8
(D) 10

206. Suppose A is a point which is at equidistant from X (1,3), Y (3,5) and Z (5, 1).
Then the point A is

(A) (8, 10)
(B) (8, 10)
(C) (8,10)
(D) (8,10)

207. The midpoint of the line joining (−6, 4) and (8,−6) divides the line
joining (3, 6) and (−6,−3) in the ratio
(A) 2:7 externally
(B) 2:7 internally
(C) 3:7 internally
(D) 3:7 externally

208. The sum of the distances from a point to the two perpendicular lines is 2.
The locus of the point is
(A) a square
(B) a pair of straight lines
(C) an ellipse
(D) a parabola

209. If a point P(2,1) is shifted by a distance 2 units parallel to the line x  y  0,
then the new position of P is

(A) (1, 2)
(B) (1, 2)
(C) (1, 2)
(D) (1, 2)

210. The length of the common chord of intersection of the circles
x2  y 2  2x  4 y  4  0 and x2  y 2  2x  6 y  6  0 is

(A) 0
(B) 1
(C) 2
(D) 3

211. The equation of the tangents to the circle x2  y 2  25 with 3 as x coordinate are

(A) 3 x  5 y  25
(B) 3x  4 y  5
(C) 3x  4 y  25
(D) 3x  5 y  5

212. The equation of the circumcircle of the triangle formed by the lines
x  2, y  0 and x  y  6  0 is

(A) x2  y 2  8x  4 y  12  0
(B) x2  y 2  8x  4 y  12  0
(C) x2  y 2  8x  4 y  12  0
(D) x2  y 2  8x  4 y  12  0

2
213. The equation of a parabola is y = 4x. P(1, 3) and Q(1, 1) are two points in the
xy-plane. Then, for the parabola
(A) P and Q are exterior points
(B) P is an interior point while Q is an exterior point
(C) P and Q are interior points
(D) P is an exterior point while Q is an interior point

2
214. A circle having its center at (2, 3) is cut orthogonally by the parabola y = 4x.
The possible intersection point of these curves can be

 
(A) (1, 2) or 3,3 3
(B) (9, 6) or  2, 2 2 
(C) (1, 2) or (4, 4)

(D) (1, 3) or 2, 2 2 

x2 y2
215. If the polar of y 2  4ax is always touching the ellipse   1,
a 2 b2
then the locus of the pole is

(A) 4a2 x2  b2 y 2  4a4
(B) 4a2 x2  b2 y 2  4a4
(C) 4a2 x2  b2 y 2  4b4
(D) 4a2 x2  b2 y 2  4b4

x2 y 2
216. The radius of the circle passing through the foci of the ellipse  1
16 9
and having its center (0, 3) is

(A) 4
(B) 3
(C) 12
7
(D)
2

217. The equation to the hyperbola having its eccentricity 2 and
the distance between foci as 8, is

x2 y 2
(A)  1
4 12
x2 y 2
(B)  1
12 4
x2 y 2
(C)  1
2 4
x2 y 2
(D)  1
4 2

25
218. The equation of the hyperbola whose vertices are at (5, 0) and (−5, 0) and x  as
7
one of its directrices, is

x2 y 2
(A)  1
25 24
x2 y 2
(B)  1
24 25
x2 y 2
(C)  1
16 25
x2 y 2
(D)  1
25 16

d  1  3x  x3  
219.  tan  2  
is equal to
dx   1  3x  

3 1
(A) 2
x
1 9x 3
9 1
(B) 2
x
1 x 3
3 1
(C) 2
x
1 x 3
1 1
(D) 2
x
9 x 3

2
 dy 
220. Let x  sec  cos and y  sec   cos  . Then   
2 2
 dx 

(A)

4 y2  4 
x2  4

(B)

4 y2  4 
x2  4

(C)

4 y2  4 
x2  4

(D)

4 y2  4 
x2  4

x2 y 2
221. Given that the line y = 3x + c touches the curve   1. The value of c is
4 9
(A) an integer
(B) always a rational number
(C) always an irrational number
(D) sometimes a rational number

222. Let f ( x)  cos x  sin x . Then f '  2 3 

1 3
(A)
2
3 1
(B)
2
(C) 0
3 1
(D)
2

    dy
223. If x  a cos   log tan    and y  a sin  , then is
  2  dx

(A) cot 
(B) tan 
(C) sin 
(D) cos

224. If f ( x)  x 1 g ( x)  f  f ( x)  , then, for all x  2, g '( x ) 

(A) 1
(B) 2
(C) 1
(D) 0

225.
    
