KCET 2027 Sample Paper

SAMPLE PAPER

S A M P L E Q U E S T I O N P A P E R

KCET 2027
Modelled on the actual exam pattern
.

QUESTIONS MAX MARKS TIME MARKING

180 180 180 Min +1 / 0

GENERAL INSTRUCTIONS

1. This paper contains 180 multiple-choice questions. All questions are compulsory.

2. Each question has four options — (A), (B), (C) and (D) — of which only one is correct.

3. Each correct answer carries 1 mark; there is no negative marking.

4. Total time allowed is 180 minutes. Manage your time across all sections.

5. Use of calculators, mobile phones or any electronic device is not permitted.

6. Attempt the paper first, then check your answers against the Answer Key at the end.

Candidate Name: Roll No.: Date:

SAMPLE PAPER

KCET 2027
SAMPLE QUESTION PAPER

Questions 180 Max Marks 180 Time 180 Min Marking +1 / 0

Attempt all questions. Choose the one correct option for each.

PHYSICS

1. The figure gives the electric potential V as a function 2. A cup of tea cools from 65°5°C to 62:5°C in 1 minute in
of distance through four regions on x- axis. Which of the a room at 22:5°C. How long will it take to cool from
following is true for the magnitude of the electric field E 46°5°C to. 40-5°C in the same room ?
in these regions?
(A) 4 minutes
(A) E > E > E > E (B) 2 minutes
A B C D
(B) E = E and E E (C) 1minute
A C B D
(C) E = E and E E (D) 3 minutes
B D A C
(D) E E E E
A B C D

3. A 100 W bulb is connected to an AC ’ source of 220 V, 4.  A particle shows a distance-time curve as shown in the
50 Hz. Then the current flowing through the bulb is figure. The maximum instantaneous velocity of the
particle is around the point
(A) 5/11 A

(B) ½ A (A) P

(C) 2 A (B) S

(D) ¾ A (C) R

(D) Q

5. If E and B represent electric and magnetic field 6. A linear object of height 10 cm is kept in front of a
vectors of an electromagnetic wave, the direction of concave mirror of radius of curvature 15 cm, at a
propagation of the wave is along distance of 10 cm. The image formed is

(A) E (A) magnified and erect

(B) B (B) magnified and inverted

(C) E × B (C) diminished and erect

(D) B × E (D) diminished and inverted

7. A hydrogen atom in ground state absorbs 10.2 eV of 8. An electromagnetic wave is travelling in x-direction
energy. The orbital angular momentum of the electron is with electric field vector given by, E =E (kx-ω t) j . The
y 0
increased by correct expression for magnetic field vector is

(A) 1.05 x 10-34 Js (A) B =E C (kx-ω t) j
y 0
(B) 2.11 x 10-34Js (B) B =E C (kx-ω t) j
z 0
(C) 3.16 x 10-34Js (C) B =E C (kx-ω t) j
y 0
(D) 4.22 x 10-34Js (D) B =E C (kx-ω t) j
z 0

9. If the last band on the carbon resistor is absent, then 10. A system of two charges separated by a certain
the tolerance is distance apart stores electrical potential energy. If the
distance between them is increased, the potential energy
(A) 5%
of the system.
(B) 20%
(A) E > E > E > E
(C) 10% A B C D
(B) decreases in any case
(D) 15%
(C) may increase or decrease

(D) remains the same

11. The scientist who is credited with the discovery of 12. The phenomenon involved in the reflection of radio-
‘nucleus’ in an atom is waves by ionosphere is similar to

(A) J.J. Thomson (A) reflection of light by plane mirror

(B) Rutherford (B) total internal reflection of light in air during a mirage

(C) Niels Bohr (C) dispersion of light by water molecules during the

(D) Balmer formation

(D) scattering of light by air particles

13. Two protons are kept at a separation of 10nm. Let F 14. Ohm’s Law is applicable to
n
and F be the nuclear force and the electromagnetic
e (A) Diode
force between them
(B) Transistor
(A) F = F
e n (C) Electrolyte
(B) Fe>>Fn
(D) Conductor
(C) Fe Fn

(D) Fe and Fn differ only slightly

15. In Karnataka, the normal domestic power supply AC 16. The number of turns in a coil of Galvanometer is
is 220 V, 50 Hz. Here 220 V and 50 Hz refer to tripled, then

(A) Peak value of voltage and frequency (A) Voltage sensitivity increases 3 times and current

(B) rms value of voltage and frequency sensitivity remains constant

(C) Mean value of voltage and frequency (B) Voltage sensitivity remains constant and current
sensitivity increases 3 times
(D) Peak value of voltage and angular frequency
(C) Both voltage and current sensitivity remains constant

(D) Both voltage and current sensitivity decreases by 33%

17. A straight wire of length 50 cm carrying a current of 18. Five identical resistors each of resistance R = 1500 Q
2.5 A is suspended in mid-air by a uniform magnetic field are connected to a 300 V battery as shown in the circuit.
of 0.5 T (as shown in figure). The mass of the wire is ( g = The reading of the ideal ammeter A is
10 m s ^ - 2 )
(A) ⅕ A
(A) 62.5 gm (B) ⅗ A
(B) 250 gm (C) ⅖ A
(C) 125 gm (D) ⅘ A
(D) 100 gm

19. A piece of copper is to be shaped into a conducting 20. A step-up transformer operates on a 230 V line and a
wire of maximum resistance. The suitable length and load current of 2 A. The ratio of primary and secondary
diameter are _______ and _______ respectively. windings is 1 : 25. Then the current in the primary is

