Bihar Secondary Teacher 2023: TRE 2.0, Class 9 to 10, Mathematics
Text of page 1
23/MAV/M–2023–09 Booklet Series
Serial No.
Candidate’s Roll Number
Question Booklet
A
LANGUAGE, GENERAL STUDIES AND MATHEMATICS
Time Allowed : 2:30 Hours Maximum Marks : 150
Read the following instructions carefully before you begin to answer the questions.
IMPORTANT INSTRUCTIONS
1. This Question Booklet is divided into three Parts—Part–I, Part–II and Part–III. Part–I contains
questions of Language (Qualifying), Part–II contains questions of General Studies and Part–III
contains questions of Mathematics.
2. Part–I consists of Question Nos. 1 to 30, Part–II consists of Question Nos. 31 to 70 and Part–III
consists of Question Nos. 71 to 150. The questions and their responses are printed in English
and Hindi versions both of Part–II and Part–III.
3. All questions carry equal marks.
4. Immediately after commencement of the examination, you should check up your Question
Booklet and ensure that the Question Booklet Series is printed on the top right-hand corner
of the Booklet. Please check that the Booklet contains 48 printed pages including two pages
(Page Nos. 46 and 47) for Rough Work and no page or question is missing or unprinted or
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5. You must write your Roll Number in the space provided on the top of this page. Do not write
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PART—I
( LANGUAGE )
Directions (Q. Nos. 1 and 2) : Fill in 5. Today is Sunday. The day before
the blanks with suitable articles like yesterday was
‘a’, ‘an’ and ‘the’ : (A) Tuesday
1. In this school, all _____ students (B) Friday
are given free education. (C) Thursday
(A) an
(D) More than one of the above
(B) a
(E) None of the above
(C) the
(D) More than one of the above
6. November comes after the
(E) None of the above
month of
2. I have a friend in Mumbai who (A) September
is _____ actress. (B) December
(A) a
(C) January
(B) an
(D) More than one of the above
(C) the
(D) More than one of the above (E) None of the above
(E) None of the above
7. Husband’s brother is
3. Which of the following is not
(A) cousin
a river?
(A) Bay of Bengal (B) son
(B) Godavari (C) brother-in-law
(C) Ganga (D) More than one of the above
(D) More than one of the above (E) None of the above
(E) None of the above
8. Mother’s parents are
4. Which of the following is not
a part of drawing room? (A) son-in-laws
(A) Washing machine (B) maternal grandparents
(B) Chimney
(C) paternal grandparents
(C) Sofa set
(D) More than one of the above
(D) More than one of the above
(E) None of the above (E) None of the above
23/MAV/M–2023–09/S3 (S)/116-A 2
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PART—II
( GENERAL STUDIES )
31. The cost of 5 bats and 18 balls is 34. The lengths of two sides of a
R 6,500 and the cost of 2 bats triangle are 8 cm and 9 cm, and
and 20 balls is R 4,200. What its area is 12 5 cm 2 . What is
are the costs of one bat and one the length of the third side?
ball respectively?
(A) R 850, R 125 (A) 5 cm
(B) R 630, R 115
(C) R 780, R 150 (B) 9 cm
(D) More than one of the above
(C) 7 cm
(E) None of the above
32. A shopkeeper purchases an item (D) More than one of the above
at R 615 and sells it at R 820.
What is his percentage profit? (E) None of the above
(A) 25%
(B) 33·33%
(C) 35·50% 35. There are 50 numbers. Each
number is subtracted from 53,
(D) More than one of the above
and the mean of the numbers so
(E) None of the above obtained is found to be -3 × 5.
