JK Diploma Polytechnic 2018 Question Paper

Question Booklet Series: Question Booklet Number:

Polytechnic Entrance Test - 2018

A
Maximum Time Allowed : 3 Hours
QUESTION BOOKLET
INSTRUCTIONS
No. of Questions: 180
Negative Marking : 0.25 Marks Maximum Marks: 180

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Page 1 of 24

5) Complete the sentence by choosing the past perfect
Section 1 – English
tense of the verb given in the brackets.

1) Choose the correct pattern for the given sentence. Tina went to the party, after she _______ (finish) her
assignment.
When he was seven, Ganguly moved to Delhi.
A) had finished
A) Subject+Verb B) finished
B) Subject+Verb+Indirect Object C) has finished
C) Object+Subject+Verb D) having finished
D) Adjunct+Subject+Object+Adjunct
6) Complete the sentence by choosing the correct
2) Choose the correct pattern for the given sentence. pronoun.

Meeta cooks deliciously. _______ is the book I left in your house.

A) Subject+Verb+Object A) Those
B) Subject+Verb B) This
C) Subject+Verb+Adverb C) These
D) Subject+Verb+Indirect Object D) Whose

3) Complete the sentence with the infinitive form of the 7) Choose the suitable modal to complete the sentence.
verb.
You _______ talk badly of our teacher.
They set off early from their home _______ traffic.
A) to capture A) should
B) to avoid B) would
C) to blocking C) shouldn't
D) to meeting D) wouldn't

4) Complete the sentence by choosing the correct 8) Select the suitable conjunction to complete the
pronoun. sentence.

The children do not like Hindi movies so, this video is not He said that he'll call me, _______ he arrives at the
for _______. destination.
A) him
B) you A) after
C) her B) and
D) them C) although
D) or

Page 2 of 24

9) Select the correct conjunction to join the sentence. 14) Choose the suitable modal to complete the sentence.

_______ he was cleaning the dishes, she was cooking Be careful, the kids _______ swallow these small
the food. objects.

A) After A) couldn't
B) While B) should
C) Once C) would
D) Or D) may

10) Choose the sentence with the pattern:
15) Choose the correct modal to complete the sentence.

Subject+Verb+Object+Adverb
There are plenty of vegetables in the refrigerator;
you_______ buy any.
A) I love a sunny day.
B) I like moderate weather, very much. A) wouldn't
C) It is a fantastic day. B) couldn't
D) Moderate weather is good. C) should
D) needn't
11) Choose the sentence that has the pattern:
16) Identify the sentence that is in Reported Speech.
Subject+Verb+Indirect Object+Direct Object.
He said, " I like this movie."
A) My friend sent me a present.
B) Birds fly in the sky. A) He said that he liked that movie.
C) The officer wants to retire. B) He said that he liked this movie.

D) The flower is beautiful. C) He said he liked this movie.
D) He said that he liked a movie.
12) Identify the clause in the underlined part of the
17) Complete the sentence by choosing the correct
sentence.
pronoun.

He is healthy, because he eats healthy food.
The car is _______ ; I bought it yesterday.

A) relative
A) my
B) independent
B) her
C) dependent
C) him
D) noun
D) mine

13) Choose the suitable conjunction to join the sentence. 18) Choose the correct conjunction to join the sentence.

He ran the marathon, _______ his ankle was injured. I don't like sugar in my coffee _______ I like milk in it.

A) as A) and
B) because B) or
C) or C) so
D) although D) but

Page 3 of 24

19) Identify the sentence that is in the reported speech. 23) Identify the clause in the underlined part of
the sentence.
She said,"I will water the plants".
They decided to go to the park, although the weather was
A) She said I would water the plants. not very good.
B) She said that she will water the plants.
A) relative
C) She said that she would water the plants.
B) adverbial
D) She said she would water the plants.
C) dependent
20) Complete the sentence by choosing the past perfect D) independent
tense of the verb given in the brackets.
24) Identify the sentence that is in reported speech.
She _______ (be) to Mumbai before 2016.
He said, "I was playing video games, when the house
A) have not been caught fire”.
B) has been going
A) He said that the house caught fire, when I was
C) had not been
playing the video games.
D) has been
B) He said that he had been playing video games, when
the house caught fire.
21) Identify the clause in the underlined part of the
C) He said that he was playing video games, when the
sentence.
house caught fire.
Sheena played with her baby brother, before she left to D) He said he is playing video games, when the house
school. caught fire.

A) dependent 25) Choose the correct modal to complete the sentence.
B) independent
You _______ stop when the traffic light is red.
C) relative
D) adverbial A) musn't
B) could
22) Choose the correct sentence with the pattern:
C) need
Adjunct+Subject+Verb+Indirect Object+ Direct D) must
Object+Adjunct
26) Choose the infinitive form to complete the sentence.
A) The dog ran across the farm.
He went to the Automated Teller Machine(ATM) ______
B) The cows wandered, all around the field.
some money.
C) The judge punished the criminal.
D) At the beginning of the race, the driver showed his A) to draw
partner the route, on his mobile.
B) saving
C) counting
D) to supplying

Page 4 of 24

27) Complete the sentence by choosing the past perfect
Section 2 – Physics
tense of the verb given in the brackets.