(A) L and d (A) 25 A

(B) 2 L and d (B) 50 A

(C) L/2 and 2 d (C) 15A

(D) 2 L and d/2 (D) 12.5A

21. Which of the following properties is ‘False’ for a bar 22. Two cells of internal resistances r and r and of
1 2
magnet ? same emf are connected in series, across a resistor of
resistance R. If the terminal potential difference across
(A) Its poles cannot be separated.
the cells of internal resistance r, is zero, then the value
(B) It points in North-South direction when suspended.
of R is
(C) Its like poles repel and unlike poles attract.
(A) R = 2(r + r )
1 2
(D) It doesn’t produce magnetic field.
(B) R = r - r
2 1
(C) R = r - r
1 2
(D) R = 2(r - r )
1 2

23. In Young’s double slit experiment, using 24. A cylindrical container containing water has a small
monochromatic light of wavelength λ , the intensity of hole at height of H = 8 cm from the bottom and at a
light at a point on the screen where path difference is λ is depth of 2cm from the top surface of the liquid. The
K units. The intensity of light at a point where path maximum horizontal distance travelled by the water
difference is λ/3 is before it hits the ground (x) is

(A) K (A) 8 cm

(B) K/4 (B) 4√2 cm

(C) 4K (C) 4cm

(D) 2K (D) 6 cm

25. A particle of mass m and charge q is placed at rest in 26. The trajectory of a projectile projected from origin is
uniform electric field E and then released. The kinetic given by the equation y=x-2 x25 The initial velocity of the
energy attained by the particle after moving a distance y projectile is
is
(A) ⅖ ms-1
(A) qEy2 (B) 5 ms-1
(B) qE2y (C) 25 ms-1
(C) qEy (D) 5/2 ms-1
(D) q2Ey

27. Which of the following graphs correctly represents 28. For which combination of working temperatures, the
the variation of ‘g’ on the Earth ? efficiency of ‘Carnot’s engine’ is the least ?

(A) (A) 60 K, 40 K

(B) (B) 40 K, 20 K

(C) (C) 80 K, 60 K

(D) (D) 100 K, 80 K

29. The waves set up in a closed pipe are 30. In Young’s double-slit experiment if yellow light is
replaced by blue light, the interference fringes become
(A) Transverse and Progressive

(B) Longitudinal and Stationary (A) wider

(C) Transverse and Stationary (B) narrower

(D) Longitudinal and Progressive (C) brighter

(D) darker

31. Which of the following, represents the variation of 32. A coil of inductive reactance 1 / √( 3 ) Ω and
inductive reactance (X ) with the frequency of voltage resistance 1 Ω is connected to a 200 V, 50 Hz A.C. supply.
L
source (v) ? The time lag between maximum voltage and current is

(A) (A) ( 1 )/( 300 ) s

(B) (B) ( 1 )/( 600 ) s

(C) (C) ( 1 )/( 500 ) s

(D) (D) ( 1 )/( 200 ) s

33. Kirchhoff’s junction rule is a reflection of 34. Two spheres of electric charges +2 nC and −8 nC are
placed at a distance ‘d’ apart. If they are allowed to
(A) Conservation of current density vector
touch each other, what is the new distance between them
(B) Conservation of energy
to get a repulsive force of same magnitude as before?
(C) Conservation of momentum
(A) ( 4 d )/( 3 )
(D) Conservation of charges
(B) ( 3 d )/( 4 )

(C) d

(D) ( d )/( 2 )

35. The end product of decay of 90Th32 is 82Pb208. The 36. In the given circuit, the current through 2Ω resistor
number of and particles emitted are respectively is

(A) 3, 3 (A) 0.2A

(B) 6, 4 (B) 0.3A

(C) 6, 0 (C) 0.4A

(D) 4, 6 (D) 0.1A

37. A point object is moving uniformly towards the pole 38. The strength of the Earth’s magnetic field
of a concave mirror of focal length 25cm along its axis as
(A) Constant everywhere
shown below. The speed of the object is 1 ms-1. At t = 0,
(B) Zero everywhere
the distance of the object from the mirror is 50cm. the
average velocity of the image formed by the mirror (C) Having very high value

between time t = 0 and t = 0.25 s is: (D) Varying from place to place on the Earth’s surface

(A) 40 cm s-1

(B) 20 cm s-1

(C) zero

(D) Infinity

39. The power dissipated in resistance in the following 40. The minimum value of effective capacitance that can
circuit is be obtained by combining 3 capacitors of capacitances 1
pF, 2 pF and 4 pF is
(A) 0.75 W

(B) 0.25 W (A) ( 4 )/( 7 ) p F

(C) 1 W (B) 1 pF

(D) 0.5 W (C) ( 7 )/( 4 ) p F

(D) 2 pF

41. During inelastic collision between two objects, which 42. The particles emitted in the decay of to _ 92 ^ 238 U
of the following quantities always remains conserved? to _ 92 ^ 234 U

(A) Total kinetic energy (A) 1 α and 2 β

(B) Total mechanical energy (B) 1 α only

(C) Total linear momentum (C) 1 α and 1 β

(D) Speed of each body (D) 2 α and 2 β

43. In a cyclotron a charged particle 44. In a permanent magnet at room temperature

(A) undergoes acceleration all the time (A) magnetic moment of each molecule is zero

(B) speeds up between the dees because of the magnetic (B) the individual molecules have non zero magnetic
field moment which are all perfectly aligned.