The mean of the given numbers
33. A hacker finds that the ATM PIN is
of a person has first two digits
ranging from 3 to 8, and the
(A) 56·5
fourth digit is either 0 or 9. How
many attempts must the hacker
try in order to decode the PIN? (B) 53·5
(A) 48
(C) 49·5
(B) 24
(C) 720
(D) More than one of the above
(D) More than one of the above
(E) None of the above (E) None of the above
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36. The ratio of the ages of two 39. The Sun observation point of
brothers is 4 : 3. If the elder Aditya-L1 satellite is
brother is 6 years older than the
younger one, then their ages (in (A) L1
years) are
(B) L2
(A) 24, 18
(B) 36, 30 (C) L3
(C) 15, 9 (D) More than one of the above
(D) More than one of the above
(E) None of the above
(E) None of the above
37. The value of 40. Ginger is an underground stem
and not a root because
æ 1ö æ 1ö æ 1ö æ 1ö
ç1 - ÷ ç1 - ÷ ç1 - ÷ L ç1 - ÷
è 2ø è 3ø è 4ø è nø (A) it stores food material
is (B) it has nodes and inter-
n -1 nodes
(A)
n
(C) it lacks chlorophyll
1
(B)
n (D) More than one of the above
1
(C) (E) None of the above
n +1
(D) More than one of the above
41. The focal length of a convex lens
(E) None of the above
is f L = 10 cm. On immersing in
water, it will act as a
38. The quadratic equation with
roots -1 and 4 is (A) convex lens of f L = 10 cm
(A) x 2 - 3x - 4 = 0
(B) concave lens of f L = 10 cm
2
(B) x + 3x + 3 = 0
(C) convex lens of f L > 10 cm
(C) x 2 - 4x + 1 = 0
(D) More than one of the above
(D) More than one of the above
(E) None of the above (E) None of the above
23/MAV/M–2023–09/S3 (S)/116-A 8
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42. Though water is transparent to 44. The speed of an electron in the
visible light, it is not possible to orbit of the hydrogen atom in
see distant objects in fog which the ground state is
consists of fine drops of water.
This is so because (A) c
(B) c /2
(A) fine drops of water are
opaque to visible light (C) c /137
(D) More than one of the above
(B) most of the light is scattered
to create apparent opacity (E) None of the above
(C) light rays suffer total 45. A blackbody radiates energy at
internal reflection and so the rate of E watt per metre 2 at
unable to reach observer’s a high temperature T K. When
eyes the temperature is reduced to
T /3 K, the radiant energy
(D) More than one of the above (in watt per metre 2 ) will be
(A) E /16
(E) None of the above
(B) E /27
(C) E /81
43. Monochromatic light enters from
one medium to the other. Which (D) More than one of the above
one of the following properties
(E) None of the above
does not change?
(A) Frequency 46. The acid which can destroy the
colour of acidic KMnO 4 is
(B) Amplitude (A) CH 3COOH
(B) C 6H 8O 7
(C) Velocity
(C) CH 3CH 2COOH
(D) More than one of the above
(D) More than one of the above
(E) None of the above (E) None of the above
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47. Who was the writer of ‘Banglar 50. Azali Assoumani, who attended
Mati, Banglar Jal’, which was the G20 Summit in New Delhi as
originally a protest song against the current Chairperson of the
the Partition of Bengal in 1905 African Union which has
by Lord Curzon, and for which become the newest member of
the West Bengal Assembly G20, is the President of which
passed a resolution as the new country in the African Union?
State Anthem recently?
(A) Kazi Nazrul Islam (A) Republic of the Congo
(B) Rabindranath Tagore
(C) Sukanta Bhattacharya (B) Gabon
(D) More than one of the above
(E) None of the above (C) Comoros
48. Who is the architect of the new (D) More than one of the above
Parliament of India building
inaugurated recently?
(E) None of the above
(A) Bimal Patel
(B) Rahul Mehrotra
(C) Yogesh Kapoor
51. When is the ‘Human Rights Day’
(D) More than one of the above
celebrated annually?
(E) None of the above
(A) 10th November
49. Which one of the following
Indian films was screened at
the 76th Cannes Film Festival (B) 10th December
in May 2023?
(A) Anurag Kashyap’s Kennedy
(C) 24th October
(B) Kanu Behl’s Agra
(C) Neeraj Pandey’s Khakee (D) More than one of the above
(D) More than one of the above
(E) None of the above (E) None of the above
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52. Who was the founder of ‘Indian 55. In which of the following states
National Army (INA)’? is black soil found?
(A) Subhash Chandra Bose
(A) Karnataka
(B) Mohan Singh
(C) Lala Lajpat Rai (B) Gujarat
(D) More than one of the above
(C) Uttarakhand
(E) None of the above
(D) More than one of the above
53. ‘ Tana Bhagat Movement’ was
related to
(E) None of the above
(A) Dalit Movement
(B) Tribal Movement
56. How many types of species of
(C) Peasant Movement flora and fauna are there in
India?
(D) More than one of the above
(E) None of the above (A) 81000 species of fauna and
47000 species of flora
54. In which State is ‘Raksha
Bandhan’ celebrated as ‘ Tree (B) 70000 species of fauna and
Safety Day’? 50000 species of flora
(A) Madhya Pradesh
(C) 50000 species of fauna and
(B) Uttar Pradesh 40000 species of flora
(C) Bihar
(D) More than one of the above
(D) More than one of the above
(E) None of the above (E) None of the above
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57. Minerals are deposited and 60. Stalactite and stalagmite
accumulated in the strata of structures are formed by
which of the following rocks?