The children picked up the mangoes that _______ (fall)
31) Which of the following defects can be corrected by
from the trees.
using a convex lens eye glasses of appropriate power?

A) have fallen
A) Hypermetropia
B) had fallen
B) Myopia
C) fell
C) Presbyopia
D) have been falling
D) Cataract

28) Complete the sentence by choosing the infinitive form
32) A wire of resistance 40Ω is bent to form a square. The
of the verb.
resistance which will be available across the diagonal of
that square is
It was hard _______ Lata singing in the party.

A) 5 Ω
A) imagining
B) 10 Ω
B) to seeing
C) 15 Ω
C) to imagine
D) 25 Ω
D) hearing

33) The power consumed by a bulb of rating 220 volt and
29) Choose the correct pattern for the given sentence.
60 Watt when it is connected to a 110-volt source is

I wish you happy birthday.
A) 25 W

A) Subject+Verb B) 20 W

B) Subject+Verb+Object C) 30 W

C) Subject+Verb+Indirect Object+Direct Object D) 15 W

D) Subject+Verb+Indirect Object
34) The image formed by a converging lens which has a
focal length of 20cm and has an object kept at a distance
30) Complete the sentence by using the correct pronoun.
of 50cm will be at a distance of approximately

_______ horse won the race at the Derby?
A) 15 cm

A) What B) 24 cm

B) That C) 33 cm

C) Which D) 42 cm

D) Those
35) The amount of electric energy consumed when an
electric appliance of 1-watt power is used for 1 hour is
known as

A) One kilowatt-hour
B) One Watt
C) One Watt-hour
D) One Joule

Page 5 of 24

36) The relation connecting charge ‘Q’, potential 41) The fuel which exists in liquid state at room
difference ‘V’ and work done ‘W’ is temperature is

A) V = W/Q A) Water gas
B) V = Q/W B) Petroleum
C) W = V/Q C) Bagasse
D) V = WQ D) Briquettes

37) The current drawn by an electric toaster of power 42) The substitute for gasoline or propane fuel is
rating 1 kW which is operated in a domestic electric circuit
of 220V and 5A is A) Nuclear energy
B) Biogas
A) 1.54 A
C) Freon
B) 15.4 A
D) Compressed Natural Gas
C) 4.54 A
D) 44 A 43) The heat ’H’ produced in a conductor which consists
of resistance ‘R’, current ‘I’ flowing through it for ‘t’
38) A thin membrane which covers the eyeball and acts seconds is
like a lens to refract the light entering the eye is
A) H = I2Rt J
A) Retina B) H = IRt cal
B) Aqueous Humour C) H = I R2t /4.18 J
C) Cornea D) H = I2Rt/ 4.18 J
D) Pupil
44) The approximate equivalent resistance of a combined
39) Two light waves having wavelength 2800 A° and circuit which consists of a 12Ω resistance cut into three
5600 A° travel through vacuum. The ratio of their equal parts and connected in parallel is
velocities are
A) 1 Ω
A) 1:1 B) 1.3 Ω
B) 1:2 C) 2.5 Ω
C) 2:1 D) 4 Ω
D) 1:3
45) If an electric heater consumes 1250W at 220V, then
40) The focal length of the lens which is used for the electric current in the circuit approximately is
correcting the distant vision of a person who uses a lens
of power -5D is A) 0.18 A
B) 2.75 kA
A) (- 2) cm
C) 3.4 A
B) (5) cm
D) 5.7 A
C) (0.20) cm
D) (- 20) cm

Page 6 of 24

46) A circuit consists of an ammeter and a nichrome wire 51) The approximate resistance of the device which has
connected in series across a battery. The ammeter a rating of 220V and 60W is
reading when the experiment is repeated with a nichrome
wire of twice its initial length and same thickness is A) 200 Ω
B) 320 Ω
A) Half of the initial
C) 524 Ω
B) Same as initial
D) 806 Ω
C) Twice as initial
D) One-fourth of the initial 52) The type of corrective lens which should be used by
a myopic defect person who cannot see objects beyond
47) A mirror which has an object placed at a distance of 1.5m distinctly is
20cm from it has an image formed at a distance of 4cm
to the right of the mirror. The mirror and the focal length A) Concave lens
of the mirror used is
B) Convex lens
C) Bifocal lens
A) Convex, 3cm
D) Plano- convex lens
B) Concave, 3cm
C) Convex, 5cm
53) The energy in kWh consumed by a bulb in 4 hours, if
D) Concave, 5cm it has a resistance of 100Ω and draws a current of 2A is

48) The number of electrons that will cross any A) 8 kWh
cross-section of a conductor in one second when a
B) 1.6 kWh
current of one Ampere flows through it is
C) 3.2 kWh

