JK Diploma Polytechnic 2019 Question Paper

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Question Booklet Series: Question Booklet Number:
Polytechnic Entrance Test — 2019

QUESTION BOOKLET
850288

INSTRUCTIONS

Maximum Time Allowed: 3 Hours No. of Questions: 180
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Page 1 of 24

Section 1 — English 7) Choose the correct option to complete the sentence:
His father was very strict; he had no choice but
1) Fill in the blank with the correct option: (obey).
Each of them a pen.
A) to obey
A) was B) obeying
B) has C) be obeying
C) have D) to obeying
D) is

8) Fill in the blank with the correct option:
2) Fill in the blank with the correct option: you speak Russian?
I ask a question?
A) Could have been
A) Might be B) Could have
B) Might have C) Can be
C) May D) Can
D) Could have

9) Choose the correct verb form and fill the blank:
3) Fill in the blank with the correct option: The students their assignments before the
The girl was from New Delhi. teacher asked them to.

A) Which scooty we purchased A) was submitting
B) Whose scooty we purchased B) are submitting
C) That scooty we purchased C) had submitted
D) What scooty we purchased D) may submit

4) Choose the correct verb form and fill the blank: 10) Turn the following sentence into indirect speech.
Only in the evening, my father reminded me to finish my The little girl said, 'My mother teaches me French at
assignment but I it earlier. home.'

A) have finished A) The little girl said that her mother taught her French
at home
B) had finished
B) My mother was teaching me French when I am at
C) am finishing
home the little girl said.
D) should finish
C) I was taught French while I was at home by my
mother.
D) Teaching of French when I was at home was done
5) She is ill today.
by my mother.
Which of these is a Negative of this sentence?

A) She may be sick today.
11) Fill in the blank with correct option:
B) She is not ill today. Has the HR manager signed the latest sales proposal
C) She need not be ill today. provided us last month?
D) She will not be ill today.
A) What the finance expert
B) Which the finance expert
6) Fill in the blank with proper pronoun. C) That the finance expert
I Will do it
D) Who the finance expert
A) thyself
B) myself
C) yourself
D) himself

Page 2 of 24

12) Fill in the blank with a suitable conjunction: 18) Fill in the blank with the correct option:
Rohit Sam are the best of friends. He is taller than

A) or A) me
B) but B) she
C) and C) I
D) also D) he

13) Fill in the blank with a suitable conjunction: 19) Choose the correct option to join the two sentences:
The offer was tempting that I could not refuse Take your cardigan with you you are not cold
it. later in the evening.

A) also A) so that
B) as B) as soon as
C) so C) as if
D) both D) not only

14) Complete the sentence using the correct Infinitive of 20) Name the type of sentence:
the verb given in brackets. We sat down.
As the deadline is tomorrow, there is no time
(waste) A) Assertive sentence
B) Interrogative sentence
A) for wasting
C) Exclamatory sentence
B) to waste
D) Imperative sentence
C) to wasting
D) to be wasting
21) Fill in the blank with the appropriate option:
The rich help the poor.
15) Use proper Interrogative pronoun.
Your Father, does he do? A) Should
B) Be
A) who
C) Is
B) what
D) Ought
C) whose
D) whom
22) Which of the following is a Declarative sentence.

16) Fill in the blank with the correct option: A) The sun rises in the east.
Can you see the old lady
B) Please let me work.
A) Which is sitting near that old tree? C) How hot it is!
B) Whose is sitting near that old tree? D) Have you done your home -work?
C) Who is sitting near that old tree?
D) Whom is sitting near that old tree? 23) Identify the Imperative sentence.

A) Will you have a little more Tea?
17) Name the type of sentence:
B) Have you done your work?
How is this possible?
C) The boys made a noise.
A) Interrogative sentence D) Please convey my heartfelt condolences to your
B) Negative sentence parents.
C) Exclamatory sentence
D) Imperative sentence

Page 3 of 24

24) Fill in the blank with the correct option: 29) Name the type of sentence:
Why she take care of his issues? Being tired, he sat down.

A) Can be A) Simple sentence
B) Should B) Compound sentence
C) Could have C) Complex sentence
D) Should have D) Exclamatory sentence

25) Choose the correct verb form and fill the blank: 30) Choose the correct answer:
I had taken a tablet before I my dinner. They were relieved the traffic flowing more
easily.
A) ate
B) was eating A) find
C) will eat B) to find
D) had eaten C) finding
D) found

26) Choose the correct option to join the two sentences:
I suspect she will forget the appointment
reminded her twice.