(A) wind action
(A) Sedimentary rocks
(B) underground water
(B) Metamorphic rocks
(C) snow action
(C) Igneous rocks
(D) More than one of the above
(D) More than one of the above
(E) None of the above
(E) None of the above
61. April 22 is celebrated as the
58. Which one of the following is a
leguminous crop? (A) World Earth Day
(A) Pulse (B) World Health Day
(B) Jowar (C) World Ozone Day
(C) Millet
(D) More than one of the above
(D) More than one of the above
(E) None of the above
(E) None of the above
62. Topographical map of India is
59. Which two of the following prepared by which organization?
extreme locations are connected
(A) The Geological Survey of
by the East-West Corridor?
India
(A) Mumbai and Nagpur
(B) The Survey of India
(B) Mumbai and Kolkata
(C) The Zoological Survey of
(C) Silchar and Porbandar India
(D) More than one of the above (D) More than one of the above
(E) None of the above (E) None of the above
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63. Who first described the Revolt of 67. Who was the President of the
1857 as the ‘First Indian War of Indian National Congress at the
Independence’? Gaya Session of 1922?
(A) V. D. Savarkar (A) Chittaranjan Das
(B) Bal Gangadhar Tilak (B) Hakim Ajmal Khan
(C) R. C. Majumdar (C) Mahatma Gandhi
(D) More than one of the above (D) More than one of the above
(E) None of the above
(E) None of the above
68. Who led the peasants of Bihar
64. Which of the following events
during the Non-Cooperation
happened first?
Movement?
(A) Santhal Rebellion (A) Raj Kumar Shukla
(B) Rebellion of Birsa Munda (B) Swami Vidyanand
(C) Tana Bhagat Movement (C) Rajendra Prasad
(D) More than one of the above (D) More than one of the above
(E) None of the above (E) None of the above
65. Which revolt is mentioned in 69. Who founded Hindu College at
Bankim Chandra Chatterjee’s Calcutta in 1817?
novel, Anandamath? (A) Henry Vivian Derozio
(A) Sannyasi (B) David Hare
(B) Pagalpanthi (C) Jonathan Duncan
(C) Indigo (D) More than one of the above
(E) None of the above
(D) More than one of the above
(E) None of the above 70. Who among the following said
that “Congress is to tottering to
66. When were ‘Swadeshi’ and its fall and one of my great
‘Boycott’ first adopted as forms ambitions while in India is to
of struggle in India? assist it to a peaceful demise”?
(A) Partition of Bengal (A) Dufferin
(B) Home Rule Movement (B) Minto
(C) Non-Cooperation Movement (C) Curzon
(D) More than one of the above (D) More than one of the above
(E) None of the above (E) None of the above
23/MAV/M–2023–09/S3 (S)/116-A 18
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PART—III
( MATHEMATICS )
2x - 3 x -3
æaö æb ö 74. The LCM of x 2 + 5x + 6 and
71. If ç ÷ =ç ÷ , then the
èb ø èaø x 2 + 4x + 4 is
value of x is (A) x + 2
(A) 2 (B) (x + 2)(x + 3)
(C) (x + 2)(x + 2)(x + 3)
(B) 4
(D) More than one of the above
(C) 1 (E) None of the above
(D) More than one of the above
75. The sum of cubes of first n
natural numbers is
(E) None of the above
n (n + 1)
(A)
1 2
72. If x - = 2, then the value of
x n (n + 1)(2n + 1)
1 (B)
x4+ is 6
x4
2
(A) 38 æ n (n + 1) ö
(C) ç ÷
è 2 ø
(B) 36
(D) More than one of the above
(C) 16
(D) More than one of the above (E) None of the above
(E) None of the above
76. If the length of the shadow of a
pole on a level ground is twice
73. The value of (27)1/3 + (243)1/5 is the length of the pole, then the
angle of elevation of the Sun is
(A) 6
(A) 30º
(B) 1
(B) 45º
(C) 2 (C) 60º
(D) More than one of the above (D) More than one of the above
(E) None of the above (E) None of the above
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77. The value of sin 3000º is 80. The probability of getting at
least a head by throwing three
3 unbiased coins is
(A)
2
1
(A)
1 8
(B)
2
7
(B)
8
3
(C) -
2
3
(C)
8
(D) More than one of the above
(D) More than one of the above
(E) None of the above
(E) None of the above