A) 6.25 x 1018 D) 6.4 kWh

B) 1.6 x 1018
54) An object kept between the focus and centre of
C) 3.2 x 1018
curvature of a concave mirror forms a real image beyond
D) 6.45 x 1018 the centre of curvature. This position of the mirror is
mainly used in
49) The percentage change in the resistance of a
resistance wire which is stretched uniformly to increase A) Shaving mirrors
its length by 20 percentage is
B) Flood lights
C) Torches
A) 14%
D) Solar devices
B) 20%
C) 24%
55) If ‘I’ is the current flowing through a wire at a given
D) 44% voltage ‘V’ and if the wire is divided into two equal halves,
then the resistance of each half is
50) The linear magnification of a diverging lens of focal
length 18cm which forms an image at a distance of 15cm
A) R/2
from the lens is
B) 2R
A) 0.13 C) R
B) 0.16 D) R/4
C) 2
D) 3

Page 7 of 24

56) The position of the object for a converging mirror of 61) A spherical mirror whose outer curved side is the
radius of curvature 40 cm which forms an erect image reflecting surface and inner surface is polished is a
which is 4 times the size of the object is
A) Concave mirror
A) -15 cm B) Plano -concave mirror
B) +15 cm C) Convex mirror
C) +25 cm D) Plane mirror
D) -25 cm
62) Heat energy generated and stored in the earth is
57) The refractive index of alcohol is 1.36, water is 1.33,
ice is 1.31 and that of kerosene is 1.44. The light will A) Wind energy
travel faster in
B) Nuclear energy
C) Tidal energy
A) ice
D) Geo-thermal energy
B) water
C) alcohol
63) If the frequency of the light incident on a convex
D) kerosene mirror is increased, then the focal length of the mirror will

58) A tiny magnetic needle when placed above or below A) increase
a straight conductor deflected, when a current was
B) decrease
passed through the conductor. This was observed by
C) become infinite

A) Faraday D) not change

B) H. C. Oersted
64) The magnetic field at the centre of a coil of 5 turns
C) Ampere
which carries a current of 0.1A and has a circular coil of
D) James Maxwell radius 0.10m is

59) If a net charge ‘Q’ flows through the matter for a time A) 0.314 x 10-7T
‘t’, then the electric current ‘I’ flowing through it is given
B) 314 x 10-7T
by
C) 3.14 x 10-7T

A) I = Qt D) 31.4 x 10-7T

B) I = Q/t
65) A cylindrical coil containing several number of close
C) I = t/Q
turns of insulated wire whose length is greater than its
D) I = 1/Qt radius is a

60) The main source of energy used in traffic signals or A) electromagnet
wireless transmission systems in remote locations is
B) solenoid
C) bar magnet
A) Fossil fuels
D) motor
B) Solar cells
C) Transmitter
D) Solar heater

Page 8 of 24

66) The device which works on the phenomenon in which 71) What is the flux density at the centre of a solenoid of
induced current is produced due to the relative motion length 1m, which has 4 layers of 1200 turns each and a
between the magnet and the coil is current of 2A flowing through it?

A) Electric lamp A) 0.012 T
B) Electric fan B) 0.017 T
C) Electric kettle C) 0.12 T
D) Electric heater D) 0.17T

67) A person visits a barber shop and sees two plane 72) Sometimes, the thermal power plants make use of
mirrors kept parallel to each other. The number of images natural gas as a fuel because it consists primarily of
that will be formed is
A) Methane
A) Zero B) Nitrogen
B) Three C) Carbon dioxide
C) Infinity D) Hydrogen sulphide
D) One
73) A current carrying loop when placed in a magnetic
68) The focal length of the combination of two thin lens of field experiences a force and the direction of rotation of
powers +5D and -2D which are in contact is the loop is given by "Fleming’s left-hand rule". This is the
working principle of
A) 3.33 cm
B) 14.2 cm A) Electric generator
C) 33.33 cm B) Electric motor
D) 0.14 cm C) Solenoid
D) Galvanometer
69) The direction of magnetic field at 0.5m above a
current carrying wire which carries current from west to 74) A device which checks the overflow of current in the
east is circuit and hence protects the appliance connected to the
circuit is
A) North to South
B) South to North A) Split ring
C) West to East B) Brushes
D) East to West C) Fuse
D) Cell
70) The potential energy of water at a height or the kinetic
energy of flowing water is used in 75) The law that helps in determining the magnetic field
at a point near a current element is
A) Solar cells
B) Ocean thermal energy A) Laplace’s law
C) Hydro power plants B) Maxwell’s law
D) Wind energy C) Ampere’s law
D) Gauss’s law

Page 9 of 24

76) The burning of fossil fuels releases oxides of carbon,
Section 3 - Chemistry
nitrogen and sulphur which are acidic oxides. This is
primarily the reason for
81) An element P forms an oxide which is acidic in nature.
A) Green house effect It is a solid and non- conductor of heat and electricity.
From its salt solution, the element P is precipitated on
B) Acid rain
passage of electric current releasing two electrons per
C) Biomass anion. The element P must be occurring in the periodic
D) Solar energy table in the group:

77) The example of a renewable energy source is A) Group 1
B) Group 2
A) Coal C) Group 12
B) Sunlight D) Group 16
C) Oil
D) Natural gas 82) This element has the electronic configuration
[Ar] 3d104s2. It is a silvery-white metal with a blue tinge. It
78) The defect which happens to human eye due to the tarnishes in air. To which group of the periodic table does
gradual weakening of ciliary muscles is this element belong?

