Bihar Secondary Teacher 2023: TRE 1.0, Class 9 to 10, Mathematics
Text of page 1
17/MV/M–2023–09 Booklet Series
Candidate’s Roll Number
Question Booklet
A Serial No.
GENERAL STUDIES AND MATHEMATICS
Paper—3
Time Allowed : 2 Hours Maximum Marks : 120
Read the following instructions carefully before you begin to answer the questions.
IMPORTANT INSTRUCTIONS
1. This Question Booklet is divided into two Parts—Part–I and Part–II. Part–I contains questions of
GENERAL STUDIES. Part–II contains questions of MATHEMATICS.
2. Part–I consists of Question Nos. 1 to 40 and Part–II consists of Question Nos. 41 to 120. All
questions and their responses are printed in English and Hindi versions both.
3. Attempt questions from Part–I and Part–II.
4. All questions carry equal marks.
5. 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
torn or repeated. If you find any defect in this Booklet, get it replaced immediately by a
complete Booklet of the same series.
6. You must write your Roll Number in the space provided on the top of this page. Do not write
anything else on the Question Booklet.
7. An Answer Sheet will be supplied to you separately by the Invigilator to mark the answers. You
must write your Name, Roll No., Question Booklet Series and other particulars in the space
provided on Page–1 of the Answer Sheet provided, failing which your Answer Sheet will not
be evaluated.
8. You should encode your Roll Number and the Question Booklet Series A, B, C or D as it is
printed on the top right-hand corner of the Question Booklet with Black/Blue ink ballpoint pen in
the space provided on Page–2 of your Answer Sheet. If you do not encode or fail to encode the
correct series of your Question Booklet, your Answer Sheet will not be evaluated correctly.
9. Each question comprises of five responses—(A), (B), (C), (D) and (E). You are to select ONLY ONE
correct response and mark it in your Answer Sheet. In any case, choose ONLY ONE response for
each question. Your total marks will depend on the number of correct responses marked by you in
the Answer Sheet.
10. In the Answer Sheet, there are five circles— A , B , C , D and E against each question. To
answer the questions, you are to mark with Black/Blue ink ballpoint pen ONLY ONE circle of your
choice for each question. Select only one response for each question and mark it in your Answer
Sheet. If you mark more than one answer for one question, the answer will be treated as wrong.
Use Black/Blue ink ballpoint pen only to mark the answer in the Answer Sheet. Any erasure
or change is not allowed.
11. For each question for which a wrong answer has been given by the candidates, one-fourth of the
marks assigned to that question will be deducted as penalty.
12. You should not remove or tear off any sheet from the Question Booklet. You are not allowed to
take this Question Booklet and the Answer Sheet out of the Examination Hall during the
examination. After the examination has concluded, you must hand over your Answer Sheet
to the Invigilator. Thereafter, you are permitted to take away the Question Booklet with you.
13. Failure to comply with any of the above instructions will render you liable to such action or
penalty as the Commission may decide at their discretion.
14. Candidates must assure before leaving the Examination Hall that their Answer Sheets will be kept
in Self Adhesive LDPE Bag and completely packed/sealed in their presence.
‹`mZ X| : AZwXoem| H$m {h›Xr Í$nm›Va Bg nwpÒVH$m Ho$ Ap›V_ n•> na N>nm h°ü&
Text of page 2
PART—I
( GENERAL STUDIES )
1. 10 years ago the ratio of ages 3. The average monthly income of
of Ramesh and Rajeev was 1 : 3. P and Q is R 5,050. The average
5 years hence this ratio will monthly income of Q and R is
become 2 : 3. What is the ratio R 6,250 and the average
of their ages at present? monthly income of P and R is
R 5,200. The monthly income of
(A) 2 : 5 P is
(A) R 3,500
(B) 3 : 5
(B) R 4,050
(C) 1 : 2 (C) R 4,000
(D) More than one of the above
(D) More than one of the above
(E) None of the above
(E) None of the above
4. If 30% of P is added to 40%
of Q , it becomes 80% of Q .
Accordingly, what is the
2. If I walk with a speed of 5 km percentage of Q with respect
per hour from my house to the to P ?
station, my train would have left (A) 40%
the station 7 minutes before my
(B) 50%
arrival. But, if I walk with a
speed of 6 km per hour, I will (C) 75%
reach the station 5 minutes (D) More than one of the above
before the departure of my (E) None of the above
train. Accordingly, what is the
distance between my house and
5. A sum of money is to be
the station?
distributed among A, B, C, D in
the proportion of 5 : 2 : 4 : 3. If
(A) 7 km
C gets R 1,000 more than D,
(B) 6·5 km what is B’s share?
(A) R 500
(C) 6 km (B) R 1,500
(C) R 2,000
(D) More than one of the above
(D) More than one of the above
(E) None of the above (E) None of the above
17/MV/M–2023–01–10 (S)/11-A 2
Text of page 4
6. A shopkeeper gives a discount 9. Which of the following photo-
of 5% on the selling price of a electric devices is the most
watch. If he gives a discount of suitable for digital applications?