78. The empirical relationship
among mean, mode and 81. If A and B are any two events,
median is then P (A È B ) is
(A) mode = 3 median – 2 mean (A) P (A ) + P (B )
(B) median = 3 mode – 2 mean (B) P (A ) + P (B ) - P (A Ç B )
(C) mean = 3 median – 2 mode (C) P (A ) P (B )
(D) More than one of the above (D) More than one of the above
(E) None of the above (E) None of the above
79. If A is an event of getting 13 by 82. The circumference of the base of
throwing two unbiased six-faced a cylinder is 44 cm and the
dice, then A is called height is 22 cm. Its volume is
(A) a certain event (A) 3388 cm 3
(B) a null event (B) 968 cm 3
(C) an impossible event (C) 3368 cm 3
(D) More than one of the above (D) More than one of the above
(E) None of the above (E) None of the above
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83. The whole surface area of a 86. The ratio of the sides of a
24 cm long, 14 cm broad and triangle is 3 : 4 : 5. If the
7·5 cm high cuboid is circumference of the triangle is
144 cm, then its area is
(A) 2520 cm 2
(A) 684 cm 2
(B) 1260 cm 2
(B) 764 cm 2
2
(C) 1242 cm
(C) 864 cm 2
(D) More than one of the above
(D) More than one of the above
(E) None of the above
(E) None of the above
84. The value of
1 87. The areas of a circle and a
5¸ square are same. The ratio of the
1
6¸ side of the square and the
1
10 ¸ radius of the circle is
18
(A) 1 : p
is
(B) p :1
(A) 5400
(C) 1 : p
(B) 5200
(D) More than one of the above
(C) 4800
(E) None of the above
(D) More than one of the above
(E) None of the above 88. An equilateral triangle is made
by taking a copper wire. The
85. The internal circumference of a area of the triangle is
circular park is 440 m. A track 2
121 3 cm . If a circle is made
of breadth 14 m is constructed by taking the same wire, then its
outside the park. The diameter area is
of the outer circle is
(A) 364·5 cm 2
(A) 168 m
(B) 693·5 cm 2
(B) 169 m
(C) 144 m (C) 346·5 cm 2
(D) More than one of the above (D) More than one of the above
(E) None of the above (E) None of the above
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89. If the length of a diagonal of a 92. If the purchasing price of 12
rhombus is 80% of its other oranges is same as the selling
diagonal, then the area of the price of 9, then the percentage of
rhombus is x times the square profit is
of the larger diagonal, where x is
(A) 25
2
(A)
5 1
(B) 33
3
4
(B)
5 (C) 20
1
(C) (D) More than one of the above
2
(D) More than one of the above (E) None of the above
(E) None of the above
93. The areas of two similar
90. The area of the circle that can be triangles are 81 cm 2 and
2
inscribed in a rectangle of length 49 cm respectively. The ratio of
10 cm and width 8 cm is their corresponding heights is
(A) 16p cm 2 (A) 9 : 7
(B) 7 : 9
(B) 20p cm 2
(C) 48 : 81
(C) 25p cm 2
(D) More than one of the above
(D) More than one of the above (E) None of the above
(E) None of the above
94. The bases of a hemisphere and
91. If 8 metallic balls of diameter a cone are same. If their heights
4 cm each are melted to form a are also equal, then the ratio of
big ball, then the radius of the their curved surfaces is
big ball is (A) 1 : 2
(A) 2 cm
(B) 2 :1
(B) 4 cm
(C) 8 cm (C) 1 : 2
(D) More than one of the above (D) More than one of the above
(E) None of the above (E) None of the above
23/MAV/M–2023–09/S3 (S)/116-A 26
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95. The diameters of the wheels 98. A student instead of multiplying
of a cycle are 66 cm and 72 cm. a number by 0·72 multiplied it
If the bigger wheel rotates by 7·2. In this multiplication,
1188 times to cover a fixed he got 2592 more than
distance, then the number of its correct value. The initial
times the smaller one will rotate number is
to cover up the same distance is
(A) 400
(A) 1356
(B) 420
(B) 1426
(C) 500
(C) 1296
(D) More than one of the above
(D) More than one of the above
(E) None of the above