A) Cataract A) Group 1
B) Presbyopia B) Group 2
C) Astigmatism C) Group 12
D) Myopia D) Group 16

79) The electrons that can come out of the negative 83) An element X has three electron shells (electronic
terminal of a cell in 4 minutes when a 4V cell is connected configuration [Ne]3s23p5) and occurs in group 17. The
to a 2Ω resistor is element occurring in the next period in the same group
will be:
A) 12.24 x 1020
B) 22.34 x 1020 A) Astatine

C) 30 x 1020 B) Fluorine

D) 120 x 1020 C) Iodine
D) Bromine
80) The speed of light in vacuum is 3x 10 8 ms-1 and the
refractive index of glass is 1.45. If the light enters from air 84) There are four test tubes. The first one contains
to glass, then the speed of light in glass is muriatic acid [pH =1], the second one contains citric acid
[pH =2.3], the third one contains acetic acid [pH =2.9] and
A) 0.48 x 10-8 ms-1 the fourth one contains boric acid [pH =5.2]. On reaction
with granulated zinc, the one which will be able to release
B) 2.1 x 108 ms-1
hydrogen the fastest will be:
C) 3 x 108 ms-1
D) 3.2 x 108 ms-1 A) Muriatic acid
B) Citric acid
C) Acetic acid
D) Boric acid

Page 10 of 24

85) In a chemical process, at high temperature, carbon 89) Two organic compounds A and B share the same
reduces zinc oxide to zinc and itself gets oxidised to molecular formula C3H8O, but their chemical and physical
carbon monoxide. This zinc which may contain impurities properties are totally different. The relation between
like cadmium, carbon, arsenic and iron is known as: A and B is:

A) Zinc spelter A) They are homologous
B) Zinc blende B) They are isomers
C) Sphalerite C) They are isotopes
D) Zincite D) They are isochores

86) On touching nettle leaves a stinging sensation is 90) In industries, vegetable oil can be turned to vegetable
experienced. On washing the place with baking soda ghee by which of the following reactions?
solution, the stinging sensation goes away. One of the
reasons for the stinging sensation is because nettle A) Polymerisation reaction
leaves contain:
B) Condensation reaction
C) Hydrogenation reaction
A) Magnesium hydroxide
D) Compression reaction
B) Oxalic acid
C) Ethanoic acid
91) Beautiful golden yellow spangles are formed when
D) Methanoic acid lead nitrate solution is added to potassium iodide
solution. This is an example of:
87) Metals have a lot of characteristic properties. The
property of malleability in metals is exhibited because of: A) Displacement reaction
B) Double displacement reaction
A) Metals having rigid crystalline structures
C) Nitration reaction
B) Metals having metallic bonds extending in multi-
D) Iodoform reaction
directions
C) Metals having metallic bonds only in uni-direction
92) Identify out of the following, which one is an example
D) Metals having amorphous micro crystalline of oxidation reaction?
structures
A) While storing salt in the rainy season, it forms lumps
88) Few drops of liquid X are heated with few drops of
B) While storing cement, it turns solid if not properly
glacial acetic acid in the presence of concentrated H2SO4,
packed
when a sweet-smelling compound is produced. What is
C) While storing butter for a long duration, it turns bitter
X?
D) While storing biscuits, they turn soggy if not kept in
A) Ethene an air-tight container

B) Ethane 93) When alkaline potassium permanganate is heated
C) Ethanol with ethanol, the pink colour of alkaline potassium
D) Ethanal permanganate gradually disappears. This is due to
conversion of ethanol to

A) Ethyl ethanoate
B) Ethyl permanganate
C) Ethanoic acid
D) Ethoxyethane

Page 11 of 24

94) Ethanol is the only alcohol which is fit for human 99) The hybridisation in ethane is:
consumption. But consumption of even a small quantity
of methanol of the same homologous series can lead to A) sp
death because it gets converted to:
B) dsp2
C) sp2
A) Methyne
D) sp3
B) Methane
C) Methanoic acid 100) Sulphur has been used in skin ointments since
D) Menthol ancient times to treat skin ailments like acne, because:

95) An allotrope of a non-metal is used in the tip of A) It has good anti-bacterial properties
oil-drilling machines and for cutting glass. The structure B) It ensures the fragrance helps in removing acne
of the allotrope is: C) It detoxifies the blood and makes it pure and
improves circulation
A) Hexagonal D) It improves the complexion making it fairer, removing
B) Tetrahedral melatonin
C) Rhombohedral
101) Identify which among the following statements is
D) Octahedral FALSE regarding a chemical reaction:

96) What is the IUPAC name of the following structure? A) The total number of atoms of reactants and products
are the same
B) No new element is either created or destroyed
C) The total mass of the reactants and products are the
same
A) Pentane D) The energy content of the reactants is equal to the
B) Butane energy content of the products