(C) speeds up in dee (C) domains are partially aligned

(D) slows down within a dee and speeds up between dees (D) domains are all perfectly aligned

45. A motor pump lifts 6 tonnes of water from a well of 46. Pressure of an ideal gas is increased by keeping
depth 2 m to the first floor of height 35 m from the temperature constant. The kinetic energy of molecules
ground floor in 20 minutes. The power of the pump (in
(A) Decreases
kW) is [ g = 10 m s ^ - 2 ] .
(B) Increases
(A) 1.85
(C) Remains same
(B) 6
(D) Increases or decreases depending on the nature of gas
(C) 3

(D) 12

47. If P, Q and R are physical quantities having different 48. The equation of a stationary wave is y=2 ((π x)/(15))
dimensions, which of the following combinations can (48 π t) . The distance between a node and its next
never be a meaningful quantity? antinode is

(A) (P-Q)/(R) (A) 7.5 units

(B) PQ - R (B) 1.5 units

(C) PQ/R (C) 22.5 units

(D) PR-Q2R (D) 30 units

49. A charge q is accelerated through a potential 50. The angle between velocity and acceleration of a
difference V. It is then passed normally through a particle describing uniform circular motion is
uniform magnetic field, where it moves in a circle of
(A) 45 ^ °
radius r. The potential difference required to move it in a
(B) 60 ^ °
circle of radius 2r is
(C) 90 ^ °
(A) 2V
(D) 180 ^ °
(B) 4V

(C) 1V

(D) 3V

51. The half-life of tritium is 12.5 years. What mass of 52.
tritium of initial mass 64 mg will remain undecayed after
Light from the Sun passes through a prism and a
50 years ?
spectrum is produced on a screen. A thermometer placed
(A) 32mg at point X shows a temperature increase. For the given
(B) 8 mg diagram, which type of radiation causes this temperature

(C) 16 mg increase? Select the most appropriate option.

(D) 4 mg

(A) X-rays

(B) Ultraviolet Rays

(C) Infra-red Rays

(D) Visible light

53. Two particles of masses m and m have equal kinetic 54. The magnitude of point charge due to which the
1 2
energies. The ratio of their momenta is electric field 30 cm away has the magnitude 2 NC-1 will
be
(A) m : m
1 2
(B) m : m (A) 2 x 10-11 C
2 1
(C) √ m :√ m (B) 3 x 10-11 C
1 1
(D) m : m (C) 5 x 10-11 C
1 3
(D) 9 x 10-11 C

55. The conductivity of semiconductor increases with 56. An electric dipole is kept in non-uniform electric
increase in temperature because field. It generally experiences

(A) number density of charge carriers increases (A) A force and torque

(B) relaxation time increases (B) A force but not a torque

(C) both number density of charge carriers and relaxation (C) A torque but not a force
time increase (D) Neither a force nor a torque
(D) number density of current carriers increases, relaxation
time decreases but effect of decrease in relaxation time is
much less than increase in number density

57. A capacitor of capacitance C charged by an amount Q 58. Masses of three wires of copper are in the ratio 1 : 3
is connected in parallel with an uncharged capacitor of : 5 and their lengths are in the ratio 5 : 3 : 1. The ratio of
capacitance 2C. The final charges on the capacitors are their electrical resistance are

(A) Q/2, Q/2 (A) 1 : 3 : 5

(B) Q/4, 3Q/4 (B) 5 : 3 : 1

(C) Q/3, 2Q/3 (C) 1 : 15 : 125

(D) Q/3, 4Q/3 (D) 125 : 15 : 1

59. An aluminium sphere is dipped into water. Which of 60. In the figure shown, if the diode forward voltage
the following is true? drop is 0.2 V, the voltage difference between A and B is

(A) Buoyancy will be less in water at 0°C than that in water (A) 1.3 V
at 4°C (B) 2.2 V
(B) Buoyancy will be more in water at 0°C than that in water (C) 0
at 4°C
(D) 0.5 V
(C) Buoyancy in water at 0°C will be same as that in water
at 4°C

(D) Buoyancy may be more or less in water at 4°C
depending on the radius of the sphere

CHEMISTRY

61. Hydrogenation of vegetable oils in presence of finely 62. The vitamin that helps to clotting of blood is
divided Nickel as catalyst. The reaction is
(A) A
(A) Heterogeneous catalysis (B) C
(B) Homogeneous catalysis (C) B
2
(C) Enzyme catalysed reaction (D) K
(D) Liquid catalysed reaction

63. Relative lowering of vapour pressure of a dilute 64. Which of the following element forms bond with
solution of glucose dissolved in 1kg of water is 0.002. The itself ?
molality of the solution is
(A) N
(A) 0.004 (B) P
(B) 0.222 (C) Se
(C) 0.111 (D) Te
(D) 0.021

65. The reaction quotient ^ ′ Q _ c ^ ′ is useful in 66. Reduction of ketones cannot be carried out with
predicting the direction of the reaction. Which of the which of the following reagents?
following is incorrect ?
(A) Sodium borohydride or Lithium Aluminium hydride
(A) If Q _ c > K _ c , the reverse reaction is favoured (B) Zinc amalgam and concentrated HCl
(B) If Q _ c K _ c , the forward reaction is favoured (C) Hydrazine and KOH in ethylene glycol
(C) If Q _ c =K _ c , No reaction occur (D) Hydrogen in presence of palladium in Barium sulphate
(D) If Q _ c > K _ c , forward reaction is favoured and quinoline.