(E) None of the above
99. The ratio of incomes of A and B
96. The difference of prices by is 2 : 3 and the ratio of their
selling a substance at profits 6% expenditures is 1 : 2. If the
and 4% is R 3. Its purchase savings of each of them is
price is R 24,000, then the income of
(A) R 100 A is
(B) R 150 (A) R 24,000
(C) R 175 (B) R 48,000
(D) More than one of the above (C) R 72,000
(E) None of the above (D) More than one of the above
(E) None of the above
97. In a mixture of 200 litres, water
is 15% and rest milk. The
amount of milk to be added to 100. In a class, the boys are 12%
the mixture so that the amount more than the girls over the
of milk in the mixture will be whole. The ratio of boys to the
87·5% is girls is
(A) 30 litres (A) 11 :14
(B) 35 litres (B) 14 :11
(C) 40 litres (C) 28 : 25
(D) More than one of the above (D) More than one of the above
(E) None of the above (E) None of the above
23/MAV/M–2023–09/S3 (S)/116-A 28
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101. The ratio of simple interests 104. Pipe A can fill a cistern in
earned by a certain amount at 36 minutes and pipe B in
the same rate of interest for 48 minutes. If both the pipes are
6 years and that for 9 years is opened together and the cistern
is full in 24 minutes, then pipe
(A) 3 : 2 B is closed after
(B) 2 : 3 (A) 16 minutes
(C) 1 : 2 (B) 10 minutes
(D) More than one of the above (C) 12 minutes
(D) More than one of the above
(E) None of the above
(E) None of the above
102. The number of years required
105. When a plot is sold for R 18,700,
for a sum of R 12,500 to become
the owner loses 15%. In order to
R 17,500 at the rate of 10% per
gain 15%, the plot must be sold
annum is
for
(A) 4 years (A) R 25,800
(B) 1 year (B) R 22,500
(C) 2 years (C) R 25,300
(D) More than one of the above (D) More than one of the above
(E) None of the above
(E) None of the above
106. If A and B can complete a work
103. The compound interest on a in 8 days, B and C in 12 days,
sum of R 25,000 after 3 years C and A in 24 days, they can
at the rate of 12% per annum is complete the work working
together in
(A) R 10,123·20
(A) 6 days
(B) R 9,720
(B) 8 days
(C) R 9,000·30
(C) 9 days
(D) More than one of the above (D) More than one of the above
(E) None of the above (E) None of the above
23/MAV/M–2023–09/S3 (S)/116-A 30
Text of page 32
107. A quantity X is 25% more than 110. 1100 boys and 700 girls are
Y . The percent that Y is less examined in a test. 42% of the
than X is boys and 30% of the girls pass.
The percentage of total failed is
(A) 20%
2
(B) 25% (A) 62
3
(C) 15%
(B) 58
(D) More than one of the above
(C) 55
(E) None of the above
(D) More than one of the above
108. Three pipes A, B and C can fill a (E) None of the above
tank in 6 hours. After working
at it together for 2 hours, C is
111. The area of a rectangle is
closed, and A and B can fill the
460 square metres. If the length
remaining part in 7 hours. C can
is 15% more than the breadth,
alone fill the tank in
then what is the breadth of the
(A) 8 hours rectangle?
(B) 10 hours (A) 20 metres
(C) 14 hours (B) 15 metres
(C) 34·5 metres
(D) More than one of the above
(D) More than one of the above
(E) None of the above
(E) None of the above
109. A batsman scores 120 runs
112. The ratio of the outer and the
which include 3 boundaries and
inner perimeters of a circular
8 sixes. The percentage of his
path is 23 : 22. If the path is
total score by running between
5 metres wide, then the
the wickets is
diameter of the inner circle is
(A) 40
(A) 55 metres
(B) 50 (B) 110 metres
(C) 60 (C) 220 metres
(D) More than one of the above (D) More than one of the above
(E) None of the above (E) None of the above
23/MAV/M–2023–09/S3 (S)/116-A 32
Text of page 34
113. The radius of the circumcircle 116. Which of the following numbers
of an equilateral triangle of side has a non-terminating repeating
12 cm is decimal expansion?