C) Hexane
102) Which of the following is NOT a property of alloys?
D) Octane

A) They enhance the hardness of a metal
97) Some substances called indicators are used to study
B) They reduce the tensile strength of a metal
different pH of solutions. Indicators are:
C) Alloys lower the melting point of a metal
A) Salts of organic acids D) Alloys enhance corrosion resistance of a metal
B) Salts of inorganic acid
103) Adding of water to concentrated acid is dangerous
C) Weak organic acids or base
because:
D) Weak inorganic acids or base

A) It forms an explosive mixture because of high amount
98) What is the commonality between an aqueous
of hydronium ion generation
solution of inorganic acid and alkali?
B) It forms an explosive mixture because of the
generation of high heat of hydration
A) Both contain hydronium ions
C) It forms an explosive mixture because of very high
B) Both contain hydroxyl ions
ionisation of acid
C) Both contain a mixture of cations and anions
D) It forms an explosive mixture because concentrated
D) Both contain mixture of hydronium and hydroxyl ions acid has high dissociation constant

Page 12 of 24

104) Normal lubricating oils cannot work when applied on 109) Two elements A and B occur in the same period.
moving parts of machines working at high temperature. Both A and B combine to form a salt which when
But, the fine powder of a non-metal can be applied there electrolysed, ions of A migrate towards anode and ions
as a lubricating agent because of its structure being: of B migrate towards cathode. A and B must be
respectively:
A) Rigid
B) Amorphous A) A ⇒ metal; B ⇒ non-metal
C) Layered B) A ⇒ non-metal; B ⇒ metal
D) Multi-directional C) Both A and B non-metal
D) Both A and B metal
105) Write a balanced chemical equation for the following
reaction: 110) There are four solutions A, B, C and D having pH
2.3 ,4.8, 8.4, 12.9 respectively. The one which has the
Calcium hydroxide + carbon dioxide → Calcium HIGHEST hydrogen ion concentration will be:
carbonate + water
A) A
A) Ca(OH)3 + CO2 → CaCO3 + H2O
B) B
B) Ca(OH)2 + CO2 → CaCO3 + H2O
C) C
C) CaOH + CO2 → CaCO3 + H2O
D) D
D) Ca(OH)2 + CO2 → Ca(CO3)2 + H2O

106) Zinc is widely used for making dry cells. The process Section 4 – Mathematics
by which its main ore is concentrated is:
111) The values of x, if 51+𝑥 + 51−𝑥 =26, are
A) Gravity separation
B) Froth floatation A) 1, 0
C) Electro refining B) 1, -1
D) Electromagnetic separation C) 1, 5
D) 2, 3
107) A metal container is used for storing radio-isotopes.
The main ore of this metal from among the given options 112) By what number should 1679 be divided to get
is: 27 as quotient and 32 as remainder?

A) Pyrites A) 61
B) Galena B) 32
C) Casseterite C) 63
D) Horn silver D) 37

108) Identify among the following the CORRECT ore 113) The area of the quadrilateral whose vertices are
from which a silvery white metal is extracted which is (3, 0), (4, 5), (-1, 4) and (-2, -1) taken in order is
used for making cold drink cans.
A) 12 Sq. Units
A) Fluorspar
B) 16 Sq. Units
B) Cryolite
C) 28 Sq. Units
C) Bauxite
D) 24 Sq. Units
D) Galena

Page 13 of 24

114) A cylindrical tub of radius 5 cm and length 9.8 cm is 118) Any point X inside the triangle ΔDEF is joined to
full of water. A solid in the form of a right circular cone its vertices. From a point P in DX, PQ is drawn parallel to
mounted on a hemisphere is immersed into the tub. If the DE meeting XE at Q and QR is drawn parallel to EF
radius of hemisphere is 3.5 cm and height of the cone meeting XF at R. Then
outside the hemisphere is 5 cm, then volume of water
(take  =22/7) in the tub is A) PR || DF
B) PQ || QR
A) 154 cm3
C) PR || DE
B) 616 cm3
D) XQ || XR
C) 338 cm3
D) 465 cm3 119) If (1, y), (4, 3), (6, 6), (x, 5) are the vertices of a
parallelogram taken in order, then the values of x and y
115) If the given points (a, b+c), (b, x) and (c, a+b) are are
collinear, then the value x =
A) x=3, y=2
A) a+b B) x=4, y=3
B) a+c C) x=5, y=2
C) a-c D) x=1, y=2
D) b-c
120) If (x cos θ + y sin θ) = a, (x sin θ - y cos θ) = b,
116) The age of father is 4 years more than 4 times the then x2 + y2 =
son's age. 4 years hence, the age of the father will be
10 years more than twice the age of the son. The present A) 4ab
age of father is B) a+b
C) 1
A) 24 years
D) a2+b2
B) 33 years
C) 40 years 121) The seventh term in the given sequence 1, 25, 49,
D) 54 years 73 is