67. Gold sol is not a 68. Which one of the following metallic oxide exhibit
amphoteric nature ?
(A) Lyophobic sol

(B) Negatively charged sol (A) CaO

(C) Macromolecular sol (B) Na _ 2 O

(D) Multimolecular colloid (C) BaO

(D) Al _ 2 O _ 3

69. The reagent ‘X’ used for the following reaction is 70. The Vant Hoff’s factor ‘i’ accounts for

(A) Ni (A) extent of solubility of solute

(B) Pd/C (B) extent of dissociation of solute

(C) LiAlH (C) extent of dissolution of solute
4
(D) Na/Liquid NH (D) extent of mobility of solute
3

71.  array l If 3.01 × 10 ^ 20 molecules are removed from 72.  Which of the following possess net dipole moment?
98 mg of H _ 2 SO _ 4 , then number of moles of H _ 2 SO _
(A) SO
2
4 left are array
(B) BF
3
(A) 0.1 × 10 ^ - 3 mol
(C) BeCl
2
(B) 0.5 × 10 ^ - 3 mol
(D) CO
2
(C) 66 × 10 ^ - 3 mol

(D) 9.95 × 10 ^ - 2 mol

73. 74. The first ionization enthalpy of the following
elements are in the order:

(A) C N Si P

(B) P Si N C

(C) P Si C N

(D) Si P C N

R and S form benzyl benzoate when treated with each
other. Hence P is

(A) C H CHO
6 5
(B) C H CH OH
6 5 2
(C) C H COCl
6 5
(D) C H COOH
6 5

75. Select wrong chemical reaction among the following : 76. Which of the following will be the most stable
diazonium salt (R N + X)?
(A) array l MnO _ 2 + 4 HCl MnCl _ 2 + Cl _ 2 + 2 H _ 2 O 2

array (A) CH N + X+
3 2
(B) 8 NH _ 3 + 3 Cl _ 2 6 NH _ 4 Cl + N _ 2 (B) C H N + X+
6 5 2
(C) 2 NaOH + Cl _ 2 2 NaCl + H _ 2 + O _ 2 (C) CH CH N + X+
3 2 2
(D) array l 2 Ca ( OH ) _ 2 + 2 Cl _ 2 Ca ( OCl ) _ 2 + CaCl _ 2 (D) C H CH N + X-
6 5 2 2
+ 2 H _ 2 O array

77. (CH ) SiCl is used during polymerization of organo 78. The electronic configuration of transition element
3 3
silicons because “X”, is +3, oxidation state is [Ar]3d5. What is its atomic
number ?
(A) The chain length of organosilicon polymers can be
controlled by adding (CH ) SiCl (A) 25
3 3
(B) (CH ) SiCl improves the quality and yield of the polymer (B) 26
3 3
(C) (CH ) SiCl does not block the end terminal of silicone (C) 27
3 3
polymer (D) 24
(D) (CH ) SiCl acts as a catalyst during polymerisation
3 3

79. Which of the following ions will cause hardness in 80. The charge required for the reduction of 1 mole of
water ? MnO to MnO is
4 2

(A) Ca2+ (A) 1F

(B) Na+ (B) 3F

(C) Cl- (C) 5F

(D) K+ (D) 7F

81. The number of π-bonds and σ-bonds present in 82. 1mole of NaCl is doped with 10-5 mole of SrCl . The
2
naphthalene are respectively number of cationic vacancies in the crystal lattice will be

(A) 6, 19 (A) 6.022 x 1018

(B) 5, 19 (B) 6.022 x 1015

(C) 5, 11 (C) 6.022 x 1023

(D) 5, 20 (D) 12.044 x 1020

83. The monomer used in Novolac, a polymer used in 84. array l By passing electric current, NaClO _ 3 is
paints converted into NaClO _ 4 according to the \ following
equation \ NaClO _ 3 + H _ 2 O NaClO _ 4 + H _ 2 \ How
(A) Phenol and Formaldehyde
many moles of NaClO _ 4 will be formed when three
(B) Melamine and Formaldehyde
Faradays of charge is passed through NaCl O _ 3 ? array
(C) Butadiene and Styrene
(A) 0.75
(D) Butadiene and Acrylo Nitrile
(B) 1.0

(C) 1.5

(D) 3.0

85. Which of the following is an example of 86. Toluene reacts with halogen in presence of Iron (III)
homogeneous catalysis? chloride giving ortho and para halo compounds. The
reaction is
(A) oxidation of NH in Ostwald’s process
3
(B) oxidation of SO in contact process (A) Electrophilic elimination reaction
3
(C) oxidation of SO in lead chamber process (B) Electrophilic substitution reaction
2
(D) manufacture of NH by Haber’s process (C) Free radical addition reaction
3
(D) Nucleophilic substitution reaction

87. Which of the following is generally water insoluble? 88. The process which is responsible for the formation of
delta at a place where rivers meets the sea is
(A) Fibrous protein

(B) Vitamin-C (A) Coagulation

(C) Amylose (B) Colloid formation

(D) Glycine (C) Emulsification

(D) Peptization

89. Solubility of AgCl is least in 90. Lower members of aliphatic carboxylic acid are
soluble in water. This is due to
(A) 0.1 M NaCl

(B) Pure water (A) Formation of hydrogen bonds with water.