6
4 2 (A)
(A) cm 15
3
21
(B)
(B) 4 2 cm 280
117
4 3 (C)
(C) cm 62 ´ 5 3
3
(D) More than one of the above
(D) More than one of the above
(E) None of the above
(E) None of the above
117. If f (x ) = ax 2 + bx + c has no real
zeroes and a + b + c < 0, then
114. The height of a right circular
(A) c = 0
cylinder is 14 cm and its curved
surface is 704 sq. cm. Its volume (B) c > 0
is (C) c < 0
(A) 1408 cm 3 (D) More than one of the above
(E) None of the above
(B) 2816 cm 3
(C) 5632 cm 3 118. If a, b, g are the zeroes of the
polynomial
(D) More than one of the above
f (x ) = x 3 - px 2 + qx - r
(E) None of the above
1 1 1
then + + is equal to
ab bg ga
115. If the surface areas of two
spheres are in the ratio of 4 : 25, r
(A)
then the ratio of their volumes is p
p
(A) 8 :125 (B)
r
(B) 4 : 25 p
(C) -
(C) 125 : 8 r
(D) More than one of the above (D) More than one of the above
(E) None of the above (E) None of the above
23/MAV/M–2023–09/S3 (S)/116-A 34
Text of page 36
119. The zeroes of the quadratic 122. The pair of linear equations
polynomial y = 0 and y = -5 has
f (x ) = x 2 + 99x + 127 (A) one solution
are (B) two solutions
(A) both positive (C) infinitely many solutions
(B) both negative
(D) More than one of the above
(C) one positive and one
negative (E) None of the above
(D) More than one of the above
(E) None of the above 123. If c and d are roots of the
equation
120. If the pair of linear equations
(x - a )(x - b ) - k = 0
(3k + 1) x + 3y - 5 = 0 and
2x - 3y + 5 = 0 then a , b are roots of the
has infinite number of solutions, equation
then the value of k is
(A) (x - c )(x - d ) + k = 0
(A) 1
(B) (x - c )(x - d ) - k = 0
(B) 0
(C) –1 (C) (x - a )(x - c ) + k = 0
(D) More than one of the above (D) More than one of the above
(E) None of the above
(E) None of the above
121. If
2 3 5 4 124. The number of real roots of the
+ = 13 and - = -2 equation
x y x y
then x + y equals (x - 1) 2 + (x - 2) 2 + (x - 3) 2 = 0
1
(A) is
6
1 (A) 1
(B) -
6
(B) 2
5
(C)
6 (C) 3
(D) More than one of the above (D) More than one of the above
(E) None of the above (E) None of the above
23/MAV/M–2023–09/S3 (S)/116-A 36
Text of page 38
125. The sum of n terms of the series 128. If the points A ( a 2, 0 ), B ( 0, b 2 )
2 + 8 + 18 + 32 + ... and C (1, 1) are collinear, then
1 1
is (A) + =1
a b
n (n + 1)
(A)
2 (B) a 2 + b 2 = 1
n (n + 1) 1 1
(B) (C) + =1
2 2
a b2
(C) 2n (n + 1)
(D) More than one of the above
(D) More than one of the above
(E) None of the above
(E) None of the above
129. DABC is such that AB = 3 cm,
126. The coordinates of the fourth
BC = 2 cm and CA = 2 × 5 cm. If
vertex of the rectangle formed by
DABC ~ DDEF and EF = 4 cm,
the points O (0, 0), A (2, 0) and
then the perimeter of DDEF is
B (0, 3) are
(A) (3, 0) (A) 7·5 cm
(B) (0, 2) (B) 15 cm
(C) (2, 3) (C) 30 cm
(D) More than one of the above (D) More than one of the above
(E) None of the above
(E) None of the above
127. If D (1, 2 ), E ( 4, - 3 ), F ( - 2, 4 ) are
midpoints of the sides BC, CA, 130. In DABC, ÐB = 90º, BD ^ AC . If
AB respectively of DABC, then AC = 9 cm and AD = 3 cm, then
the coordinates of the centroid BD is equal to
of DABC are
(A) 2 2 cm
(A) (1, 1)
(B) 2 3 cm
(B) (1, 0 )
(C) 3 2 cm
(C) (1, 2 )
(D) More than one of the above (D) More than one of the above
(E) None of the above (E) None of the above