117) The bisector of interior ∠B of a triangle ABC meets A) 123
AC in D and the bisector of exterior ∠B meets AC B) 145
AD
produced in E. Then = C) 121
AE
CD D) 90
A)
CE
AC (1+𝑐𝑜𝑡𝜃+𝑡𝑎𝑛𝜃)(𝑠𝑖𝑛𝜃−𝑐𝑜𝑠𝜃)
B) 122) The value of =
AE 𝑠𝑒𝑐 3 𝜃−𝑐𝑜𝑠𝑒𝑐 3 𝜃

BD
C)
BE A) SinθCosθ
AB B) Sin2θ – Cos2θ
D)
AC C) Sin2θCos2θ
D) 1

Page 14 of 24

123) The area of a rectangular plot is 528 sq.m. The 𝑐𝑜𝑠 𝐴 𝑐𝑜𝑠 𝐴
128) If 0° < 𝐴 < 90° 𝑎𝑛𝑑 + = 4, 𝑡ℎ𝑒𝑛 𝐴 =
1−sin 𝐴 1+sin 𝐴
length of the plot is one more than twice its breadth. The
length of the plot is
A) 30o

A) 16 m B) 60o

B) 12 m C) 45o

C) 20 m D) 15o

D) 33 m
129) ABC and DEF are two similar triangles such that BC
= 6 cm, the corresponding side EF = 8 cm and the area
124) From the top of a tower 50 m high the angle of
of triangle ABC is 81 sq.cm. Then the area of the triangle
depression of the top and bottom of a pole are observed
DEF is
to be 30o and 60o respectively, then the height of the pole,
if the pole and tower stand on the same plane is
A) 108 cm2

A) 21.13 m B) 144 cm2
C) 112 cm2
B) 58√3m
D) 150 cm2
C) 57.73̅m
D) 33.33 m
130) The ratio of the area of the triangle ABC to the area
of the triangle formed by joining the midpoints of the sides
125) ABC is a right-angled triangle at A. A circle is of this triangle, where vertices are A (-5, -1), B (3, -5) and
inscribed in it. The length of the two sides containing the C (5, 2), is
right angle are 3 cm and 4 cm. Then the radius of the in-
circle is
A) 2 : 1
B) 4 : 1
A) 2.5 cm
C) 1 : 4
B) 2 cm
D) 1 : 8
C) 0.5 cm
D) 1 cm
131) If tan A + sin A = m, tan A - sin A = n, then 4√𝑚𝑛 =
7 2
126) The quadratic polynomial whose zeros are , is A) m2-n2
√3 √3
B) m2+n2
28
A) 𝑥 2 − √3𝑥 − 3 C) m+n
14 D) 2mn
B) 𝑥 2 − 3√3𝑥 + 3
C) 𝑥 2 − √2𝑥 + 1 132) If 𝛼, 𝛽 are the zeros of the polynomial
21
D) √3𝑥 2 − 3𝑥 + 7 f(x) = 2x2+5x+k satisfying the relation 𝛼 2 + 𝛽 2 + 𝛼𝛽 =
4
, then the value of k is
127) The altitude of an equilateral triangle with side length
of 4a cm is A) 7
B) 4
A) 2a√3 cm
C) 2
B) a√3 cm D) 1
C) 4a cm
D) a√2 cm

Page 15 of 24

133) The value of ’y' if 𝑠𝑖𝑛2 20°+𝑠𝑖𝑛2 70°
138) The value of
𝑐𝑜𝑠2 59°+𝑐𝑜𝑠2 31°
+ 𝑠𝑖𝑛35°𝑠𝑒𝑐55° =
1 1 3 1 1 −1
+ = , − =
3𝑥 + 𝑦 3𝑥 − 𝑦 4 2(3𝑥 + 𝑦) 2(3𝑥 − 𝑦) 8
A) 1
A) 2 B) 2
B) -3 C) 0
C) 1 D) 1/2
D) -1
a2 b2
139) If x = acosθ, y = bcotθ, then − 2=
x2 y
134) The H.C.F of 274170 and 17017 is

A) 1
A) 13
B) tanθ
B) 19
C) 0
C) 17
D) Sinθ
D) 15

140) In a triangle ABC, DE is parallel to the base BC with
135) A passenger train takes 4 hours less for a journey of AD 5 BC
D on AB and E on AC. If = , then =
400 km, if its speed is increased by 5 km/hr from its usual DB 3 DE

speed. Its usual speed is
A) 5/2
A) 20km/hr B) 8/5
B) 25km/hr C) 2/3
C) 16km/hr D) 4/5
D) 9km/hr
141) The coordinates of the point of trisection of a
136) The value of segment joining A (-2, 5) and B (3,2) is
3(𝑠𝑖𝑛𝑥 − 𝑐𝑜𝑠𝑥)4 + 6(𝑠𝑖𝑛𝑥 + 𝑐𝑜𝑠𝑥)2 + 4𝑠𝑖𝑛4 𝑥 + 𝑐𝑜𝑠 6 𝑥 =
A) (5,4)
A) 1 B) (8/3, 3)
B) 0 C) (4/3, 3)
C) 13 D) (6,7)
D) 15
sec 𝜃−1 sec 𝜃+1
142) The value of √ +√ =
sec 𝜃+1 sec 𝜃−1
137) If there are three points A = (3, -5), B = (5, 7) and
C = (2, -3), then the equation of a straight line passing
through B and perpendicular to the line AC is A) cosecθ + cotθ
B) 2cosecθ
A) x + 6y - 6 = 0 1 − sin 𝜃
C)
B) 9x + y + 3 = 0 1 + cos 𝜃
C) x - 2y + 9 = 0 sin 𝜃
D)
1 + cos 𝜃
D) 2x - y - 9 = 0