A) so that
B) even though
C) in spite of
D) as if

27) Turn the following sentence into indirect speech.
The driver asked the policeman, "Will I be fined if I take
a right turn?"

A) The driver asked the policeman if he would be fined
if he took a right turn there.
B) The driver asked the police man if he will fine him if
he takes a right turn.
C) The policeman was asked by the driver if he will fine
him if he takes a right turn there.
D) By taking a right turn here will I incur a fine the driver
asked the policeman.

28) Turn the following sentence into indirect speech.
My professor said to me, 'you will have a bright future in
the US.'

A) My future in the US will be bright is what my
professor was telling to me
B) My professor told me that I would have a bright
future in the US.
C) I was being told by my professor that my future will
be bright in the US
D) I will have a bright future in the US my professor was
telling me

Page 4 of 24

Section 2 — Physics 36) The total resistance of a circuit consisting of three
resistors connected in series is 15 1(0 and two of the
31) A white colour when passes through a prism it resistors have a resistance of 2 kO each. The resistance
undergoes dispersion. The colour in the emergent beam of the third resistor is
for which the angle of deviation is maximum is
A) 3500 52
A) violet B) 7500 0
B) red C) 9000 0
C) yellow D) 11000 0
D) blue

37) The deflection in a moving coil galvanometer falls
32) The voltage across a resistor which has a resistance from 50 divisions to 10 divisions when a shunt of
of 44 D and carrying a current of 5 A is 12 Ohm is applied. The resistance of the galvanometer
is
A) 8.8 V
A) 120
B) 44 V
B) 2452
C) 152 V
C) 360
D) 220 V
D) 480

33) The optical phenomenon which is used in animation
is 38) The power of a plane glass plate is

A) Persistence of vision A) infinite
B) Power of accommodation B) zero
C) Short sightedness C) one
D) Internal reflection D) greater than one

34) Two small magnet each of magnetic moment 39) The part of the human eye which consists of light
10 Amt are placed end to end on position 0.1 m apart and colour sensitive cells is
from their centers. The force acting between them is
A) Retina
A) 0.6 x 10-7 N B) Cornea
B) 0.6 x 107 N C) Pupil
C) 0.6 N D) Lens
D) 0.6 x 105 N

40) The process involved in the energy production in a
35) The coercivity of a permanent magnet is nuclear reactor is
4 x 104 Am-1. A magnet is placed inside a solenoid of
length 15 cm long having 600 turns. A current is passed A) Nuclear fission
through the solenoid to demagnetize it complete. The B) Nuclear fusion
required current is
C) Combustion reaction
D) Double displacement
A) 20 A
B) 1A
C) 10 A 41) The commercial unit of electrical energy is
D) 100 A
A) Kilowatt hour
B) Watt hour
C) Watt
D) Kilowatt

Page 5 of 24

42) The branch of physics that deals with the 48) The part of the human eye which acts like aperture
measurement of light energy in terms of the perceived of a camera and thus regulates the amount of light
brightness of human eye is entering the eyes is

A) radiometry A) Sclera
B) photometry B) Lens
C) optics C) Pupil
D) spectrometry D) Retina

43) Due to high pressure and temperature, the plants 49) The equivalent resistance of a circuit consisting of
that got buried under swamps inside the earth gets three resistors 120 0, 150 0 and 220 0 connected in
converted into series connection is

A) wood A) 350 0
B) oil B) 375
C) hydel energy C) 490 0
D) coal D) 575 0

44) If a convex lens of focal length 'f' is cut into two parts 50) The work done in moving 6 C of charge between two
along a plane passing through the principal axis, then points having potential difference of 20 V is
the focal length of each part is
A) 3 J
A) f B) 60 J
B) f/2 C) 120 J
C) 2f D) 210 J
D) f/4

51) In India, the frequency of power supply is
45) The most commonly used conductor in electric
circuits is A) 50 Hz
B) 20 Hz
A) Gold
C) 60 Hz
B) Silver
D) 70 Hz
C) Aluminium
D) Copper
52) A convex lens of focal length 20 cm has an object
placed at a certain distance and it produces a real image
46) If 'R' is the resistance, 'L' the length and 'A' the area whose magnification is 4 times. The object distance is
of cross-section of the conductor, then resistivity 'p' is
defined by the equation A) (-0.05 m)
B) (0.15 m)
A) p = RAL
C) (- 0.25 m)
B) p = RA/L
D) (-0.50 m)
C) p = R/AL
D) p = A/LR
53) An alpha particle (positive charge particle) enter a
magnetic field at right angle. In which direction does the
47) A lens which diverges a beam of light and which is force act on the alpha particle?
thinner at the centre as compared to its edges is
A) Circular
A) Concave lens B) Upward
B) Convex lens C) Parallel
C) Plano-convex lens D) Horizontal
D) Plano-concave lens