23/MAV/M–2023–09/S3 (S)/116-A 38
Text of page 39
125. loUr 2 + 8 + 18 + 32 + ... Ho$ n 128. `{X {~ßXw A ( a 2, 0 ), B ( 0, b 2 ) Am°a
nXm| H$m `moJ h° C (1, 1) gßaoIr h¢, Vmo
n (n + 1) 1 1
(A) (A) + =1
2 a b
n (n + 1) (B) a 2 + b 2 = 1
(B)
2
1 1
(C) + =1
2
(C) 2n (n + 1) a b2
(D) Cn`w©∫$ _| go EH$ go A{YH$ (D) Cn`w©∫$ _| go EH$ go A{YH$
(E) Cn`w©∫$ _| go H$moB© Zht
(E) Cn`w©∫$ _| go H$moB© Zht
129. DABC Bg ‡H$ma h° {H$ AB = 3 go0 _r0,
126. {~›Xw O (0, 0), A (2, 0) Am°a B (0, 3) go ~Zo
BC = 2 go0 _r0 Am°a CA = 2 × 5 go0 _r0ü&
Am`V Ho$ Mm°Wo erf© Ho$ {ZX}emßH$ h¢
`{X DABC ~ DDEF Am°a EF =
(A) (3, 0) 4 go0 _r0 h°, Vmo DDEF H$m n[a_mn h°
(B) (0, 2) (A) 7·5 go0 _r0
(C) (2, 3) (B) 15 go0 _r0
(D) Cn`w©∫$ _| go EH$ go A{YH$ (C) 30 go0 _r0
(E) Cn`w©∫$ _| go H$moB© Zht (D) Cn`w©∫$ _| go EH$ go A{YH$
(E) Cn`w©∫$ _| go H$moB© Zht
127. `{X D (1, 2 ), E ( 4, - 3 ), F ( - 2, 4 )
H´$_eÖ DABC H$s ^wOmAm| BC , CA, AB 130. DABC _|, ÐB = 90º, BD ^ AC h°ü& `{X
Ho$ _‹`q~Xw h¢, Vmo DABC Ho$ Ho$›–H$ Ho$ AC = 9 go0 _r0 Am°a AD = 3 go0 _r0
{ZX}emßH$ h¢ h°ß, Vmo BD ~am~a h°
(A) (1, 1) (A) 2 2 go0 _r0
(B) (1, 0 ) (B) 2 3 go0 _r0
(C) (1, 2 ) (C) 3 2 go0 _r0
(D) Cn`w©∫$ _| go EH$ go A{YH$ (D) Cn`w©∫$ _| go EH$ go A{YH$
(E) Cn`w©∫$ _| go H$moB© Zht (E) Cn`w©∫$ _| go H$moB© Zht
23/MAV/M–2023–09/S3 (S)/116-A 39 [P.T.O.
Text of page 40
131. If in two triangles DEF and PQR, 134. PT is a tangent to the circle at
ÐD = ÐQ and ÐR = ÐE, then a point T and PAB is a secant
which of the following is not to the circle. If PA = 9 cm and
true? AB = 7 cm, then PT is equal to
DE EF (A) 12 cm
(A) = (B) 16 cm
PQ RP
(C) 9 cm
EF DF (D) More than one of the above
(B) =
PR PQ (E) None of the above
DE DF 135. From a point P which is at
(C) =
QR PQ a distance 13 cm from the
centre O of a circle of radius
(D) More than one of the above 5 cm, the pair of tangents PQ
(E) None of the above and PR to the circle is drawn.
The area of the quadrilateral
132. If PA and PB are two tangents PQOR is
to a circle with centre O such (A) 60 cm 2
that ÐAOB = 110º, then ÐAPB is (B) 65 cm 2
equal to (C) 30 cm 2
(A) 60º (D) More than one of the above
(E) None of the above
(B) 70º
136. If 0 £ A, B £ 90º such that
(C) 80º
1 1
(D) More than one of the above sin A = and cosB = , then
2 2
(E) None of the above A + B is equal to
(A) 0º
133. The length of the tangent AP , (B) 60º
from an external point A is (C) 90º
24 cm. If the distance of the (D) More than one of the above
point A from the centre O of (E) None of the above
the circle is 25 cm, then the
137. If tan 2A = cot(A + 60º), where
diameter of the circle is
2A is an acute angle, then the
(A) 15 cm value of A is
(B) 14 cm (A) 10º
(B) 20º
(C) 7 cm
(C) 60º
(D) More than one of the above (D) More than one of the above
(E) None of the above (E) None of the above
23/MAV/M–2023–09/S3 (S)/116-A 40
Text of page 42
138. If sin q + cos q = 2 cos q, q ¹ 90º, 142. The radius of a circle whose
then tanq is circumference is equal to the
(A) 2 +1 sum of the circumferences of the
two circles of diameters 36 cm
(B) 2
and 20 cm is
(C) 2 -1
(A) 56 cm
(D) More than one of the above (B) 42 cm
(E) None of the above
(C) 28 cm
139. The value of (D) More than one of the above
1 (E) None of the above
cos 2 q +
1 + cot 2 q
143. If a solid sphere with total
