HTET TGT MATHEMATICS LEVEL 2

PRACTICE SET

• Try to solve these questions in time limit of 60-75 minutes.

• Join Telegram Channel of Continuum: https://t.me/continuuumm for more
educational information.

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1) A,B and C alone can complete a work in 50 days, 80 days and 120 days
respectively. If they together earn 22050 to complete the work, then what
will be the share of both A and B together?
A) ₹ 17550
B) ₹ 15750
C) ₹ 18650
D) ₹ 16250
2) Speed of a train is 40% more than the speed of a car. Both start from point
P at the same time and reach point Q, at the same time. P and Q are 280
apart from each other. On the way train stops for 60 minutes at a station.
What is the speed of the train?
A) 110 km/h
B) 115 km/h
C) 108 km/h
D) 112 km/h
3) In first lot, Rohan purchased 11 articles for ₹12 and sold 12 articles of the
same type for ₹11. In second lot, Shyam purchased 16 articles for ₹15 and
sold 15 articles of the same type for ₹16. What is the profit/loss percentage
for Rohan and Shyam respectively?
A) 16.27% loss, 13.77% profit
B) 13.77% loss, 15.97% profit
C) 15.97% profit, 13.77% profit
D) 15.97% loss, 13.77% profit
4) If a number 867Y8 is exactly divisible by 6, then what can be the value of
Y?
A) 2
B) 1
C) 3
D) 5
5) For a collection of 10 items, ∑x = 155, then Arithmetic mean is:
A) 10
B) 10.5
C) 15
D) 15.5

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6) Which shows the correct ascending order of given value?
𝟑
A) √𝟓, √𝟏𝟏, 𝟐(𝟔 √𝟑)
𝟑
B) √𝟓, 𝟐(𝟔 √𝟑), √𝟏𝟏
𝟑
C) √𝟏𝟏, √𝟓, 𝟐(𝟔 √𝟑)
𝟑
D) 𝟐(𝟔 √𝟑), √𝟏𝟏, √𝟓
7) A is 30% of B, C is 45% of B. B is how much percentage less than (A+B+C)?
A) 28.56%
B) 42.86%
C) 57.14%
D) 35.56%
𝟐+𝟖−𝟏𝟕×𝟓+𝟏𝟖÷𝟑×𝟑𝟔 𝟕𝟖÷𝟑𝟗+(𝟓𝟕÷𝟏𝟗)×𝟐−𝟓(𝟐𝟖÷𝟏𝟒+𝟓)
8) If 𝑨 = 𝒂𝒏𝒅 𝑩 = , then what is the
𝟐×𝟐÷𝟏 𝟓
value of A+B?
A) 23.2
B) 22.8
C) 24.6
D) 23
9) The area of a rhombus is 252 cm². If the length of one of its diagonals is
14cm, then what is the length of the other diagonal?
A) 18cm
B) 12cm
C) 36cm
D) 24cm
10) The radius of the base of a cylinder is 55 cm and its height is 15 cm.
14 times of the curved surface area of the cylinder is equal to the total
surface area of a cube. What is the side of a cube?
A) 110 cm
B) 120 cm
C) 150 cm
D) 140 cm
11) The diameter of a bicycle wheel is 4.2 cm. A cyclist takes 90 minutes
to reach a destination at a speed of 23.1 km/h. How many revolutions will
the wheel make during the journey?
A) 226500
B) 172500
C) 316400
D) 262500

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12) What is the probability that a leap year has 52 Monday?
A) 2/7
B) 4/7
C) 5/7
D) 6/7
13) If the arithmetic mean of 7, 8, x, 11, 14 is x, then x=?
A) 9
B) 9.5
C) 10
D) 10.5
14) The maximum volume of a cone that can be curved out of a solid
hemisphere of radius r is
A) 3πr²
𝝅𝒓𝟑
B) 𝟑
𝝅𝒓𝟐
C) 𝟑
D) 3πr³
15) If a perimeter of a circle is equal to that of a square, then the ratio
of their areas is:
A) 13:22
B) 14:11
C) 22:13
D) 11:14
16) Rajesh covers a distance in 8 hours and Monu covers the same
distance in 4 hours. If the speed of Monu is 10km/h more than the speed
of Rajesh then which of the following statement(s) is are correct?
Statement I. Monu’s speed is 30km/h
Statement II. The distance covered by Rajesh is 80 km.
A) Neither I nor II
B) Only I
C) Only II
D) Both I and II