Page 6 of 24

54) A Magnetizing field of 1600 Am-1 produces a 60) Energy consumed by an appliance that draws 2 A
magnetic flux of 2.4 x 10-5 wb in an iron bar of cross- from a 6 V battery for 3 hours is
sectional area 0.2 cm2. The susceptibility of the bar is
A) 12 Wh
A) 298 B) 63 Wh
B) 596 C) 36 Wh
C) 1192 D) 2160 Wh
D) 1788

61) A device which is usually connected in parallel and
55) The power of a microscope with angular is used to measure the potential difference is
magnification 10 and near vision 25 cm is
A) Voltmeter
A) 0.4 D B) Ammeter
B) 4D C) Galvanometer
C) 40 D D) Ohmmeter
D) 0.04 D

62) The nerve layer which carries the impulses formed
56) The energy given to each coulomb of charge for by the retina and it connects the eye to brain is
passing through a 12 V battery is
A) Viterous humour
A) 1.6 x 10-19 J B) Optic nerve
B) 21 J C) Cornea
C) 12J D) Blind spot
D) 6.1 x 10-19 J

63) What is the approximate number of electrons
57) For any medium, the value of absolute refractive passed through a lamp in 2 minutes if the current
index is always through it is 200 mA?

A) less than one A) 12 x 1018
B) equal to one B) 24 x 1018
C) greater than one C) 48 x 1018
D) zero D) 150 x 1018

58) From the harnessing and utilization point, the energy 64) The source of energy which can produce both power
which will lead to least environment pollution is and manure is

A) Nuclear energy A) Hydroelectric plants
B) Thermal energy B) Nuclear plants
C) Solar energy C) Biogas plants
ID) Geothermal energy D) Thermal plants

59) The magnetic field inside a long straight solenoid is 65) An alternating current has a frequency of 50 Hz.
How many times will it change its direction in one
A) Zero second?
B) Variable
A) 100 times
C) Same at all points
B) 200 times
D) Non uniform
C) 10 times
D) 150 times

Page 7 of 24

523574D

66) If the focal length of a convex lens is 25 cm, then the 72) A circuit has a fuse of 5A. How many number of
power of the lens would be lamps of 100 Watt, 220 Volt can be used in the circuit?

A) (4D) A) 11
B) (-4D) 6) 20
C) (0.4D) C) 5
D) (-0.4D) D) 15

67) The most common material used in nuclear reactors 73) The relative permeability of a medium is 0.075. The
for shielding from radiations is magnetic susceptibility of that medium will be

A) Thin galvanised sheets A) 0.925
B) Lead or concrete B) -0.925
C) Carbon papers C) 1.075
D) Graphite D) -1.075

68) Which among the given medium has highest 74) Resistivity of a given material usually depends on
refractive index? the

A) Diamond A) length of the material
B) Water B) nature of the material
C) Glass C) shape of the material
D) Immersion oil D) thickness of the material

69) The mirror which is used in anti-shoplifting devices 75) A circuit consists of three resistors connected in
is series. If the circuit is reconnected by removing one of
the resistors from the circuit, then the flow of current
A) convex mirror through the circuit
B) planoconcave mirror
A) increases
C) concave mirror
B) remains constant
D) plane mirror
C) decreases
D) decreases by half
70) A circuit consists of resistors with resistances
3 Q and 5 C2 connected in parallel and a current of
15 A divides between the branches of these resistors. 76) The angular dispersion produced by a prism of angle
The current through each resistor is 4° and refractive index of 1.65 & 1.55 for violet and red
colour respectively, is
A) 4.9 A, 6.5 A
B) 9.4 A, 5.6 A A) 0.4°
C) 9.4 A, 6.5 A B) 0.04°
D) 4.9 A, 5.6 A C) 4°
D) 40°

71) The potential difference of battery when 50 J of work
is done in moving a charge of 5 C from one terminal of 77) The volatile liquid which is boiled using the heat from
the battery to the other is the hot water at the surface of the ocean to run the
turbines for generating ocean thermal energy is
A) 10 V
B) 20 V A) Acetone
C) 250 V B) Ammonia
D) 200 V C) Ethanol
D) Alcohol