Page 16 of 24

143) From a window (h meters high above the ground) of 147) If cosθ = 3/5, then the value of cotθ – cosecθ =
a house in a street, the angle of elevation and depression
of the top and foot of another house on the opposite side A) 1/2
of the street are α and β respectively. The height of the
B) 2
opposite house is
C) -1
h tan 𝛼 D) -1/2
A)
tan 𝛽 − tan 𝛼
148) Two dice are thrown once. The probability of
B) h(tan 𝛼 + cot 𝛽)
obtaining a total more than 7 is
2h sec 𝛼
C)
tan 𝛽 − tan 𝛼
A) 1/6
D) h(1 + tan 𝛼 cot 𝛽)
B) 1/12
C) 5/36
144) On dividing the polynomial f(x) = x3-3x2+x+2 by a
polynomial g(x), the quotient is q(x) and remainder is r(x) D) 5/12
where q(x) = x-2 and r(x) = -2x+4 respectively. The
polynomial g(x) = 149) A bag contains 6 black, 5 red and 3 white balls. A
ball is drawn from the bag at random. The probability that
A) x2-x+1 the ball drawn is red or white is
B) 8x2+8x+4
A) 4/7
C) 6x2-3
B) 7/15
D) 4x2+4x+20
C) 3/14
145) The value of ’x’, D) 2/7
𝑥𝑦 6 𝑥𝑦
if = , = 6, 𝑥𝑦 ≠ 0, 𝑦 − 𝑥 ≠ 0
𝑥+𝑦 5 𝑦−𝑥
150) A man bought a certain number of toys for Rs.160.
He kept one for his own use and sold the rest for one
A) x = 3 rupee each more than he gave for them. Besides getting
B) x = -3 his own toy for nothing he made a profit of Rs.11. Then
C) x = 2 the number of toys are
D) x = 1
A) 10
146) A box contains 20 balls bearing numbers 1, 2, 3, 4, B) 30
.... , 20. A ball is drawn at random from the box. Then the C) 20
probability that the number on the ball is a composite D) 15
number is
151) A fraction becomes 9 / 11, if 2 is added to both the
A) 4 / 5 numerator and the denominator. If 3 is added to both the
B) 11 / 20 numerator and denominator it becomes 5/6, then the
C) 13 / 20 fraction is
D) 1 / 2
A) 4 / 9
B) 4 / 7
C) 7 / 9
D) 5 / 9

Page 17 of 24

152) ABC is an isosceles triangle with AB=AC=15 cm. 157) If the equation kx(x-2)+6 = 0 has two real equal
The length of altitude from A on BC is 9 cm. Then BC = roots, then the value of 'k' is

A) 20 cm A) ±2√6
B) 18 cm B) 10
C) 12 cm C) 1/2
D) 24 cm D) 6

158) A spiral wire is made up by joining successive
153) The values of x and y, if the system of equations is
semicircles of wires of radius 1 cm, 1.5 cm, 2.0 cm,
given by ax+by = a-b, bx-ay = a+b, are
2.5 cm and so on. What is the total length (taking π =
22/7) of the spiral made up from 14 consecutive
A) -1, 1 semicircles?
B) -1, -1
C) 1, 2 A) 187 cm
D) 1, -1 B) 143 cm
C) 168 cm
154) The roots of the quadratic equation D) 209 cm
2y2 + 2√2 y + 1 = 0 are
159) The value of
1 1 tan2 60°+4 cos2 45°+3 cosec2 60°+2 cos2 90°
A) ,
2 2 9 =
4cosec 30°+3 sec 60°− cot2 30°
B) 1 ,4 3
1 1 A) 5/3
C) − ,−
√2 √2 B) 2√3
1 1
D) , C) 9
√2 2
D) 9/5

155) The horizontal distance between two towers is 160) The equation of the line that cuts off intercepts 'a'
150 m. The angle of depression of the top of the first and 'b' on the X-axis and Y-axis respectively, such that
tower when seen from the top of the second tower is a+b = 4 and ab = 3, is
45o. If the height of the first tower is 50 m, then the height
of the second tower is A) 3x+y=3 or x+3y=3
B) 2x+y=2 or x+2y=2
A) 200 m
C) x-3y=3 or 3x-y+3=0
B) 140.83 m
D) 2x+3y=1 or 9x-10y=74
C) 119 √3 m
161) A piggy bank contains hundred 50 p coins, fifty Re.1
D) 150 √3 m
coins, thirty Rs. 2 coins and five Rs. 5 coins. If it is equally
likely that one of the coin will fall out when the bank is
1 1 1 1 turned upside down. The probability that the coin will NOT
156) The value of x, if = + + , is
a+b+𝑥 a b 𝑥 be a Rs. 5 coin is