(C) 0.1 M BaCl (B) Van der-Waals interaction with water molecules.
2
(D) 0.1 M AlCl (C) Water is non electrolyte
3
(D) Due to London forces

91. Bactericidal antibiotics among the following is 92. The TUPAC name of [Co(NH ) Cl(NO )]Cl is
3 4 2

(A) Ofloxacin (A) tetraamminechloridonitrito-N- cobalt(III) chloride

(B) Erythromycin (B) tetraamminechloridonitrocobalt(I]) chloride

(C) Tetracycline (C) tetraamminechloridonitrocobalt(I) chloride

(D) Chloramphenicol (D) tetraamminechloridodinitrocobalt(III) chloride

93. The elements in which electrons are progressively 94. Ziegler-Natta catalyst is used to prepare
filled in 4f orbital are called
(A) Low-density polythene
(A) Actinoids (B) Teflon
(B) Transition elements (C) High density polythene
(C) Lanthanoids (D) Nylon-6
(D) Halogens

95. The formula of penta aquanitrato chromium (III) 96. In the following reaction the compound Z is
nitrate is,
(A) Benzoic acid
(A) [Cr(H O) (NO ) (B) Benzaldehyde
2 6 3 3
(B) [Cr(H O) (NO ) (C) Acetophenone
2 6 2 2
(C) [Cr(H O)5NO ](NO ) (D) Benzene
2 3 3 2
(D) [Cr(H O)5NO ]NO
2 2 3

97. For the redox reaction x MnO- + y H C O + zH+ --- 98. When PbO reacts with concentrated HNO , the gas
4 2 2 4 2 3
> m Mn2+ + n CO + p H O The values of x, y, m and n evolved is
2 2
are
(A) NO
2
(A) 10, 2, 5, 2 (B) O
2
(B) 2, 5, 2, 10 (C) N
2
(C) 6, 4, 2, 5 (D) N O
2
(D) 3, 5, 2, 10

99. Dry ice is 100. Addition of excess of AgNO to an aqueous solution
3
of 1 mole of PdCl .4NH gives 2 moles of AgCl. The
(A) Solid CO 2 2
conductivity of this solution corresponds to
(B) Solid SO
2
(A) 1:1 electrolyte
(C) Solid CO
2
(B) 1:3 electrolyte
(D) Solid O
2
(C) 1:2 electrolyte

(D) 1:4 electrolyte

101. Phenol can be distinguished from ethanol 102. The two forms of D-Glucopyranose are called

(A) Bromine water (A) Diastereomers

(B) Sodium metal (B) Anomers

(C) Iron metal (C) Epimers

(D) Chlorine water (D) Enantiomers

103. In the reaction B (OH) + 2H O --------> [B(OH) ]- + 104. Which of the following halides undergoes hydrolysis
3 2 4
H O+ B OH functions are on warming with water/aqueous NaOH?
3 3

(A) Protonic acid (A)

(B) Lewis base (B)

(C) Bronsted acid (C)

(D) Lewis acid (D)

105. Gabriel phthalimide synthesis is used in the 106. Which one of the following is a polyamide polymer ?
preparation of primary amine from phthalimide, which of
(A) Terylene
the following reagent is not used during the process?
(B) Nylon-6,6
(A) KOH
(C) Buna-S
(B) NaOH
(D) Bakelite
(C) HCl

(D) Alkyl Halides

107. H O is 108. Which of the following is more basic than aniline ?
2 2

(A) An oxidising agent (A) Diphenylamine

(B) A reducing agent (B) Triphenylamine

(C) Both oxidising and reducing agent (C) p-nitroaniline

(D) Neither oxidising nor reducing agent (D) Benzylamine

109. Which of the following bases is not present in DNA ? 110. The Glycosidic linkage present in sucrose is
between
(A) Adenine

(B) Guanine (A) C - 1 of α -glucose and C - 2 of β -fructose

(C) Cytosine (B) C - 1 of α -glucose and C - 4 of α -glucose

(D) Uracil (C) C - 1 of β -galactose and C - 4 of α glucose

(D) C - 1 of α -glucose and C - 4 of β -fructose

111. Which one of the following noble gas has an 112. Which of the following oxidation states is common
unusual property of diffusing through the materials such for all lanthanides ?
as rubber, glass or plastic ?
(A) +2
(A) Ne (B) +3
(B) Ar (C) +4
(C) Kr (D) +5
(D) He

113. The magnetic nature of elements depends on the 114. Eutrophication causes
presence of unpaired electrons. Identify the configuration
(A) increase of nutrients in water
of transition elements which shows highest magnetic
(B) reduction in water pollution
moment?
(C) reduction in dissolved oxygen
(A) 3 d ^ 7
(D) decreases BOD
(B) 3 d ^ 5

(C) 3 d ^ 8

(D) 3 d ^ 2

115. Among the following, the branched chain polymer is 116. In a face centred cubic arrangement of A and B
atoms in which ‘A’ atoms are at the corners of the unit
(A) Polyvinyl chloride
cell and ‘B’ atoms are at the face centers. One of the ‘A’
(B) Bakelite
atom is missing from one corner in unit cell. The simplest
(C) Low density polythene formula of compound is
(D) High density polythene
(A) A _ 7 B _ 24

(B) A _ 7 B _ 8

(C) AB _ 3

(D) A _ 7 B _ 3

117. Extraction of chlorine from brine solution is based 118. Anti-histamine among the following is
on
(A) Bromopheneramine
(A) Oxidation (B) Morphine
(B) Chlorination (C) Amoxycillin
(C) Reduction (D) Chloroxylenol
(D) Acidification

119. When the pure solvent diffuses out of the solution 120. During the fusion of organic compound with sodium
through the semi-permeable membrane then the process metal, nitrogen present in the organic compound is
is called converted into

(A) Osmosis (A) NaNO
2
(B) Reverse osmosis (B) NaNH
2
(C) Sorption (C) NaCN

(D) Dialysis (D) NaNC

MATHEMATICS

121. ∫ ( x + 3 ) e ^ x ( x + 4 ) ^ 2 d x is equal to 122. The integrating factor of (d y)/(d x)+y=(1+y)/(x) is
is
(A) 1 ( x + 4 ) ^ 2 + C