Page 8 of 24

78) The part of the solar cooker which is responsible for
green house effect is

A) Mirror
B) Glass sheet
C) Black colour coating
D) Outer cover of solar cooker

79) Charcoal is considered as a better fuel than wood
because, charcoal

A) produces lot of smoke
B) has higher calorific value
C) has low calorific value
D) is not convenient to use

80) The defect which arises due to the decrease in the
focal length of the crystalline lens or elongation of the
eye ball can be corrected by using

A) Convex lens
B) Concave lens
C) Concavo-convex lens
D) Bi-focal lens

Page 9 of 24

Section 3 — Chemistry 87) The correct order of first ionization potentials of Na,
Mg, Al and Si are
81) A metal 'X' obtained in the form of ribbon is burned
in air to get a white solid 'Y' which is soluble in water to A) Na < Mg > Al < Si
give a basic solution. The solution becomes basic due B) Na < Mg < Al > Si
to the formation of
C) Na > Mg > Al > Si
A) Zn(OH)2 D) Na > Mg > Al < Si
B) Mg(OH)2
C) Ca(OH)2 88) Which statement is INCORRECT with respect to
D) Al(OH)3 phenols?

A) Phenol can be prepared from diazonium salts
82)
80°C H 0/heat B) The hydroxyl group in phenol acts as electron
C2H4 + H2SO4 >A >B withdrawing group
Identify "A" and "B" products in the reaction? C) Phenols are weaker acids than alcohols and water
D) Phenol molecule is less stable when compared to
A) C2I-16, C2H5OH phenoxide ion
B) C2H2, C2H5OH
C) C2H5OSO3H, CH3OH
D) C2H5OSO3H, C2H5OH 89) Among the following compounds, which molecule is
an "Achiral" molecule?

83) Which of the following compound is known as A) 2-Bromopropane
vitamin B5? B) Pentan-2-ol
C) 2-Bromobutane
A) Lactic acid
D) 2-Chloropropanal
B) Formic acid
C) Ascorbic acid
D) Pantothenic acid 90) During respiration, the combustion of sugar
produces

84) How many different structural isomers having the A) carbon dioxide and hydrogen
molecular formula C5H12 are there? B) carbon dioxide and water
C) carbon dioxide and methane
A) 2
D) ethane and water
B) 3
C) 4
D) 5 91) The number of elements present in 5th period

A) 8
85) Which of the following is used to detect nitrogen and B) 18
sulphur in organic compounds?
C) 19
A) Carius test D) 32
B) Fehling's test
C) Tollen's test
92) Which of the following statements is INCORRECT
D) Lassaigne's test with regards to properties of a base?

A) It can accept proton
86) What is the property called where there is tendency B) It can donate electron pair
of self combination of carbon?
C) It turns blue litmus red
A) Isomerism D) Gives Oft ions in solution
B) Catenation
C) Tetravalency
D) Electromeric effect

Page 10 of 24

93) When a metal reacts with hydrochloric acid which of 99) C6H5COOH is a weaker acid than H2SO4 because
the following products are formed?
A) it is less corrosive than H2SO4
A) Metal hydride and chlorine gas B) it ionizes partially in aqueous solution
B) Metal salt and hydrogen gas C) it has less thermal stability
C) No chemical reactions take place D) it ionizes completely in aqueous solution
D) Metal containing weak acid and hydrogen gas

100) Which of the following pairs of elements are
94) Aqua regia is the mixture of metalloids?

A) H2SO4 + HCI (3:1) A) Sodium and Potassium
B) H2SO4 + HCI (1:3) B) Fluorine and Bromine
C) HNO3 + HCI (3:1) C) Radium and Germanium
D) HNO3 + HCI (1:3) D) Arsenic and Silicon

95) Hoopes process is used for the refining of 101) Lucas Reagent is used to classify alcohols of low
molecular weight. What is Lucas Reagent?
A) Al
B) Cs A) Concentrated HCI + ZnCl2
C) Ag B) Concentrated H2SO4 + ZnSO4
D) Au C) Concentrated HNO3+ ZnSO4
D) Concentrated HNO3 + ZnCl2