6%, he will earn a profit which (A) Photo-voltaic cell
is R 15 less than the before.
(B) Photo-emissive cell
Accordingly, what is the marked
selling price of that watch? (C) Photo-diode
(D) More than one of the above
(A) R 1,400
(E) None of the above
(B) R 1,500
(C) R 1,800 10. The critical mass of a fissionable
(D) More than one of the above material is
(E) None of the above (A) one kilogram equivalent
(B) the minimum mass needed
for chain reaction
7. Three numbers are in the ratio
(C) the rest mass equivalent to
3 : 4 : 5. The total of the largest
1010 joules
and the smallest numbers is
equal to the other number (D) More than one of the above
plus 52. Accordingly, which is (E) None of the above
the smallest number?
(A) 27 11. Which of the following gases is
used to force the ripening of
(B) 39
fruits?
(C) 52 (A) Ethane
(D) More than one of the above (B) Ethylene
(E) None of the above (C) Methylene
(D) More than one of the above
1 (E) None of the above
8. If 2 2n -1 = n - 3 , then the value
8
of n is 12. Which one of the following has
zero octane number?
(A) 3
(A) Iso-octane
(B) 2
(B) Neo-octane
(C) – 2 (C) n-octane
(D) More than one of the above (D) More than one of the above
(E) None of the above (E) None of the above
17/MV/M–2023–01–10 (S)/11-A 4
Text of page 6
13. The edible part of Litchis is 17. In which year was NGT (National
(A) aril Green Tribunal) for protection
of environment and forest
(B) thalamus established by the Government
(C) seed coat of India?
(D) More than one of the above (A) 2010
(B) 2011
(E) None of the above
(C) 2012
(D) More than one of the above
14. The physical process involved in (E) None of the above
the release of molecular oxygen
from leaves is
18. Which city of India started first
(A) diffusion under-water metro?
(B) transpiration (A) Kochi
(B) Visakhapatnam
(C) osmosis
(C) Bengaluru
(D) More than one of the above
(D) More than one of the above
(E) None of the above (E) None of the above
15. The process of finding the 19. Under India’s G20 Presidency,
relative location of genes on a where was the Tourism Working
chromosome is called Group Meeting held?
(A) Patna (Bihar)
(A) genome walking
(B) Srinagar (Jammu and
(B) chromosome walking Kashmir)
(C) gene mapping (C) Ramnagar (Uttarakhand)
(D) More than one of the above (D) More than one of the above
(E) None of the above
(E) None of the above
20. Who among the following got
16. Spore mother cell in bryophytes the Silver Medal in the National
is Under-17 Girls Wrestling
(A) haploid Championship?
(A) Liza Tomar
(B) diploid
(B) Nirjala
(C) triploid
(C) Pushpa Yadav
(D) More than one of the above (D) More than one of the above
(E) None of the above (E) None of the above
17/MV/M–2023–01–10 (S)/11-A 6
Text of page 8
21. Who won the International 25. Match List–I with List–II :
Booker Prize, 2022 for the novel,
Tomb of Sand ? List—I List—II
(A) Geetanjali Shree and Daisy a. Char 1. Punjab plain
Rockwell
(B) David Diop and Anna b. Kankar 2. Delta
Moschovakis
c. Kayal 3. Bangar
(C) Marilyn Booth and Jokha
Alharthi d. Mand 4. Coastal plain
(D) More than one of the above
Select the correct answer using
(E) None of the above
the codes given below.
22. Who was the Chief Guest on (A) a b c d
India’s 74th Republic Day? 1 4 2 3
(A) Mohammed bin Salman
(B) Abdel Fattah El-Sisi (B) a b c d
(C) Sheikh Mohammed bin 2 3 4 1
Rashid Al Maktoum
(D) More than one of the above (C) a b c d
3 1 4 2
(E) None of the above
(D) More than one of the above
23. In which district of Bihar, the
first floating solar power plant
(E) None of the above
has been built?
(A) Darbhanga
(B) West Champaran
26. Which of the following
(C) Madhubani
tributaries does not join
(D) More than one of the above Brahmaputra river from north?
(E) None of the above
(A) Subansiri
24. Which of the following has got
GI Tag in Bihar? (B) Belsiri
(A) Maghai Paan
(C) Manas
(B) Basmati Rice
(C) Chanderi Saree
(D) More than one of the above
(D) More than one of the above
(E) None of the above (E) None of the above
17/MV/M–2023–01–10 (S)/11-A 8
Text of page 10
27. Likhapani glacier is located in 30. Arrange the following seaports of
which State of India? India from north to south :
1. Kakinada
(A) Arunachal Pradesh
2. Machilipatnam
(B) Himachal Pradesh 3. Nagapattinam
(C) Sikkim 4. Visakhapatnam
Select the correct answer using
(D) More than one of the above the codes given below.