(B) e ^ x ( x + 4 ) ^ 2 + C (A) xex

(C) e ^ x ( x + 4 ) + C (B) xe1/x

(D) e ^ x ( x + 3 ) + C (C) exx

(D) xex

123. If cos y = x cos(a+y) with cos a ≠ ±1, then dy/dx is 124. The rate of change of volume of a sphere with
equal to respect to its surface area when the radius is 4 cm is

(A) a 2(a+y) (A) 4 cm ^ 3 / cm ^ 2

(B) 2(a+y) a (B) 2 cm ^ 3 / cm ^ 2

(C) a 2(a+y) (C) 6 cm ^ 3 / cm ^ 2

(D) 2(a+y) a (D) 8 cm ^ 3 / cm ^ 2

125. Let f(x)=x-(1)/(x) then f’(-1) is 126. If x = 2 t 1 + t ^ 2 , y = 2 t 1 - t ^ 2 , then ( d y )/( d
x ) is equal to
(A) 0

(B) 2 (A) 1

(C) 1 (B) 0

(D) -2 (C) − 1

(D) 2

127. The value of the expression ((1)/(2) -1 2√(5)) 128. If an LPP admits optimal solution at two consecutive
vertices of a feasible region, then
(A) 2 - √5

(B) √5 - 2 (A) the required optimal solution is at the midpoint of the
line joining two points.
(C) √(5)-22
(B) the optimal solution occurs at every point on the line
(D) 5 - √2
joining these two points

(C) the LPP under consideration is not solvable

(D) the LPP under consideration must be reconstructed

129. ∫ e x ·(( x+1)/( x)) d x is equals to 130. If a matrix A is both symmetric and skew
symmetric, then
(A) sin x. esin x + c

(B) cos x. esin x + c (A) Ais diagonal matrix

(C) esin x + c (B) Aisa zero matrix

(D) esin x (sin x + 1) + c (C) Ais scalar matrix

(D) Ais square matrix

131. If f(x)= -1[2x+11+4x] then f’(0) = 132. The area of the region bounded by Y-axis, y = cos x
and y = sin x 0 ≤ x ≤ π/2 is
(A) (2 2)/(5)

(B) 2 log 2 (A) √2 + 1 Sq.units

(C) (2 2)/(7) (B) √2 -1 sq. units

(D) log 2 (C) 2- √2 Sq. units

(D) √2 Sq. Units

133. √[3]y √(x) √[6](x+y)5 then dy/dx 134. If x = 1 sec2θ , y = a tan2θ then d2 yd x2=

(A) x – y (A) 0

(B) x/y (B) 2a

(C) y/x (C) 4

(D) x + y (D) 1

135. If P (n) : 2n n! Then the smallest positive integer for 136. If f(x) = |cos x —sinx|, then f’(π/6) is equal to
which P (n) is true, is
(A) -(1)/(2)(1+√(3))
(A) 4 (B) (1)/(2)(1+√(3))
(B) 2 (C) -(1)/(2)(1-√(3))
(C) 5 (D) (1)/(2)(1-√(3))
(D) 3

137. Reflexion of the point ( α , β ,γ ) in XY plane is 138. The locus represented by xy + yz = 0 is

(A) ( α , β , 0 ) (A) a pair of perpendicular lines

(B) ( 0,0 , γ ) (B) a pair of parallel lines

(C) ( - α , - β , γ ) (C) a pair of parallel planes

(D) ( α , β , - γ ) (D) a pair of perpendicular planes

139. If a = 2 i + λ j + k and b = i + 2 j + 3 k are 140. If P(n) : 22n - 1 is divisible by k for all n ∈ N” is true,
orthogonal, then the value of λ is then the value of ‘k’ is

(A) 0 (A) 6

(B) 1 (B) 3

(C) 3/2 (C) 7

(D) - 5/2 (D) 2

141. If ^ - 1 x + ^ - 1 y = ( 4 π )/( 5 ) , then ^ - 1 x + ^ - 1 142. ∫ 1 √((1+x)/(1-x)) d x=
0
y is equal to
(A) π/2
(A) π (B) (π/2) -1
(B) ( π )/( 5 ) (C) 1/2
(C) ( 2 π )/( 5 ) (D) (π/2) + 1
(D) ( 3 π )/( 5 )

143. Let A be a square matrix of order 3 x 3, then |5A| = 144. ∫ √ x ^ 2 + 2 x + 5 d x is equal to

(A) 5|A| (A) array l ( 1 )/( 2 ) ( x + 1 ) √ x ^ 2 + 2 x + 5 + 2 \ | x + 1

(B) 125|A| + √ x ^ 2 + 2 x + 5 | + C array

(C) 25|A| (B) array c ( x + 1 ) √ x ^ 2 + 2 x + 5 + 2 \ | x + 1 + √ x ^ 2
+ 2 x + 5 | + C array
(D) 15|A|
(C) array c ( x + 1 ) √ x ^ 2 + 2 x + 5 - 2 \ | x + 1 + √ x ^ 2
+ 2 x + 5 | + C array

(D) array c ( x + 1 ) √ x ^ 2 + 2 x + 5 + ( 1 )/( 2 ) \ | x + 1 +
√ x ^ 2 + 2 x + 5 |+ C array

145. The equation of the curve passing through the point 146. If a=i+λ j+2 k ; b=μ i+j-k are orthogonal and |a|=|b|
(1, 1) such that the slope of the tangent at any point (x, then (λ,µ )=
y) is equal to the product of its co-ordinates is
(A) (¼, 7/4)
(A) 2 log y = x2 – 1 (B) (7/4, ¼)
(B) 2 log x = y2 – 1 (C) (¼, 9/4)
(C) 2 log x = y2 + 1 (D) (-¼, 9/4)
(D) 2 log y = x2 + 1