96) Which of the following group of elements forms a
Dobernier triad? 102) What are the products obtained when ethyl phenyl
ether reacts with excess HI?
A) Chlorine, bromine and iodine
B) Platinum, neon and fluorine A) Ethyl iodide and lodobenzene
C) Hydrogen, oxygen and nitrogen B) Ethyl alcohol and phenol
D) Titanium, zirconium and palladium C) Ethyl iodide and phenol
D) Ethyl alcohol and iodobenzene

97) The correct order of following metals in the
decreasing order of their reactivity with HCI 103) What is the IUPAC name of Phenyl isopentyl
ether?
A) Fe > Zn > Al > Mg
B) Fe > Al > Zn > Mg A) 3-methyl phenoxy butane
C) Mg > Al > Zn > Fe B) 3-methyl butoxy benzene
D) Mg > Zn > Al > Fe C) 2-methyl butoxy-6-benzene
D) 2-methyl phenoxy butane

98) When iron nails are added into copper sulphate
solution, the iron nails become brownish in colour and 104) Which catalyst is used for reduction of alkyne into
the blue colour of the copper sulphate solution becomes Cis-Alkene?
faded. The balanced chemical equation for this reaction
is A) Palladised Charcoal
B) Sodium in liquid Ammonia
A) Fe + Cu2SO4 FeSO4 + 2Cu C) Alcoholic KOH
B) Fe + CuSO4 FeSO4 + Cu
D) Aqueous KOH
C) 2Fe + CuSO4 Fe2SO4 + Cu
D) Fe + Cu3SO4-- FeSO4 + 3Cu

Page 11 of 24

105) When a copper plate is dipped in silver nitrate
solution, a black layer is observed on the surface of
copper plate. The reaction responsible for this
phenomenon is

A) 2Ag2NO3 + Cu '—> Cu(NO3)2(aq)+ 4Ag(s)
B) AgNO3 + Cu (s) -4 CuNO3(aq)+ Ag(s)
C) Ag2NO3 + Cu -4 CuNO3(aq)+ 2Ag(s)
D) 2AgNO3(aq) + Cu --> Cu(NO3)2(aq)+ 2Ag(s)

106) Which of the following species are produced as a
product of neutralization reactions?

A) H+ and acid
B) OH- and base
C) H2O and salt
D) H30+ and alcohol

107) Cryolite is an uncommon mineral of very limited
natural distribution. Chemically, cryolite is

A) Sodium fluoride
B) Aluminium fluoride
C) Sodium aluminium fluoride
D) Calcium fluoride

108) A brown substance 'X' on heating in air forms a
substance 'Y'. When hydrogen gas is passed over
heated 'Y' it again changes back to 'X'. Substance 'Y' is

A) MgO
B) CuO
C) FeO
ID) ZnO I

109) Flash bulbs produce a short-duration high-intensity
light flash for taking photographs. In flash bulbs, Mg wire i
is present in an atmosphere of I

A) N2
B) He
C) SO2
D) 02

110) The element with atomic number 36 belongs to
which of the following groups?

A) Alkali metals
B) Alkali earth metals
C) Halogens
D) Noble gases

Page 12 of 24

Section 4 - Mathematics 117) Which term in the arithmetic progression -7, -2, 3,
8, .... is 88 ?
111) Which of the following is TRUE for the value of 'p'
for which the equation px2 + 4x + 1 = 0 has only real A) 15th
roots? B) 10th
C) 20th
A) p = 4
D) 21st
B) p >= 7
C) p >= 4
D) p > 8 118) What is the volume of the largest possible right
circular cone that can be cut out of a cube of edge length
42 cm?
112) A cone of height 10 cm with diameter of its base
20 cm is carved out from a wooden solid sphere of A) 924 cu. cm
radius 10 cm. What is the percentage of the wood B) 22997 cu. cm
consumed in the cone?
C) 882 cu. cm
D) 19404 cu. cm
A) 25%
B) 50%
C) 75% 119) If in A PQR which is right angled at Q,
D) 20% PR + QR = 25 cm and PQ = 5 cm, then sin P=

A) 12/13
113) If 0 < A < Tr/2, then (1 + tan2 A) / (1 + cot2 A) = B) 1/3
A) sec2 A C) 2/13
B) cosec2 A D) 5/12
C) cote A
D) tan2 A
120) If both the diameter and height of a right circular
cone are increased by 40%, then its volume is increased
114) If tan 2A = cot(A - 18°), where 2A is acute angle, by
then
A) 274.40%
A) A = 35° B) 174.40%
B) A = 30° C) 150.50%
C) A = 36° D) 125%
D) A = 42°