If y  sin cos1 sin cos 1 x  , then
dy
dx
1
at x  is equal to
2

(A) 0
(B) 1
(C) 2 3
(D) 1

 5x  x2 
The function f ( x)  log10 
 4 
226. exists for
 

(A) [1, 4]
(B) [1, 0]
(C) [0, 5]
(D) [5, 0]

x3
227. The range of the function f ( x)  , x  3 is
x3

(A) {0}
(B) {0, 1}
(C) {3,3}
(D) {1,1}

2x x
228. The period of the function f ( x)  cos  sin is
7 2

(A) 7
(B) 4
(C) 14
(D) 28

0, x is irrational
229. Let f : R  R be defined as f ( x)   .
sin | x |, x is rational
Then which of the following is true?

(A) f is discontinuous for all x
(B) f is continuous for all x
(C) f is discontinuous at x  k , where k is an integer
(D) f is continuous at x  k , where k is an integer

230. The period of the function f ( x)  cosec33x  cot 4 x is


(A)
3

(B)
4

(C)
6
(D) 

x2
 x7
231. lim is equal to
x  x  3 

(A) e2
(B) e4
(C) e 4
(D) e 2

sin x n
232. Let m, n be natural numbers with n  m. lim is equal to
x0 (sin x)m

(A) 2
(B) 2
(C) 1
(D) 0

sin x  (sin x)sin x
233. lim
x 1  sin x  log sin x
2

(A) 1
(B) 2
(C) 3
(D) 4

2
234. If the curve y = x + bx + c touches the line y = x at the point (1, 1), then the values of
x for which the curve has a negative gradient are

3
(A) x
2
3
(B) x
2
1
(C) x
2
1
(D) x
2

2
235. The sub tangent, ordinate and sub normal to the parabola y = 4ax
at a point (different from the origin) are
(A) in Harmonic Progression
(B) in Geometric Progression
(C) in Arithmetic Progression
(D) equal


236. If 0  x  , then
2

(A) cos(sin x)  sin(cos x)
(B) sin(cos x)  cos x
(C) cos(sin x)  sin(cos x)
(D) cos(sin x)  cos x

 
 2 x  2 x 1 sin x
2 2
 
237. The minimum value of e is

(A) 0
(B) 1
(C) 2
(D) 3

dx
238.  x2  4x  5 is equal to
1  1 x2 
(A)  tan ( x  2)  2 c
2 x  4x  5 
1  1 x 
(B)  tan ( x  2)  2 c
2 x  4x  5 
1  1 x2 
(C)  tan ( x  2)  2 c
2 x  4x  5 
1  1 x 
(D)  tan ( x  2)  2 c
2 x  4x  5 

2
 x2 x
239.   x  4  e dx is equal to
 x 
(A) ex  c
 x4
 x2
(B) ex  c
 x4
 x2
(C) ex  c
 x4

x  2 xe
x
(D) e  c
 x4

1
1
240. The value of I   x x  dx is equal to
0 2

1
(A)
2
1
(B)
3
1
(C)
4
1
(D)
8

 1   1 
241. Consider the group  R \   ,*  where a * b  a  b  2ab for all a, b  R \   .
 2  2
Then the inverse of arbitrary element a is

a
(A)
a 1
a
(B)
2a  1
a
(C)
2a  1
a
(D)
a 1

2
242. The area bounded by y = 2x − x and y -axis is

(A) 3 sq. units
(B) 2 sq. units
(C) 1 sq. units
(D) 0 sq. units

243. If the position vector of three points are a  2b  3c ,3a  4b  5c , a  8b  11c ,
then the three points are

(A) non-coplanar
(B) non-collinear
(C) collinear
(D) unit vectors

244. The sides of a parallelogram are a  i  2 j  3k , b  i  j  2k . Then the unit vector
parallel to one of the diagonals is