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17) The area of a circle is 1848 cm². The circumference of this circle is
equal to the length of the longest rod that can be placed in a cube. What is
the total surface area of this cube?
A) 64256 cm²
B) 54548 cm²
C) 52422 cm²
D) 46464 cm²
18) Selling price of an article A is 25% more than its cost price. Selling
price of an article B is 60% more than selling price of A and the loss
incurred on selling article B at this price is 33.33%. Cost price of an article
B is how much percent more/less than the cost price of an article A?
A) 200% more
B) 300% more
C) 200% less
D) 300% less
19) It is found that on walking x meters towards a chimney in a
horizontal line through its base, the elevation of its top changes from 30°
to 60°. The height of chimney is:
A) 𝟑√𝟐𝒙
B) 𝟐√𝟑𝒙
√𝟑
C) 𝟐
𝒙
𝟐
D) 𝒙
√𝟑
𝒄𝒐𝒕𝑨 𝒕𝒂𝒏𝑨
20) + =
𝒄𝒐𝒕𝑨−𝒄𝒐𝒕𝟑𝑨 𝒕𝒂𝒏𝑨−𝒕𝒂𝒏𝟑𝑨
A) 0
B) 1
C) -1
D) 2
21) At the one end A of a diameter AB of a circle of radius 5 cm, tangent
XAY is drawn to the circle. The length of the chord CD parallel to tangent
XY at a distance 8 cm from A is:
A) 4 cm
B) 5 cm
C) 6 cm
D) 8 cm

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 𝑨𝑩 𝑩𝑪
22) If in ∆ABC and ∆DEF, = , then ∆ABC~∆DEF when
𝑫𝑬 𝑭𝑫
A) ∠A=∠F
B) ∠A=∠D
C) ∠B=∠D
D) ∠B=∠E
23) If (-2, 1) is the centroid of the triangle having its vertex at (x, 2), (10,
-2) and (-8, y) then x and y satisfy the relation
A) 𝟑𝒙 + 𝟖𝒚 = 𝟎
B) 𝟑𝒙 − 𝟖𝒚 = 𝟎
C) 𝟖𝒙 + 𝟑𝒚 = 𝟎
D) 𝟖𝒙 = 𝟑𝒚
24) If Sn denote the sum of first n terms of an A.P. with first term ‘a’ and
common difference ‘d’ such that Sx/Skx is independent of x , then
A) d=a
B) d=2a
C) a=2d
D) d=-a
25) If the roots of the equation 𝟒𝒙𝟐 − 𝟐𝒙 + (𝒂 − 𝟒) = 𝟎, be the reciprocal
of the other, then a= ?
A) 8
B) -8
C) 4
D) -4

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26) The pie chart given below shows the production of coffee by 8
different states. The total production of coffee by all the states is 20000.
The production of coffee by a particular state is shown as a percent of the
total production of coffee by all these 8 states.

J1 = The average production of coffee by states A,D,F and G

J2 = The sum of production of coffee by the states B,C and H
What is the value of (J2-J1)?
A) 7300
B) 7200
C) 7500
D) 7400
27) What is the digit at the unit place of 5798×3525×3396?
A) 7
B) 6
C) 5
D) 4
28) For what value of k, do the equations 𝟑𝒙 − 𝒚 + 𝟖 = 𝟎 𝒂𝒏𝒅 𝟔𝒙 + 𝒌𝒚 +
𝟏𝟔 = 𝟎 represent coincident lines?
A) -½
B) ½
C) 2
D) -2

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29) If the zeros of the quadratic polynomial 𝒙𝟐 + (𝒂 + 𝟏)𝒙 + 𝒃 =
𝟎 𝒂𝒓𝒆 𝟐 𝒂𝒏𝒅 − 𝟑 𝒕𝒉𝒆𝒏,
A) a=-7, b=-1
B) a=5, b=-1
C) a=2, b=-6
D) a=0, b=-6
30) If two positive integers A and b are written as 𝒂 = 𝒙𝟑 𝒚𝟐 𝒂𝒏𝒅 𝒃 =
𝒙𝒚𝟑 ; 𝒙 𝒂𝒏𝒅 𝒚 𝒂𝒓𝒆 𝒑𝒓𝒊𝒎𝒆 𝒏𝒖𝒎𝒃𝒆𝒓𝒔, then HCF(a, b) is
A) 𝒙𝒚
B) 𝒙𝒚𝟐
C) 𝒙𝟑 𝒚𝟑
D) 𝒙𝟐 𝒚𝟐
31) A bag contains 50 coins and each coin is marked from 51 to 100. One
coin is picked at random. The probability that the number on the coin is
not a prime number, is
A) ⅕
B) ⅗
C) ⅖
D) ⅘
32) P, Q, R three set of values of x:
P: 2, 3, 7, 1, 3, 2, 3
Q: 7, 5, 9, 12, 5, 3, 8
R: 4, 4, 11, 7, 2, 3, 4
Which one of the following statement is correct?
A) Mean of P = Mode of R
B) Mean of R = Median of Q
C) Median of Q = Mode of P
D) Mean, Median and Mode of P are equal.
33) The difference between the upper and lower class limits is called
A) Mid-points
B) Class size
C) Frequency
D) Mean