(E) None of the above (A) 1, 2, 3, 4
(B) 4, 1, 2, 3
(C) 1, 3, 2, 4
28. Magadha and Anga plains are (D) More than one of the above
parts of
(E) None of the above
(A) upper Ganga plain
31. The Agreement of Kosi Irrigation
(B) middle Ganga plain
and Hydroelectricity Plan in
1954 was signed between which
(C) lower Ganga plain
two countries?
(D) More than one of the above (A) India and Bangladesh
(B) India and China
(E) None of the above
(C) India and Nepal
(D) More than one of the above
29. Which of the following pairs of (E) None of the above
waterfalls and rivers is not
correctly matched?
32. In which climatic division does
(A) Jog—Sharavati Bihar fall as per R. L. Singh’s
classification scheme?
(B) Kapildhara—Kaveri (A) Humid south-east
(C) Dhuandhar—Godavari (B) Subhumid transitional
(C) Subhumid continental
(D) More than one of the above
(D) More than one of the above
(E) None of the above (E) None of the above
17/MV/M–2023–01–10 (S)/11-A 10
Text of page 12
33. In which Session of the Indian 37. Which portfolio did Dr. Rajendra
National Congress was the Prasad hold during the Interim
resolution of ‘Purna Swaraj’ Government of 1946?
adopted? (A) Defence
(A) Kanpur Session, 1925 (B) Home
(B) Lahore Session, 1929 (C) Food and Agriculture
(C) Karachi Session, 1931
(D) More than one of the above
(D) More than one of the above
(E) None of the above
(E) None of the above
38. Who among the following
34. What was an initial objective of
particularly urged Gandhiji to
‘Kuka Movement’ in Punjab?
visit Champaran to witness the
(A) To purify the Sikh religion miseries of the Ryots?
(B) To gain political power in (A) Brijkishore Prasad
Punjab
(B) Rajkumar Shukla
(C) Organization of peasant
movement (C) Sukhram Ganesh
(D) More than one of the above (D) More than one of the above
(E) None of the above (E) None of the above
35. Who described the Revolt of 39. The ‘Day of Deliverance’ was
1857 as the ‘First Indian War of observed by the Muslim League
Independence’? on which date?
(A) V. D. Savarkar (A) 22nd December, 1939
(B) Bal Gangadhar Tilak (B) 17th October, 1939
(C) Bipin Chandra Pal (C) 22nd December, 1940
(D) More than one of the above (D) More than one of the above
(E) None of the above (E) None of the above
36. Where was the first instance of 40. Who laid the foundation stone
organized non-cooperation in of National College and Bihar
the history of Indian peasantry Vidyapeeth?
held?
(A) Dr. Rajendra Prasad
(A) Bihar and Bengal
(B) Maulana Abdul Bari
(B) Madras Presidency
(C) Mahatma Gandhi
(C) Punjab Province
(D) More than one of the above (D) More than one of the above
(E) None of the above (E) None of the above
17/MV/M–2023–01–10 (S)/11-A 12
Text of page 14
PART—II
( MATHEMATICS )
41. During conversion of a solid 44. Let x + 2y + 4 = 0 and
from one shape to another, the -4x + 2y - 3 = 0 be the equations
volume of the solid will of two straight lines. Then
(A) decrease
(A) they are parallel
(B) remain unaltered
(C) increase (B) both are passing through
the origin
(D) More than one of the above
(E) None of the above (C) one is passing through the
origin
42. The Cartesian coordinates of
three points A, B and C are (D) More than one of the above
(1, - 1), (3, - 4) and (5, - 7)
respectively. Then the D ABC is (E) None of the above
(A) isosceles
(B) equilateral 45. Pritam and Rana drive around
(C) right-angled a circular sports field. Pritam
takes 16 minutes to take one
(D) More than one of the above
round while Rana completes the
(E) None of the above round in 20 minutes. If both
start from the same point, at the
43. A sweet seller has 420 Kaju same time and in the same
Burfis and 150 Badam Burfis. direction, after how much time
He wants to stack them in such will they meet at the starting
a way that each stack has the point?
same number, and they take up
the least area of the tray. The (A) 80 minutes
number of such stacks formed is
(A) 17 (B) 32 minutes
(B) 19 (C) 40 minutes
(C) 18
(D) More than one of the above
(D) More than one of the above
(E) None of the above (E) None of the above
17/MV/M–2023–09 MAT (S)/11-A 14
Text of page 16
46. The largest number that divides 49. If the nth term of an arithmetic
450, 577 and 704, leaving progression is (2n + 1), then the
remainders 9, 10 and 11 sum of its first three terms is
respectively, is
(A) 63 (A) 6n + 3
(B) 577 (B) 15
(C) 450
(C) 12
(D) More than one of the above
(E) None of the above (D) More than one of the above
47. If a, b, g are the zeros of the (E) None of the above
polynomial x 3 - 6x 2 - x + 30,
then the value of ab + bg + ga is
(A) 1 50. DABC and DDBC are on the
(B) -1 same base BC and on the
opposite sides of BC. If O is the
(C) 6 intersection point of the
(D) More than one of the above diagonals AD and BC, then
(E) None of the above
Area of DABC
m Area of DDBC
48. If sinq = , then the value of
n
tan q + 4 is equal to
4 cot q + 1
is BO
(A)
CO
m
(A)
n2 -m AO
(B)
n DO
(B)
n2 -m AO
(C)
m CO
(C)
m2 - n 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
17/MV/M–2023–09 MAT (S)/11-A 16
Text of page 18
51. Places A and B are 100 km apart 53. Consider the following frequency
on a highway. One car starts distribution :
from A and another from B at
Class Frequency
the same time. If the cars travel
in the same direction at different 0–10 3
speeds, they meet in 5 hours. If 10–20 9
they travel towards each other, 20–30 15
they meet in 1 hour. What are 30–40 30
the speeds of the two cars?