147. The area of the region bounded by the a curve y = 148. If ((1-i)/(1+i))96 = a +ib then (a,b) is
cos x between x = 0 and x = π is
(A) (1,1)
(A) 1 sq. unit (B) (1,0)
(B) 4 sq. units (C) (0,1)
(C) 2 sq. units (D) (0,-1)
(D) 3 sq. units

149. The shaded region in the figure is the solution set 150. The probability of happening and event A is 0.5 and
of the inequations that of B is 0.3. If A and B are mutually exclusive events,
then the probability of happening neither A nor B is
(A) 5 x + 4 y ≥ 20 , x ≤ 6 , y ≥ 3 , x ≥ 0 , y ≥ 0

(B) 5 x + 4 y ≤ 20 , x ≤ 6 , y ≤ 3 , x ≥ 0 , y ≥ 0 (A) 0.4

(C) 5 x + 4 y ≥ 20 , x ≤ 6 , y ≤ 3 , x ≥ 0 , y ≥ 0 (B) 0.5

(D) 5 x + 4 y ≥ 20 , x ≥ 6 , y ≤ 3 , x ≥ 0 , y ≥ 0 (C) 0.2

(D) 0.9

151. A unit vector perpendicular to the plane containing 152. The value of (|x|)/(x) is
x arrow 0
the vectors i+2 j+k and -2 i+j+3 k is
(A) 1
(A) -i+j-k√(3) (B) -1
(B) i+j+k√(3) (C) 0
(C) -i-j-k√(3) (D) Does not exist
(D) -i+j+k√(3)

153. Two letters are chosen from the letters of the word 154. If A = {x| x ∈ N, x le 5}, B = { x | x ∈ Z, x2 – 5x + 6 =
‘EQUATIONS’. The probability that one is vowel and the 0}, then the number of onto functions from A to B is
other is consonant is
(A) 30
(A) 3/9 (B) 2
(B) 8/9 (C) 32
(C) 5/9 (D) 23
(D) 4/9

155. If α and β are roots of the equation x2 -2x - 1 = 0 156. If A and B are two events of a sample space S such
then α2 β-2 + α-2 β2 is that P(A) = 0.2, P(B) = 0.6 and P(A|B) = 0.5 then P(A’|B)=

(A) -2 (A) 1/2

(B) 0 (B) 3/10

(C) 30 (C) 1/3

(D) 34 (D) 2/3

157. Everybody in a room shakes hands everybody else. 158. The value of _ θ arrow 0 ( 1 - 4 θ )/( 1 - 6 θ ) is
The total number of handshakes is 45. The total number
(A) 4/9
of handshakes is 45. The total number of persons in the
(B) 9/4
room is
(C) 9/3
(A) 9
(D) 3/4
(B) 10

(C) 5

(D) 15

159. A box has 100 pens of which 10 are defective. The 160. Foot of the perpendicular drawn from the point (1,
probability that out of a sample of 5 pens drawn one by 3, 4) to the plane 2x – y + z + 3 = 0 is
one with replacement and at most one is defective is
(A) (1, 2, - 3)
(A) 9/10 (B) (-1, 4, 3)
(B) ( 1 )/( 2 ) ( ( 9 )/( 10 ) ) ^ 4 (C) (-3, 5, 2)
(C) ( ( 9 )/( 10 ) ) ^ 5 + ( 1 )/( 2 ) ( ( 9 )/( 10 ) ) ^ 4 (D) (0, -4, -7)
(D) ( 1 )/( 2 ) ( ( 9 )/( 10 ) ) ^ 5

161. ∫ 1 d xex+e-x is equals to 162. If 2 [ array l l 1 & 3 \ 0 & x array ] + [ array l l y & 0 \
0
1 & 2 array ] = [ array l l 5 & 6 \ 1 & 8 array ] , then the
(A) (π)/(4)- -1 (e)
value of x and y is
(B) tan-1 (e) - π/4
(A) x = 3, y = 3
(C) tan-1 (e) + π/4
(B) x = - 3, y = 3
(D) tan-1 (e)
(C) x = 3, y = - 3

(D) x = - 3, y = - 3

163. Rolle’s theorem is not applicable in which one of the 164. XY – plane divides the line joining the points A (2, 3,
following cases? - 5) and B (-1, -2, -3) in the ratio

(A) f (x) = |x| in [-2, 2] (A) 5 : 3 internally

(B) f (x) = x2 – 4x + 5 in [1, 3] (B) 2 : 1 internally

(C) f (x) = [x] in [2.5, 2.7] (C) 5 : 3 externally

(D) f (x) = x2 – x in [0, 1] (D) 3 : 2 externally

165. ∫ 1√3-6 x-9 x2 d x is equals to 166. A man speaks truth 2 out of 3 times. He picks one of
the natural numbers in the set S = {1, 2, 3, 4, 5, 6, 7}
(A) -1((3 x+1)/(2))+c
and reports that it is even. The probability that it is
(B) -1((3 x+1)/(6))+c
actually even is
(C) (1)/(3) -1((3 x+1)/(2))+c
(A) 1/10
(D) -1((2 x+1)/(3))+c
(B) 2/3

(C) 3/5

(D) 1/5

167. The value of C in Mean value theorem for the 168. Two events A and B will be independent if
function f ( x ) = x ^ 2 in [ 2,4 ] is
(A) A and B are mutually exclusive
(A) 3 (B) P ( A ^ ′ B ^ ′ ) = ( 1 - P ( A ) ) ( 1 - P ( B ) )
(B) 2 (C) P ( A ) = P ( B )
(C) 4 (D) P ( A ) + P ( B ) = 1
(D) 7/2