1
(A) (2i  3 j  k )
14
1
(B) (2i  3 j  k )
14
1
(C) ( j  5k )
26
1
(D) ( j  5k )
26

245. In a three dimensional space, the equation 8x + 7y = 0 represents

(A) the z-axis
(B) the z-plane
(C) the x-axis
(D) the plane y = 0

x y z
246. The plane x  2 y  z  6 and the line   are related as
1 2 3

(A) parallel to the plane
(B) at right angles to a plane
(C) lies in the plane
(D) meets the plane obliquely

247. If the position vectors of A,B and C are respectively iˆ  ˆj  kˆ, iˆ  2 ˆj  4kˆ and
2iˆ  3 ˆj  3kˆ, then cos2 B is equal to

1
(A)
63
4
(B)
63
6
(C)
63
11
(D)
63

dy
248. The number of solutions at x = 5 for the equation  x  7  0 is
dx

(A) 0
(B) 1
(C) 5
(D) 

dy
249. A solution of the differential equation ( x  y ) 2  4 is
dx

 x y
(A) y  2 tan 1  c
 2 
 x y
(B) y  2 tan 1  c
 2 
 x y
(C) y  tan 1  c
 2 
 x y
(D) y  tan 1  c
 2 

2
250. I    x  1  x  2  dx 
3

(A) 10
(B) 12
(C) 15
(D) 18

FINAL ANSWER KEY
Subject Name: 101 B TECH 16-S2
SI No. Key SI No. Key SI No. Key SI No. Key SI No. Key SI No. Key SI No. Key SI No. Key SI No. Key
1 C 31 C 61 A 91 C 121 A 151 B 181 C 211 C 241 C
2 A 32 B 62 A 92 C 122 C 152 A 182 A 212 C 242 D
3 B 33 A 63 C 93 B 123 B 153 A 183 A 213 D 243 C
4 D 34 D 64 D 94 B 124 B 154 B 184 D 214 C 244 B
5 B 35 D 65 D 95 D 125 B 155 B 185 B 215 B 245 A
6 D 36 B 66 A 96 C 126 C 156 C 186 D 216 A 246 A
7 B 37 C 67 A 97 A 127 B 157 D 187 B 217 A 247 B
8 C 38 D 68 B 98 A 128 B 158 B 188 D 218 A 248 A
9 D 39 C 69 B 99 D 129 C 159 D 189 A 219 C 249 B
10 A 40 D 70 B 100 B 130 C 160 B 190 D 220 B 250 C
11 B 41 D 71 D 101 D 131 D 161 D 191 B 221 C
12 A 42 C 72 C 102 C 132 C 162 C 192 A 222 B
13 C 43 A 73 B 103 B 133 C 163 D 193 D 223 B
14 A 44 B 74 C 104 D 134 A 164 B 194 A 224 A
15 C 45 A 75 C 105 B 135 D 165 B 195 A 225 B
16 C 46 A 76 A 106 A 136 B 166 D 196 B 226 A
17 D 47 C 77 D 107 C 137 C 167 B 197 C 227 D
18 B 48 C 78 A 108 B 138 D 168 D 198 D 228 D
19 C 49 C 79 C 109 C 139 D 169 A 199 B 229 D
20 D 50 C 80 B 110 D 140 C 170 B 200 D 230 D
21 A 51 A 81 A 111 C 141 D 171 B 201 D 231 B
22 A 52 B 82 A 112 B 142 A 172 D 202 A 232 D
23 D 53 B 83 A 113 B 143 C 173 B 203 C 233 B
24 B 54 C 84 A 114 B 144 A 174 A 204 A 234 D
25 A 55 C 85 B 115 C 145 C 175 C 205 D 235 B
26 B 56 B 86 A 116 A 146 A 176 C 206 A 236 C
27 D 57 D 87 A 117 B 147 C 177 D 207 B 237 B
28 D 58 C 88 C 118 A 148 C 178 A 208 A 238 A
29 B 59 A 89 A 119 B 149 D 179 D 209 D 239 A
30 D 60 C 90 C 120 C 150 A 180 D 210 A 240 D