40–50 18
50–60 5
(A) 60 km/hr, 40 km/hr
(B) 30 km/hr, 70 km/hr The modal class is
(A) 20–30
(C) 20 km/hr, 80 km/hr
(B) 30–40
(D) More than one of the above
(C) 40–50
(E) None of the above (D) More than one of the above
(E) None of the above
52. The sum of the squares of two
positive integers is 306. If 54. If two diagonals AC and DB of
the square of the larger integer a quadrilateral ABCD intersect
is 25 times the smaller integer, at a point E such that
then the difference between the
two integers is AE : EC :: 1 : 2 and BE : ED :: 3 : 6
(A) 6 then ABCD is
(B) 10 (A) an arbitrary quadrilateral
(B) a rhombus
(C) 1
(C) a parallelogram
(D) More than one of the above
(D) More than one of the above
(E) None of the above (E) None of the above
17/MV/M–2023–09 MAT (S)/11-A 18
Text of page 20
55. Find the two numbers such that 57. A person on tour has R 4,200 for
the sum of thrice the first and his expenses. If he extends his
the second is 142, and four tour for 3 days, he has to cut
times the first exceeds the down his daily expenses by R 70.
second by 138. The original duration of the tour
will be
(A) 42, 20 (A) 14 days
(B) 12 days
(B) 32, 40 (C) 16 days
(D) More than one of the above
(C) 40, 22
(E) None of the above
(D) More than one of the above 58. A motorboat, whose speed is
18 km/hr in still water, takes
one hour more to go 24 km
(E) None of the above
upstream than to return
downstream to the same spot.
The speed of the stream is
(A) - 54 km/hr
56. If the slope of the line joining (B) 6 km/hr
1
the points (k, 4) and (-3, - 2) is , (C) 10 km/hr
2
then the value of k is (D) More than one of the above
(E) None of the above
(A) 3
59. Find the centre of a circle
passing through the points
(B) - 9
(6, - 6), (3, - 7) and (3, 3).
(A) (3, 3)
(C) 9
(B) (3, - 2)
(D) More than one of the above (C) (2, - 3)
(D) More than one of the above
(E) None of the above (E) None of the above
17/MV/M–2023–09 MAT (S)/11-A 20
Text of page 22
60. Two water taps together can fill 62. A bag contains 2 red, 3 green
3 and 2 blue balls. Two balls
a tank in 9 hours. The tap of
8 are drawn at random. The
larger diameter takes 10 hours probability that none of the balls
less than the smaller one to fill drawn is blue is
the tank separately. The time
(in hours) in which each tap can 10
separately fill the tank is (A)
21
respectively
11
(A) 10, 20 (B)
21
(B) 15, 25
2
(C)
(C) 5, 15 7
(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. In a class test, the sum of
Kamal’s marks in Mathematics 63. A man saved R 33,000 in
and English is 40. Had he got 10 months. In each month after
3 marks more in Mathematics the first, he saved R 100 more
and 4 marks less in English, the than he did in the preceding
product of the marks would month. How much did he save
have been 360. The marks in the first month?
obtained by Kamal in two
subjects separately are
(A) R 2,850
(A) 21, 19
(B) R 1,850
(B) 12, 28
(C) R 1,900
(C) 21, 12
(D) More than one of the above (D) More than one of the above
(E) None of the above (E) None of the above
17/MV/M–2023–09 MAT (S)/11-A 22
Text of page 24
64. The area of a square field is 66. For what value of k, the
24200 square metres. At the equations
rate of 6·6 km/hr, how much
time will a lady take to cross the 3(k - 1)x + 4y = 24
field diagonally? 15x + 20y = 8(k + 13)
(A) 3 minutes have infinitely many solutions?