121) What is the area of the triangle whose vertices are
115) If 0 < 9 < n/2, then (1, -1), (-4, 6) and (-3, -5) ?
(1 + tan 0 + sec 6)(1 + cot 0 - cosec 0) =
A) 12 square units
A) 0 B) 13 square units
B) 1 C) 24 square units
C) 2 D) 15 square units
D) -1

122) The interior angles of a quadrilateral are in
116) What is the value of 'k' for which x = 1 is a root of arithmetic progression with a common difference of 10°.
the equation x2 + kx + 3 = 0 ? The angles are

A) k = 4 A) 55°, 65°, 75°, 85°
B) k = 2 B) 90°, 100°, 110°, 120°
C) k = - 4 C) 60°, 70°, 80°, 90°
D) k = 1 D) 75°, 85°, 95°, 105°

Page 13 of 24

123) In the figure below XY II BC, AY = (p-2) units , 128) Haresh tosses two coins (with two faces "head"
BY = (2p-2) units and AX / CX = 1/3. Which of the and "tail" on each) simultaneously. What is the
following is the correct value of p? probability that he gets atleast one head?

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

p-2 Y 2p-2
129) A box contains 90 discs which are numbered from
1 to 90. If one disc is drawn at random from the box,
A) 5 then what is the probability that it bears a two-digit
B) 2 number?
C) 3
D) 4 A) 9/10
B) 8/9
C) 91/100
124) Which one of the following statements is TRUE? D) 1/10

A) Every natural number is an integer
B) Every rational number is a natural number 130) One side of a rectangle exceeds its other side by
C) Every irrational number is a natural number 2 cm. If its area is 195 sq.cm, then the length of one of
the sides of the rectangle is
D) Every rational number is an integer
A) 11 cm
125) If the two zeroes of the quadratic polynomial B) 13 cm
f(x) = x2 - 6kx - 9 are numerically equal but opposite in C) 14 cm
sign, then what is the value of 'k' ? D) 17 cm

A) 1
131) The points (1 , 1) , (-1 , -1) and (43 , 43) are the
B) 0
vertices of a
C) -1
D) 2 A) Right triangle
B) Isosceles triangle
C) Equilateral triangle
126) .ABC is similar to AXYZ. If the area of .ABC is
4 times the area of AXYZ and XY = 5 units, then what is D) Scalene triangle
the length of AB which is corresponding side to XY?
132) If the points (1 , x) , (5 , 2) and (9 , 5) are collinear,
A) 20 units then the value of x =
B) 10 units
C) 100 units A) 6
D) 1.25 units B) -1
C) 7
D) 1
127) The total surface area of a solid hemisphere of
diameter 42 cm is
133) At a certain time of the day, a boy 5 feet tall casts
A) 1202 sq. cm his shadow 9 feet long. What is the length of the shadow
cast by a building 30 feet high at the same time which is
B) 4158 sq. cm
next to the boy?
C) 1376 sq. cm
D) 6742 sq. cm A) 34 feet
B) 54 feet
C) 65 feet
D) 56 feet

Page 14 of 24

134) If a hollow sphere with internal and external radii 140) In triangle ABC, LABC = 90°, AB = 3 cm and
16 cm and 32 cm respectively is melted to form a cone AC = 5 cm, then BC =
with base of radius 32 cm, then the height of the cone is
A) 7 cm
A) 112 cm B) 5 cm
B) 141 cm C) 4 cm
C) 202 cm D) 6 cm
D) 198 cm

141) A root of the equation 6x2- 5x - 25 = 0 is
135) The distance between two points A(12 , 0) and
B(0 , 5) is A) 5
B) - 5/2
A) 13 units C) - 5/3
B) 12 units
D) 3/5
C) 15 units
D) 16 units
142) The angle of elevation of the top of a pillar from a
point at a distance of 30 m from its base is 30°. How
136) Angle of elevation of the top of a pole from a point much should the pillar height be increased so that angle
which is at a distance of 60 m from base of the pole is of elevation from the same point changes to 45° ?
30°. The height of the pole is (Take 43=1.732, 42=1.414)

A) 1212 m A) 10 m
B) 15 m B) 17.32 m
C) 2043 m C) 12.68 m
D) 30 m D) 15.2 m

137) A metallic cone of radius 8 cm and height 16 cm is 143) The corresponding sides of two similar triangles
melted and made into spheres of radius 4 cm each. The are 2 cms and 3 cms respectively. The ratio of their
possible number of spheres is areas is