A) -b, a A) 17/18
B) -a, -b B) 36/37
C) 0, a C) 16/25
D) a, b D) 5/9

Page 18 of 24

162) A wooden article was made by scooping out a 167) The difference of two numbers is 4 and the
hemisphere from each end of a cylinder. If the height of difference of their reciprocal is 1/8. Then the numbers are
the cylinder is 8 cm and its base diameter is 7 cm, then
the total surface area of the article when it is ready is A) 8, 12
B) 4, 8
A) 374 cm2
C) 5, 9
B) 770 cm2
D) 11, 15
C) 330 cm2
D) 253 cm2 168) A rectangular park is to be designed whose breadth
is 4 m less than its length. Its area is to be 10 sq.m more
163) If (2.6) 𝑥 = (0.26) 𝑦 = 1000, than the area of the park that has already been made in
1 1 the shape of isosceles triangle, with its base as the
then the value of − =
𝑥 𝑦
breadth of the rectangular park and the altitude 14 m.
Then the length of the rectangular park is
A) 3
B) 1/2 A) 4 m
C) 1 B) 5 m
D) 1/3 C) 7 m
164) A solid sphere of radius 6 cm is melted into a hollow D) 9 m
cylinder of uniform thickness. If the external radius of the
base of the cylinder is 4 cm and its height is 24 cm. Then 169) A metallic right circular cone with 20 cm height and
the uniform thickness of the cylinder is whose vertical angle is 60o is cut into two parts at the
middle point of its height by a plane parallel to the base.
A) 5 cm If the frustum so obtained be drawn into a wire of
1
B) 3 cm diameter cm, then the length of wire is
16

C) 4 cm
D) 2 cm A) 30400 m
B) 7964.44 m
165) The total surface area of a hemisphere of radius
C) 1068.57 m
4.2 cm (take π = 22/7) is
D) 3460. 65 m
A) 160.32 sq cm 170) If the bisector of an angle of a triangle bisects the
B) 115.5 sq cm opposite side, then the triangle cannot be
C) 167.25 sq cm
D) 166.32 sq cm A) an equilateral triangle
B) a scalene triangle
166) A right circular cone is 8 cm high and the radius of
C) a right-angled triangle
its base is 2 cm. The cone is melted and recast into a
sphere, then the diameter of the sphere is D) an isosceles triangle

A) 2 cm
B) 6 cm
C) 8 cm
D) 4 cm

Page 19 of 24

171) A conical vessel of radius 5 cm and height 12 cm is 176) Radha whose height is 150 cm is going away from
completely filled with water. A sphere is lowered into the a lamp post at a speed of 1.5 m/sec. If the lamp post is
water and its size is such that when it touches the sides, 3.5 m on the ground, then the length of her shadow after
it is just immersed, the fraction of water overflows is 4 seconds is

A) 3/8 A) 3.5 m
B) 40/81 B) 2 m
C) 53/81 C) 4.5 m
D) 63/8 D) 1.9 m

172) In the triangle ΔABC, DE || BC and 5AD = DB. If 177) In equilateral triangle ABC, the side BC is trisected
AC = 4.8 cm, then AE = at D, such that BC = 3BD, then 7AB2 =

A) 2.1 cm A) 9AD2
B) 3.5 cm B) 5BC2
C) 0.8 cm C) 4DE2
D) 1.2 cm D) 3AD2

178) ABC is a right-angled triangle, right angled at
173) If the radii of the circular ends of a conical bucket
C. If x is the length of the perpendicular from C to
which is 48 cm high are 21 cm and 7 cm, then the 1
capacity of the bucket (take  =22/7) is AB and AB = c, BC = a and CA = b, then =
𝑥2

A) 48510 cm3 1
A)
B) 10459 cm3 𝑎𝑏
1 1
C) 25667 cm3 B) 2 + 2
𝑎 𝑏
D) 32032 cm3 C) 𝑎 + 𝑏 2
2

D) 𝑎2 − 𝑏 2
174) A tent of height 3.3 m is in the form of a right circular
cylinder of diameter 12 m and height 2.2 m, surmounted 179) If α and β are the zeroes of the polynomial x2+4x+3,
by a right circular cone of the same diameter, then the the polynomial whose zeroes are (1 + β/α) and (1 + α/β)
cost of the canvas of the tent at the rate of Rs. 600 per is
m2 is
A) x2-11x+30
A) Rs. 1,18,000 B) 4x2-4x-3
B) Rs. 1,18,800 C) 3x2-16x+16
C) Rs. 8,31,600 D) 7x2-22x+7
D) Rs. 2,30,000
180) The sum of two natural numbers is 6. If the sum of
175) The radius of a conical tent is 3 m and its height is their reciprocals is 6/5, the numbers are
4 m. Then the length of canvas used in making the tent if
width of canvas is 4 m ( =22/7) is A) 4 and 2
B) 5 and 1
A) 134.2 m
C) 3 each
B) 11.78 m
D) NOT possible to determine.
C) 22.72 m
D) 150.40 m

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