169. The range of ^ - 1 x is 170. ∫ ( 2 x - 2 θ )/( x - θ ) dx is equal to

(A) [ ( - π )/( 2 ) , ( π )/( 2 ) ] (A) 2 ( x + x θ ) + c

(B) ( ( - π )/( 2 ) , ( π )/( 4 ) ) (B) 2 ( x - x θ ) + c

(C) [ 0 , π ] (C) 2 ( x + 2 x θ ) + C

(D) [ 0 , π ] - \ ( π )/( 2 ) \ (D) 2 ( x - 2 x θ ) + C

171. On the set of positive rationals, a binary operation * 172. ∫ _ - π / 2 ^ π / 2 d x e ^ x + 1 is equal to
is defined by a * b = (2ab/5) If 2 * x = 3-1 then x =
(A) 0
(A) 3/9 (B) 1
(B) 8/9 (C) - ( π )/( 2 )
(C) 125/48 (D) ( π )/( 2 )
(D) 4/9

173. The domain of the function f : R R defined by 174. The value of √24.99 is
f(x)=√x2-7 x+12 is
(A) 5.001
(A) (-∞, 3] ∩ [4,∞ ) (B) 4.999
(B) (-∞, 3] ∪ [4,∞ ) (C) 4.897
(C) (3, 4) (D) 4.899
(D) (-∞, 3] ∪ (4, ∞)

175. The area of the region above X-axis included 176. The equation of the line parallel to the line 3x - 4y +
between the parabola y2 = x and the circle x2 + y2 = 2x 2 = 0 and passing through (- 2, 3) is
in square units is
(A) 3x-4y+18=0
(A) (2)/(3)-(π)/(4) (B) 3x-4y-18=0
(B) (π)/(4)-(3)/(2) (C) 3x+4y+18=0
(C) (π)/(4)-(2)/(3) (D) 3x+4y-18=0
(D) (3)/(2)-(π)/(4)

177. The degree of the differential equation [ 1 + ( ( dy 178. ∫ _ 0 ^ π / 2 1 a ^ 2 · ^ 2 x + b ^ 2 · ^ 2 x d x is
)/( d x ) ) ^ 2 ] ^ 2 = d ^ 2 y d x ^ 2 is equal to

(A) 1 (A) ( π a )/( 4 b )

(B) 2 (B) ( π a )/( 2 b )

(C) 3 (C) ( π b )/( 4 a )

(D) 4 (D) ( π )/( 2 ab )

179. If the vectors a i+j+k, i+b j+k and i+j+c k are 180. The sides of an equilateral triangle are increasing at
coplanar then the value of abc - (a+b+c) = the rate of 4 cm/sec. The rate at which its area is
increasing, when the side is 14 cm.
(A) 2

(B) -2 (A) 42 cm2sec

(C) 0 (B) 10√3 cm2/sec

(D) -1 (C) 14 2/sec

(D) 14√3 2/sec

ANSWER KEY

1. (B) 2. (A) 3. (A) 4. (A) 5. (C) 6. (B) 7. (A)

8. (D) 9. (B) 10. (C) 11. (B) 12. (B) 13. (B) 14. (D)

15. (B) 16. (B) 17. (A) 18. (B) 19. (D) 20. (B) 21. (D)

22. (C) 23. (B) 24. (A) 25. (C) 26. (B) 27. (B) 28. (D)

29. (B) 30. (B) 31. (A) 32. (B) 33. (D) 34. (B) 35. (B)

36. (C) 37. (D) 38. (D) 39. (A) 40. (A) 41. (C) 42. (A)

43. (A) 44. (C) 45. (C) 46. (C) 47. (A) 48. (A) 49. (B)

50. (C) 51. (D) 52. (C) 53. (C) 54. (A) 55. (D) 56. (A)

57. (C) 58. (D) 59. (A) 60. (B) 61. (A) 62. (D) 63. (C)

64. (A) 65. (D) 66. (D) 67. (C) 68. (D) 69. (B) 70. (B)

71. (B) 72. (C) 73. (C) 74. (D) 75. (C) 76. (B) 77. (A)

78. (B) 79. (A) 80. (B) 81. (B) 82. (A) 83. (A) 84. (C)

85. (A) 86. (B) 87. (A) 88. (A) 89. (D) 90. (A) 91. (A)

92. (A) 93. (C) 94. (C) 95. (C) 96. (B) 97. (B) 98. (B)

99. (C) 100. (C) 101. (A) 102. (B) 103. (D) 104. (C) 105. (C)

106. (B) 107. (C) 108. (D) 109. (D) 110. (A) 111. (D) 112. (B)

113. (B) 114. (C) 115. (C) 116. (A) 117. (A) 118. (A) 119. (B)

120. (C) 121. (C) 122. (C) 123. (B) 124. (B) 125. (B) 126. (A)

127. (B) 128. (B) 129. (A) 130. (B) 131. (D) 132. (B) 133. (C)

134. (A) 135. (A) 136. (A) 137. (D) 138. (D) 139. (D) 140. (B)

141. (B) 142. (D) 143. (B) 144. (A) 145. (A) 146. (A) 147. (C)

148. (B) 149. (C) 150. (C) 151. (A) 152. (D) 153. (C) 154. (A)

155. (D) 156. (A) 157. (B) 158. (A) 159. (C) 160. (D) 161. (B)

162. (A) 163. (C) 164. (C) 165. (C) 166. (C) 167. (A) 168. (B)

169. (D) 170. (A) 171. (C) 172. (D) 173. (B) 174. (B) 175. (C)

176. (A) 177. (A) 178. (D) 179. (B) 180. (B)