A) 12 A) 3 : 2
B) 6 B) 4 : 9
C) 3 C) 6 : 4
D) 4 D) 4 : 6

138) Hemispheres P and Q have their radii 30 cm and 144) sin 25° cos 65° + cos 25° sin 65° =
10 cm respectively. The ratio of total surface area of
sphere P to sphere Q is A) 1
B) 0
A) 7 : 9
C) 2
13) 5 : 9
D) J2
C) 9 : 1
D) 5 : 1
145) What is the value of 'k' for which the pair of
equations x + y - 4 = 0 and 2x + ky - 3 = 0 has no
139) If 0 is an acute angle such that cot 0 = 7/8, then solution?
tan2 0 =
A) 2
A) 8/7 B) 4
B) (415)/8 C) 6
C) 64/49 D) 8
D) 15/64

Page 15 of 24

146) The end points of the diameter of a circle are 152) The recurring decimal expansion 1 •27 can be
(2 , 4) and (-3 , -1). The radius of the circle is expressed as the fraction

A) 5 units A) 14/11
B) 5.V2 units B) 19/15
C) 6 units C) 23/18
D) 5/V2 units D) 127/100

147) A bag contains 3 red balls and 5 black balls. A ball 153) If sin(A - B) = 1/2 , cos (A + B) = 1/2
is drawn at random from the bag. What is the probability where 0° < A+B 90°, A B, then
that the ball drawn is red?
A) A = 45° , B = 15°
A) 1/8 B) A = 30°, B = 15°
B) 3/8 C) A = 45°, B = 25°
C) 5/8 D) A = 55°, B = 15°
D) 1

154) A dice is rolled once. The sides of the dice are
148) What is the locus of the point (x , y) such that the labelled with integers 1 through 6. What is the probability
point (x , y) is equidistant from the points (3 , 6) and that the integer facing up on the dice is greater than 4?
(-3 , 4) ?
A) 1/2
A)x+y= 5 B) 4/5
B) 3x+y= 5 C) 1/3
C) 3x + 2y= 6 D) 2/3
D)x+y= 7

155) Seven years ago a man was seven times the age
149) What is the value of discriminant for the equation of his daughter. After three years, the man will be three
2x2 + x - 1 = 0 ? times the age of his daughter. Present age of the man
(in years) is
A) 3
B) 8 A) 12
C) 10 B) 35
D) 9 C) 45
D) 42

150) Which of the following is a quadratic equation
whose one root is 3? 156) The solution for (x, y) to the pair of linear equations
0.2x + 0.3y = 1.3 and 0.4x + 0.5y = 2.3 is
A) x2 - 6x - 5 = 0
B) x2 + 6x - 5 = 0 A) (1.5, 3)
C) x2 - 5x - 5 = 0 B) (2, 3)
D) x2 - 5x + 6 = 0 C) (4, 7)
D) (4.5, 6)

151) The ratio of volume of a sphere of radius 5 cm to
the volume of a cylinder with height 12 cm and radius
5 cm, is

A) 1 : 1
B) 5 : 9
C) 3 : 7
D) 4 : 5

Page 16 of 24

157) A man is standing on one side of the river on its 163) If the two zeroes of the cubic polynomial
bank. Angle of elevation when this man looks at the top ax3 + 3x2 — bx — 6 are —1 and —2. Then
of a mountain on the other side of the river is 60°. On
moving 100 m away from the river bank, the angle of A) a = 2, b = 5, third zero = 3/2
elevation changes to 30°. The width of the river is B) a = 2, b = 5, third zero = -3/2
C) a = 2, b = 3, third zero = -3
A) 5043 m
D) a = 3, b = 2, third zero = 3
B) 50 m
C) 6042 m
D) 10013 m 164) AABC and ADEF are two equilateral triangles. If
the ratio of area of AABC to area of ADEF is 1 : 2 and
AB = 3 cm, then length of DE is equal to
158) tan 48° tan 23° tan 42° tan 67° =
A) 342 cm
A) 1 B) 6 cm
B) 2 C) 4.5 cm
C) 3 D) 243 cm
D) 0

165) If A is an acute angle such that sin A = 3/4, then
159) Which of following is the correct combination of the value of cos A is
angles that can form similar triangles A ABC and A DEF?
A) 1/2
A) LA=70°, LC=40°, z_E=80°, z.F=30° B) (I7)/2
B) LA=85°, z_C=35°, LE=35°, LF=72.5° C) (47)/4
C) LA=60°, LC=40°, LE=80°, LF=40° D) (13)/7
D) zA=75°, LC=52.5°, z_E=55°, LF=52.5°