(A) 2
(B) 2 minutes
(B) -2
(C) 2·4 minutes (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
67. The value of p such that the
points A(4, 7), B ( p, 3), C (7, 3) are
the vertices of a right-angled
triangle, having right angle at B,
65. The sum of all three-digit
is
natural numbers, multiple of
A (4, 7)
11, is
(A) 44540
B (p, 3) C (7, 3)
(B) 44550
(A) 3
(C) 54540 (B) 5
(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
17/MV/M–2023–09 MAT (S)/11-A 24
Text of page 26
68. A 5 cm cube is cut into as many 70. The sum of LCM and HCF of two
1 cm cubes as possible. The numbers is 1260. If their LCM is
ratio of the surface area of the 900 more than their HCF, then
larger cube to that of the sum of the product of the two numbers
the surface areas of the smaller is
cubes is
(A) 203400
(A) 1 : 6 (B) 194400
(C) 198400
(B) 1 : 5
(D) More than one of the above
(C) 1 : 25 (E) None of the above
(D) More than one of the above 71. If the bisector of an angle of
a triangle bisects the opposite
(E) None of the above side, then the triangle is
(A) equilateral
(B) right-angled
69. In a DABC, AD is the bisector of
ÐA. If AB = 6 × 4 cm, AC = 8 cm (C) isosceles
and BD = 5 × 6 cm, then the value
(D) More than one of the above
of DC is
A (E) None of the above
72. The angles of elevation of the top
of a tower from two points at
distances of 4 m and 9 m from
B C
D the base of the tower and in the
same straight line with it are
(A) 7 cm complementary. Then the height
of the tower is
(B) 9 cm
(A) 6 m
(C) 12 cm (B) 10 m
(C) 9 m
(D) More than one of the above
(D) More than one of the above
(E) None of the above (E) None of the above
17/MV/M–2023–09 MAT (S)/11-A 26
Text of page 28
73. The area of a rhombus is 76. A bag contains 5 red balls
480 cm 2 and the length of one and some blue balls. If the
of its diagonals is 20 cm. The probability of drawing a blue
length of each side of the ball from the bag is four times
rhombus is that of a red ball, then the
number of blue balls in the
(A) 24 cm bag is
(B) 30 cm (A) 10
(C) 26 cm (B) 40
(D) More than one of the above (C) 20
(E) None of the above (D) More than one of the above
(E) None of the above
74. The factors of 2a 7 - 128a are
(A) a (a + 2) 3 (a - 2) 3 77. If sin A + sin 2 A = 1, then
cos 2 A + cos 4 A = ?
(B) 2a (a + 2)(a - 2)(a 2 + 2a - 4)
(a 2 - 2a - 4) (A) 2
(B) 1
(C) 2a (a + 2)(a - 2)(a 2 + 2a + 4)
(a 2 - 2a + 4) (C) -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
75. Which of the following pairs of 78. The probability of an event can
lines in a circle cannot be be
parallel?
(A) - 0 × 04
(A) Two chords
(B) 1·00009
(B) A chord and a tangent
18
(C)
(C) Two diameters 23
(D) More than one of the above (D) More than one of the above
(E) None of the above (E) None of the above
17/MV/M–2023–09 MAT (S)/11-A 28
Text of page 30
79. The angle of depression of a car, 82. A carton consists of 100 shirts of
parked on the road, from the top which 88 are good, 8 have minor
of a 150 m high tower is 30°. defects and 4 have major
The distance of the car from the defects. Jimmy, a trader, will
tower is only accept the shirts which are
(A) 50 3 m good, but Sujata, another
trader, will only reject the shirts
(B) 150 3 m which have major defects.
(C) 75 m One shirt is drawn at random
(D) More than one of the above from the carton. The proba-
bilities that it is not acceptable
(E) None of the above
to Jimmy and acceptable to
Sujata are
80. A hemispherical bowl of internal
diameter 36 cm is full of liquid.
(A) 0·12, 0·96
The liquid is to be filled into
cylindrical shaped bottles each
(B) 0·88, 0·96
of radius 3 cm and height 9 cm.
The number of bottles is
(C) 0·12, 0·04
(A) 96
(B) 48 (D) More than one of the above
(C) 24
(D) More than one of the above (E) None of the above
(E) None of the above
81. A kite is flying at a height of 83. Find the area of the triangle
30 m from the ground. The whose sides are 42 cm, 34 cm
length of the string from the kite and 20 cm.
to the ground is 60 m. Assuming
that there is no slack in the (A) 330 cm2
string, the angle of elevation of
the kite at the ground is (B) 360 cm2
(A) 45°
(B) 60° (C) 336 cm2
(C) 30°
(D) More than one of the above
(D) More than one of the above
(E) None of the above (E) None of the above
17/MV/M–2023–09 MAT (S)/11-A 30
Text of page 32
84. The denominator of a fraction 86. If seven times the seventh term
is two more than its numerator. of an AP is equal to eleven times
If the sum of the fraction and its eleventh term, then its
4 eighteenth term is equal to
its reciprocal is 2 , then the
15
(A) -17
fraction is
(B) -1
5 (C) 0
(A)
3 (D) More than one of the above
(E) None of the above
3
(B)
5 87. A wire is looped in the form of
a circle of radius 28 cm. It is
5 rebent into a square form.
(C)
7 Determine the length of the side
of the square.