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34) If a sphere is inscribed in a cube then the ratio of the volume of the
sphere to volume of the cube is
A) Π:2
B) Π:3
C) Π:4
D) Π:6
35) 23.434343… when expressed in the form p/q, (p, q are integers and
q≠0), is
A) 2320/99
B) 2343/100
C) 2343/999
D) 2330/199
𝟏
𝟐𝒎+𝒏 𝟑𝒑 𝒂𝟐𝒎+𝒏−𝒑
36) If 𝟐𝒏−𝒎 = 𝟏𝟔, 𝟑𝒏 = 𝟖𝟏 𝒂𝒏𝒅 𝒂 = 𝟐𝟏𝟎 , 𝒕𝒉𝒆𝒏 (𝒂𝒎−𝟐𝒏+𝟐𝒑 )−𝟏 =
A) 2
B) ¼
C) 9
D) ⅛
𝟏 𝟏
37) If 𝒙 = 𝟕 + 𝟒√𝟑 𝒂𝒏𝒅 𝒙𝒚 = 𝟏 𝒕𝒉𝒆𝒏 𝒙𝟐 + 𝒚𝟐 =
A) 97
B) 134
C) 194
D) 1/49
𝒂 𝒃
38) If 𝒃 + 𝒂 = −𝟏 𝒕𝒉𝒆𝒏 𝒂𝟑 − 𝒃𝟑 =
A) 1
B) -1
C) ½
D) 0
39) The factors of 𝒂𝟐 − 𝟏 − 𝟐𝒙 − 𝒙𝟐 𝒂𝒓𝒆
A) (𝒂 − 𝒙 + 𝟏)(𝒂 − 𝒙 − 𝟏)
B) (𝒂 + 𝒙 − 𝟏)(𝒂 − 𝒙 + 𝟏)
C) (𝒂 + 𝒙 + 𝟏)(𝒂 − 𝒙 − 𝟏)
D) None of the above

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40) If 𝒙𝟐 − 𝟏 𝒊𝒔 𝒂 𝒇𝒂𝒄𝒕𝒐𝒓 𝒐𝒇 𝒂𝒙𝟒 + 𝒃𝒙𝟑 + 𝒄𝒙𝟐 + 𝒅𝒙 + 𝒆, 𝒕𝒉𝒆𝒏
A) 𝒂 + 𝒄 + 𝒆 = 𝒃 + 𝒅
B) 𝒂 + 𝒃 + 𝒆 = 𝒄 + 𝒅
C) 𝒂 + 𝒃 + 𝒄 = 𝒅 + 𝒆
D) 𝒃 + 𝒄 + 𝒅 = 𝒂 + 𝒆
41) In the given figure, if AB||CD then, x=

A) 100°
B) 105°
C) 110°
D) 115°
42) The bisects of exterior angle at B and C of ∆ABC meet at O. If ∠A=x°
then ∠BOC=
𝒙°
A) 𝟗𝟎° + 𝟐
𝒙°
B) 𝟗𝟎° −
𝟐
𝒙°
C) 𝟏𝟖𝟎° − 𝟐
𝒙°
D) 𝟏𝟖𝟎° + 𝟐
43) In triangles ABC and PQR three equality relations between some
parts are as follows:
AB=QP, ∠B=∠P and BC=PR
State which of the following congruence conditions applies:
A) SAS
B) ASA
C) SSS
D) RHS
44) The abscissa of a point is positive in the
A) 1st and 2nd quadrant
B) 2nd and 3rd quadrant
C) 3rd and 4th quadrant
D) 4th and 1st quadrant
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45) The side of a triangle are 7 cm, 9 cm and 14 cm. Its area is
A) 12√5 cm²
B) 12√3 cm²
C) 24√5 cm²
D) 63 cm²
46) A sold a table to B at a profit of 40%, B sold it to D at a profit of 60%.
W sold a chair to X at the loss of 20%, X sold it to P at a loss of 30% and
finally P sold it to G at a loss of 50%. Price at which D bought the table
from B and the price at which P bought the chair from X is same. If the
price at which W bought the chair is ₹600, then at what price D bought
table?
A) ₹336
B) ₹396
C) ₹219
D) ₹348
47) A cone is cut into two parts by a plan parallel to its base. Volume of
the upper part which is a cone is 245 cm³. If the height of lower part is
double the height of upper part, then what is the volume of the lower
part?
A) 1775 cm³
B) 4655 cm³
C) 6370 cm³
D) 980 cm³
48) 90 trees are planted in a straight row in such a way that the
distance between any two consecutive trees is same. A bus travelling at
the speed of 54 km/h takes 30 seconds to reach the seventh tree from the
first tree. What is the distance between the 11th tree and 46th tree?
A) 2250 meters
B) 2625 meters
C) 2475 meters
D) 2525 meters
49) ABCD is a trapezium in which AB||CD. If ar(∆ABD) = 24 cm² and
AB= 8 cm then the height of ∆ABC is
A) 3 cm
B) 4 cm
C) 6 cm
D) 8 cm
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50) In given figure, chords AD and BC intersect each other at right
angles at a point P. If ∠DAB=35°, then ∠ADC is