166) If 4(24 - 10x) = 3 - 4x where (3 - 4x) > 0, then
160) Length of a rectangular garden is 5 m more than
its breadth. Perimeter of the rectangular garden is 2 m A) x = 3/8
more than the perimeter of a square garden with side B) x = 1/8
length 22 m. Length of the rectangular garden is
C) x = - 3/2
A) 15 m D) x = - 5/8
B) 20 m
C) 30 m 167) Two poles of heights 7 m and 13 m stand vertically
D) 25 m upright on a plane ground. If the distance between their
feet is 8 m, then the distance between their tops is equal
to
161) If a polynomial g(x) of degree zero is added to the
polynomial 2x3 + 5x2 — 14x + 12 so that it becomes A) 13 m
exactly divisible by 2x — 3, then B) 10 rin
C) 17 m
A) g(x) = -8
D) 25 m
B) g(x) = -9
C) g(x) = 7
D) g(x) = 8 168) The decimal expansion of an irrational number is

A) Terminating
162) (sec A + tan A)(1 - sin A) = B) Non-terminating and Recurring
C) Non-terminating and Non-recurring
A) sec A
D) NOT possible to compute
B) sin A
C) cosec A
D) cos A

Page 17 of 24

169) If the sum and the product of the roots of the 174) What is the polynomial of least degree that should
equation ax2 - 5x + c = 0 are both equal to 10, then be subtracted from the polynomial
f(x) = x4 + 2x3 — 4x2 + 6x — 3 so that f(x) becomes exactly
A) a = 1/2, c = 1/2 divisible by x2 — x + 1?
B) a = 1/2, c = 5 A) x2 — 1
C) a = 3, c = 1/2 B) x — 1
D) a = 5 , c = 3 C) x + 2
D) x + 1

170) A shopkeeper has only Rs. 1 and 50 paise coins in
his money box. If the total number of coins is 400 and 175) A triangle ABC which is right angled at A has points
the value of these coins is Rs. 250, then number of A and B at (2 , 3) and (0 , -1) respectively. If BC = 5
50 paise coins is units, then the point C is

A) 100 A) (4 , 2)
B) 300 B) (3 , 4)
C) 200 C) (5 , 1)
D) 150 D) (-4 , 2)

171) The perimeter of an isosceles triangle is 60 cm. If 176) Arjun takes 10 days less than the days taken by
its base is lengthened by 2 cm and each of its other side Bino to finish a piece of work. If both Arjun and Bino
is shortened by 7 cm, the triangle will become together can finish the work in 12 days, then how many
equilateral. Length of the base of the isosceles triangle days will be taken by Bino to finish the work?
is
A) 4 days
A) 10 cm B) 15 days
B) 12 cm C) 20 days
C) 14 cm D) 30 days
D) 16 cm

177) If AABC is an equilateral triangle such that D is the
172) A cone has base area of 5544 sq. cm and its midpoint of BC and ADIBC, then AD2 is equal to
volume is 92400 cu. cm. The lateral surface area is
A) 3/(4CD2)
A) 13241066 sq. cm B) 43/(2CD2)
1
B) 26441066 sq. cm C) (1/2)CD2
C) 2642132 sq. cm D) 3CD2
D) 6644264 sq. cm

178) A man whose height is 1.2 metres is standing at
173) The ratio of the radius to height of a right circular 6 meters from the foot of a lamp post. He observes that
cone is 5 : 9. If its volume is 225.rr cu. cm, then its slant his shadow cast by the light from the top of the lamp post
height is is 2 metres in length. How much high is the lamp from
the ground?
A) 4108 cm
B) 100 cm A) 7.5 metres
C) 300 cm B) 5.6 metres
D) 4106 cm C) 4.8 metres
D) 3.5 metres

Page 18 of 24

179) In the given figure, DE ll AB, DC = 3 BD, area of
ACDE = 27 sq. cm. What is the area of the quadrilateral
ABDE?

E

/
/

A) 18 sq. cm
B) 21 sq. cm
C) 24 sq. cm
D) 27 sq. cm

180) A ladder is resting on a vertical wall with its foot
resting on the ground 6 feet away from the wall. A
woman on the ground climbs 2/3 of the ladder. At what
distance is she now from the wall?

A) 2 feet
B) 3 feet
C) 4 feet
D) 6 feet

Page 19 of 24

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Page 20 of 24

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Page 24 of 24