(D) More than one of the above (A) 44 cm
(B) 54 cm
(E) None of the above (C) 40 cm
(D) More than one of the above
(E) None of the above
85. The cost of carpeting a room
15 m long with a carpet 75 cm 88. Given
wide at R 70 per metre is 1
R 8,400. The width of the room is x = , (x ¹ 2)
ì ü
ïï 1 ïï
2- í ý
(A) 9 m ï 2 - æç 1 ö÷ ï
ïî è 2 - x ø ïþ
(B) 8 m then x is equal to
(A) 1, 1
(C) 6 m
(B) -1, 1
(D) More than one of the above (C) -1, -1
(D) More than one of the above
(E) None of the above (E) None of the above
17/MV/M–2023–09 MAT (S)/11-A 32
Text of page 34
89. The area of a sector of angle q° of 92. Consider the system of linear
a circle with radius R is equations x - y +1 = 0 and
2pRq 3x + 2y - 12 = 0. The coordinates
(A)
180 of the vertices of the triangle
2pRq formed by these lines and the
(B)
360 y-axis are
2
(C) pR q
360 (A) (2, - 1), (0, 5) and (0, - 5)
(D) More than one of the above
(E) None of the above (B) (2, - 1), (5, 0) and (-5, 0)
90. The ratio of incomes of two (C) (2, 3), (0, 1) and (0, 6)
persons is 9 : 7 and the ratio
of their expenditures is 4 : 3. If
each of them manages to save (D) More than one of the above
R 2,000 per month, then their
monthly incomes are (E) None of the above
(A) R 18,000 and R 14,000
(B) R 27,000 and R 21,000
(C) R 36,000 and R 28,000 93. A cubical ice-cream bar of
(D) More than one of the above edge 22 cm is to be distributed
(E) None of the above among some children by filling
ice-cream cones of radius 2 cm
91. A factory manufactures 120000 and height 7 cm up to its brim.
pencils daily. The pencils are How many children will get the
cylindrical in shape, each of ice-cream cones?
length 25 cm, and circum-
ference of base is 1·5 cm. Then
(A) 163
the cost of colouring the curved
surfaces of the pencils
manufactured in one day at (B) 263
R 0·05 per dm2 is
(A) R 22,500 (C) 363
(B) R 2,25,000
(C) R 2,250 (D) More than one of the above
(D) More than one of the above
(E) None of the above (E) None of the above
17/MV/M–2023–09 MAT (S)/11-A 34
Text of page 36
94. If O is any point inside a 97. Rajveer saves R 32 during the
rectangle ABCD, then first month, R 36 during the
second month and R 40 during
(A) OB 2 + OD 2 = OA 2 + OC 2
the third month. If she
(B) OB 2 + OA 2 = OD 2 + OC 2 continues to save in this
manner, she will be able to save
(C) OA 2 + OD 2 = OB 2 + OC 2 R 2,000 in
(D) More than one of the above (A) 20 months
(E) None of the above (B) 30 months
(C) 35 months
95. If the point C (1, 1) divides the (D) More than one of the above
line segment joining A (-2, 7) and
B in the ratio 3 : 2 internally, (E) None of the above
the coordinates of B are
98. In an examination, one student
(A) (- 3, 3) secured 30% marks and failed
(B) (3, - 3) by 45 marks. Another student
secured 42% marks and got
(C) (3, 3) 45 marks more than minimum
(D) More than one of the above passing marks. Find the total
marks.
(E) None of the above
(A) 270
(B) 750
96. A manufacturer of TV sets
produced 600 sets in the third (C) 850
year and 700 sets in the seventh (D) More than one of the above
year. Assuming that the produc-
tion increases uniformly by a (E) None of the above
fixed number every year, the
production of TV sets in the 99. The mean of 20 numbers is zero.
10th year is Of them, at the most, how many
may be greater than zero?
(A) 850
(A) 19
(B) 1000
(B) 1
(C) 775 (C) 10
(D) More than one of the above (D) More than one of the above
(E) None of the above (E) None of the above
17/MV/M–2023–09 MAT (S)/11-A 36
Text of page 38
100. Suhit borrowed R 6,300 at the 103. The mean and mode of a
rate of 14% for 3 years on simple frequency distribution are 28
interest from Vikas. Suhit added and 16 respectively. The median
some amount in the principal is
amount and gave it to Mohit at (A) 24
the rate of 16% for the same
period with simple interest. (B) 23·5
During this transaction, Suhit (C) 22
earned R 618. The amount
(D) More than one of the above
which Suhit gave to Mohit was
(E) None of the above
(A) R 7,000
(B) R 6,800 104. Some money has been borrowed
(C) R 7,200 on compound interest. After
(D) More than one of the above 2 years and 3 years, the
principal turns out to be R 9,680
(E) None of the above
and R 10,648 respectively. Then
the principal is
101. For a symmetrical frequency
distribution, we have (A) R 8,000
(A) mean < median < mode (B) R 9,000
(B) mean > mode > median (C) R 7,000
(C) mean = median = mode (D) More than one of the above
(D) More than one of the above (E) None of the above
(E) None of the above
105. Two different dice are rolled
102. One wall clock was set at together. Find the probability of
8:00 a.m. in the morning. This getting the sum of numbers on
clock runs 10 minutes fast two dice to be 5.
during 24 hours. Next day when 1
(A)
this clock shows 1:00 p.m. in 9
the afternoon, the correct time is
1
(B)
(A) 40 minutes passed 12 noon 4
(B) 45 minutes passed 12 noon 1
(C)
(C) 48 minutes passed 12 noon 6
(D) More than one of the above (D) More than one of the above
(E) None of the above (E) None of the above
17/MV/M–2023–09 MAT (S)/11-A 38
Text of page 40
106. When (x 31 + 31) is divided by 109. In a lottery, there are 6 prizes
) the remainder is
(x + 1, and 24 blanks. What is the
probability of not getting a
(A) 0
prize?