is surface area 48 cm 2 is bisected
(A) 0 into two hemispheres, then the
(B) 1 total surface area of any one of
(C) 2 the hemispheres is
(D) More than one of the above (A) 48 cm 2
(E) None of the above (B) 36 cm 2
140. If sin q + cos q = 2, then (C) 24 cm 2
tan q + cot q is (D) More than one of the above
(A) 1 (E) None of the above
(B) 2
144. A solid consists of a circular
(C) 3
cylinder surmounted by a right
(D) More than one of the above circular cone. The height of the
(E) None of the above cone is h. If the total volume of
the solid is 3 times the volume of
141. If
the cone, then the height of the
cos 2 20º + cos 2 70º 2 circular cylinder is
=
2 2
2 (sin 59º + sin 31º) k 2h
(A)
3
then k is equal to
(B) 2h
(A) 3
3h
(B) 1 (C)
2
(C) 4
(D) More than one of the above
(D) More than one of the above
(E) None of the above (E) None of the above
23/MAV/M–2023–09/S3 (S)/116-A 42
Text of page 44
145. If the arithmetic mean of first n 148. If Radha deposits R 800 in
natural numbers is 15, then n is short-term deposit in a bank for
equal to 1
73 days at the rate of 7 % per
(A) 14 2
annum, then how much interest
(B) 15
will she get?
(C) 29
(A) R 8
(D) More than one of the above
(B) R 10
(E) None of the above
(C) R 12
146. If the difference between mode (D) More than one of the above
and median of a data is 24, then
the difference between median (E) None of the above
and mean is
(A) 12 149. On a sum of money, the simple
interest for 2 years is R 660,
(B) 24 while the compound interest is
(C) 8 R 696·30, the rate of interest
being the same in both the
(D) More than one of the above
cases. The rate of interest is
(E) None of the above
(A) 10%
147. If a variable
takes discrete (B) 10·5%
7 5
values x + 4, x - , x - , x - 3, (C) 12%
2 2
1 1 (D) More than one of the above
x - 2, x + , x - , x + 5, x > 0,
2 2
(E) None of the above
then the median of the data is
5
(A) x- 150. Find the discount equivalent to
2 successive discounts 20%, 10%,
5 5% of the invoice.
(B) x -
3 (A) 31·6%
5 (B) 68·4%
(C) x -
4
(C) 35%
(D) More than one of the above (D) More than one of the above
(E) None of the above (E) None of the above
23/MAV/M–2023–09/S3 (S)/116-A 44
Text of page 1
Bihar Public Service Commission
School Teacher Written (Objective) Competitive Examination (Advt. No. 27/2023)
Examination Date : 08.12.2023
FINAL ANSWER KEY : LANGUAGE, GENERAL STUDIES AND MATHEMATICS
SERIES - A
1 C 31 A 61 A 91 B 121 C
2 B 32 B 62 B 92 B 122 E
3 A 33 C 63 A 93 A 123 A
4 D 34 C 64 A 94 B 124 E
5 B 35 A 65 A 95 C 125 A
6 E 36 A 66 A 96 B 126 C
7 C 37 B 67 A 97 C 127 A
8 B 38 A 68 B 98 A 128 C
9 B 39 A 69 B 99 B 129 B
10 C 40 B 70 C 100 B 130 C
11 A 41 C 71 A 101 B 131 A
12 A 42 B 72 E 102 A 132 B
13 C 43 A 73 A 103 A 133 B
14 B 44 C 74 C 104 A 134 A
15 D 45 C 75 C 105 C 135 A
16 D 46 B 76 E 106 B 136 C
17 B 47 B 77 A 107 A 137 A
18 C 48 A 78 A 108 C 138 C
19 D 49 D 79 D 109 B 139 B
20 D 50 C 80 B 110 A 140 B
21 B 51 B 81 B 111 A 141 C
22 D 52 B 82 A 112 C 142 C
23 E 53 B 83 C 113 E 143 B
24 A 54 C 84 A 114 B 144 A
25 A 55 D 85 A 115 A 145 C
26 C 56 A 86 C 116 C 146 A
27 B 57 A 87 B 117 C 147 C
28 A 58 A 88 C 118 B 148 C
29 D 59 C 89 A 119 B 149 E
30 A 60 B 90 A 120 C 150 APage 1 of 48
Source: Bihar Public Service Commission. Question paper published by Bihar Public Service Commission.