A) 35°
B) 45°
C) 55°
D) 65°
51) The length of longest rod that can be fitted in a cubical vessel of
edge 10 cm long is
A) 10 cm
B) 10√2 cm
C) 10√3 cm
D) 20 cm
52) In a cylinder, if radius is doubled and height is halved, curved
surface area will be
A) Halved
B) Doubled
C) Same
D) Four Times
𝒂 𝒂𝒔𝒊𝒏𝑨+𝒃𝒄𝒐𝒔𝑨
53) If 𝒕𝒂𝒏𝑨 = 𝒃 , 𝒕𝒉𝒆𝒏 𝒂𝒔𝒊𝒏𝑨−𝒃𝒄𝒐𝒔𝑨 =
𝒂𝟐 +𝒃𝟐
A) 𝒂𝟐 −𝒃𝟐
𝒂𝟐 −𝒃𝟐
B)
𝒂𝟐 +𝒃𝟐
𝒂+𝒃
C) 𝒂−𝒃
𝒂−𝒃
D) 𝒂+𝒃
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54) If 𝒙 = 𝒓𝒔𝒊𝒏𝑨𝒄𝒐𝒔𝑩, 𝒚 = 𝒓𝒔𝒊𝒏𝑨𝒔𝒊𝒏𝑩 𝒂𝒏𝒅 𝒛 = 𝒓𝒄𝒐𝒔𝑨, 𝒕𝒉𝒆𝒏
A) 𝒙𝟐 + 𝒚𝟐 + 𝒛𝟐 = 𝒓𝟐
B) 𝒙𝟐 + 𝒚𝟐 − 𝒛𝟐 = 𝒓𝟐
C) 𝒙𝟐 − 𝒚𝟐 + 𝒛𝟐 = 𝒓𝟐
D) 𝒛𝟐 + 𝒚𝟐 − 𝒛𝟐 = 𝒓𝟐
55) The height of a vertical pole is √3 times the length of its shadow on
the ground then the angle of elevation of the sun at that time is
A) 30°
B) 60°
C) 45°
D) 75°
56) The area of circle whose area and circumference are numerically
equal, is
A) 2π sq. units
B) 4π sq. units
C) 6π sq. units
D) 8π sq. units
57) A number is chosen at random from the numbers
−𝟑, −𝟐, −𝟏, 𝟎, 𝟏, 𝟐, 𝟑 , the probability that |x|<2 is
A) 5/7
B) 2/7
C) 3/7
D) 1/7
58) If the mean of first n natural numbers is 15, then value of n is
A) 15
B) 30
C) 14
D) 29
59) ∆ABC~∆DEF. If BC=3 cm and EF=4 cm and ar(∆ABC)=54 cm², then
ar(∆DEF) is
A) 72 cm²
B) 96 cm²
C) 48 cm²
D) 100 cm²

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 60) Given that one zeros of the cubical polynomial 𝒂𝒙𝟑 + 𝒃𝒙𝟐 + 𝒄𝒙 +
𝒅 is zero, the product of the other two zeros is
𝒄
A) −
𝒂
𝒄
B)
𝒂
C) 𝟎
𝒃
D) −
𝒂

ANSWER KEY:

1.A 2.D 3.D 4.B 5.D

6.C 7.B 8.B 9.C 10.A

11.D 12.C 13.C 14.B 15.B

16.C 17.D 18.A 19.C 20.B

21.D 22.C 23.A 24.B 25.A

26.A 27.C 28.D 29.D 30.B

31.D 32.D 33.B 34.D 35.A

36.A 37.C 38.D 39.C 40.A

41.A 42.B 43.A 44.D 45.A

46.A 47.C 48.B 49.C 50.C

51.C 52.C 53.A 54.A 55.B

56.B 57.C 58.D 59.B 60.B

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