(B) 1
3
(A)
(C) 30 4
(D) More than one of the above 3
(B)
(E) None of the above 5
4
(C)
107. One ticket is drawn at random 5
from a bag containing tickets
(D) More than one of the above
numbered 1 to 40. The
probability that the selected (E) None of the above
ticket has a number, which is a
multiple of 7, is 110. The quadratic equation
1
(A) ax 2 + bx + c = 0 (a ¹ 0)
7
1 has two distinct real roots if
(B)
8
(A) the discriminant > 0
7
(C)
40 (B) the discriminant = 0
(D) More than one of the above (C) the discriminant < 0
(E) None of the above (D) More than one of the above
(E) None of the above
108. A person bought a horse and
a car for R 20,000. He sold the
horse with 20% profit and sold 111. a and b are two positive integers
the car with 10% loss. In this such that the least prime factor
transaction, he earned 2% of a is 2 and the least prime
profit. Then the purchase cost of factor of b is 5. Then the least
the horse is prime factor of a + b is
(A) R 7,200 (A) 3
(B) R 7,500 (B) 5
(C) R 8,000 (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
17/MV/M–2023–09 MAT (S)/11-A 40
Text of page 42
112. The line segment XY is parallel 114. Consider a polynomial
to the side AC of DABC and it
divides the triangle into two x 4 + x 3 - 9x 2 - 3x + 8
parts of equal areas. Then the
Given that two of its zeros are
AX
ratio is - 3 and 3. Then the remaining
AB
zeros are
(A) 2 + 2 (A) -3, -2
2
(B) 3, -2
(B) 2 - 2 (C) 3, 2
2
(D) More than one of the above
(E) None of the above
(C) 3 + 2
2
cos q - sin q 1 - 3
115. If = and
(D) More than one of the above cos q + sin q 1 + 3
0° < q < 90°, then the angle q is
(E) None of the above
(A) 30°
(B) 60°
113. Which term of the AP (C) 45°
(D) More than one of the above
72, 63, 54, L
(E) None of the above
is 0?
116. If tan 2 q = 1 + 2 tan 2 a , then
sin 2 q is equal to
(A) 8th
1
(A) (1 + sin 2 a )
2
(B) 9th
(B) 1 + sin 2 a
(C) 10th 1
(C) (1 + cos 2 a )
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
17/MV/M–2023–09 MAT (S)/11-A 42
Text of page 44
117. Taxi charges in a city consist of 119. A girl of height 90 cm is walking
fixed charges and the remaining away from the base of a lamp-
depending upon the distance post at a speed of 1·2 m/sec.
travelled in kilometres. If a If the lamp is 3·6 m above the
person travels 60 km, he pays ground, then the length of
R 960 and for travelling 80 km, the shadow of the girl after
he pays R 1,260. Find the fixed 4 seconds is
charges and the rate per
kilometre.
(A) 1·6 m
(A) R 60 and R 15/km
(B) 1·5 m
(B) R 40 and R 25/km
(C) R 30 and R 15/km
(C) 1·06 m
(D) More than one of the above
(D) More than one of the above
(E) None of the above
(E) None of the above
118. A vertical tower stands on a
horizontal plane and is
surmounted by a vertical
flagstaff of height h. At a point
on the plane, the angles of 120. sin q - cos q + 1 is equal to
sin q + cos q - 1
elevation of the bottom and top
of the flagstaff are a and b
respectively. Then the height of 1
(A)
the tower is sec q - tan q
tan a
(A) 1
h (tan b - tan a ) (B)
cosecq - cot q
tan a
(B)
h (tan b + tan a ) 1
(C)
cot q - tan q
h tan a
(C)
tan b - tan a
(D) More than one of the above
(D) More than one of the above
(E) None of the above (E) None of the above
17/MV/M–2023–09 MAT (S)/11-A 44
Text of page 1
Bihar Public Service Commission
School Teacher Written (Objective) Competitive Examination (Advt. No. 26/2023)
Secondary Schools - Examination Date : 26.08.2023, 1 st Sitting
FINAL ANSWER KEY : General Studies and Mathematics, Paper-3
Series-A Series-B Series-C Series-D Remarks
Q.No. Answer Q.No. Answer Q.No. Answer Q.No. Answer
1 B 19 B 29 A 39 C
2 C 20 A 30 C 40 B
3 C 21 A 31 C 33 B
4 C 22 A 32 C 34 B
5 C 23 A 25 C 35 B
6 B 24 B 26 A 36 C
7 B 17 B 27 A 37 C
8 B 18 B 28 A 38 C
9 A 27 C 37 B 7 A
10 B 28 B 38 A 8 C
11 B 29 B 39 A 1 C
12 E 30 E 40 E 2 E
13 A 31 C 33 B 3 A
14 A 32 C 34 B 4 A
15 C 25 A 35 C 5 B
16 B 26 B 36 A 6 C
17 A 35 C 5 B 15 A
18 E 36 E 6 E 16 E
19 B 37 B 7 A 9 C
20 B 38 B 8 A 10 C
21 A 39 C 1 B 11 A
22 B 40 B 2 A 12 C
23 A 33 C 3 B 13 A
24 A 34 C 4 B 14 A
25 B 3 B 13 A 23 C
26 E 4 E 14 E 24 E
27 A 5 C 15 B 17 A
28 B 6 B 16 A 18 C
29 D 7 D 9 D 19 D
30 B 8 B 10 A 20 C
31 C 1 A 11 C 21 B
32 B 2 B 12 A 22 C
33 B 11 B 21 A 31 C
34 A 12 C 22 B 32 A
35 A 13 C 23 B 25 A
36 A 14 C 24 B 26 A
37 C 15 A 17 C 27 B
38 B 16 B 18 A 28 C
39 A 9 C 19 B 29 A
40 C 10 A 20 C 30 B
Text of page 2
-2- Series-A Series-B Series-C Series-D Remarks Q.No. Answer Q.No. Answer Q.No. Answer Q.No. Answer 41 B 61 B 81 A 101 C 42 E 62 E 82 E 102 E 43 B 63 B 83 A 103 C 44 E 64 E 84 E 104 E 45 A 65 C 85 B 105 A 46 A 66 C 86 B 106 A 47 B 67 B 87 A 107 C 48 E 68 E 88 E 108 E 49 B 69 B 89 A 109 C 50 B 70 B 90 A 110 C 51 A 71 C 91 B 111 A 52 A 72 C 92 B 112 A 53 B 73 B 93 A 113 C 54 E 74 E 94 E 114 E 55 C 75 A 95 C 115 B 56 C 76 A 96 C 116 B 57 B 77 B 97 A 117 C 58 B 78 B 98 A 118 C 59 B 79 B 99 A 119 C 60 B 80 B 100 A 120 C 61 D 81 D 101 D 41 D 62 A 82 C 102 B 42 A 63 A 83 C 103 B 43 A 64 B 84 B 104 A 44 C 65 B 85 B 105 A 45 C 66 A 86 C 106 B 46 A 67 C 87 A 107 C 47 B 68 B 88 B 108 A 48 C 69 A 89 C 109 B 49 A 70 B 90 B 110 A 50 C 71 C 91 A 111 C 51 B 72 A 92 C 112 B 52 A 73 C 93 A 113 C 53 B 74 C 94 A 114 C 54 B 75 C 95 A 115 C 55 B 76 C 96 A 116 C 56 B 77 B 97 B 117 A 57 C 78 C 98 A 118 C 58 B 79 B 99 B 119 A 59 C 80 B 100 B 120 A 60 C 81 C 101 A 41 C 61 B 82 A 102 C 42 B 62 A 83 C 103 A 43 C 63 B 84 B 104 B 44 A 64 C 85 C 105 A 45 C 65 B
Text of page 3
-3-
Series-A Series-B Series-C Series-D Remarks
Q.No. Answer Q.No. Answer Q.No. Answer Q.No. Answer
86 C 106 A 46 C 66 B
87 A 107 C 47 B 67 A
88 A 108 C 48 B 68 A
89 C 109 A 49 C 69 B
90 A 110 C 50 B 70 A
91 C 111 A 51 C 71 B
92 C 112 A 52 C 72 B
93 C 113 A 53 C 73 B
94 A 114 C 54 B 74 A
95 B 115 B 55 A 75 C
96 C 116 A 56 C 76 B
97 E 117 E 57 E 77 E
98 B 118 B 58 A 78 C
99 A 119 C 59 B 79 A
100 B 120 B 60 A 80 C
101 C 41 A 61 C 81 B
102 C 42 A 62 C 82 B
103 A 43 C 63 B 83 A
104 A 44 C 64 B 84 A
105 A 45 C 65 B 85 A
106 C 46 A 66 C 86 B
107 B 47 B 67 A 87 C
108 C 48 A 68 C 88 B
109 C 49 A 69 C 89 B
110 A 50 C 70 B 90 A
111 E 51 E 71 E 91 E
112 B 52 B 72 A 92 C
113 B 53 B 73 A 93 C
114 E 54 E 74 E 94 E
115 B 55 B 75 A 95 C
116 A 56 C 76 B 96 A
117 A 57 C 77 B 97 A
118 C 58 A 78 C 98 B
119 A 59 C 79 B 99 A
120 A 60 C 80 B 100 APage 1 of 48
Source: Bihar Public Service Commission. Question paper published by Bihar Public Service Commission.