Railway Recruitment Board, Ajmer Electrical Signal Maintainer (P-way) Examination Held on 15-12-2007
1. If α, β are the roots of the equation x2 – px + 36 = 0 and α2 + β2 = 9, then p is equal to
(a) ±6
(b) ±3
(c) ±8
(d) ±9
2. If z is a complex number such that 
is purely imaginary, then |z| is equal to
(a) 0
(b) 1
(c) √2
(d) None of these
3. The value of 9 ∙ 91/2 ∙ 91/4 ∙ 91/8 …….. ∞ is
(a) 3
(b) 9
(c) 27
(d) 81
4. The term independent of x in the expansion of 
is
(a) 18C6
(b) 18C636
(c) 18C12
(d) 36
5. If 
and A2 – kA – I2 = 0, then value of k is
(a) 2
(b) −4
(c) 4
(d) 1
6. If 
then f{f cos x)} is equal to
(a) cos x
(b) 
(c) 
(d) x
7. In a triangle ABC right angled at C, the value of cot A + cot B is
(a) 
(b) a + b
(c) 
(d) 
8. The solution of the equation 
is
(a) x = 3
(b) x = 1/√5
(c) x = 0
(d) None of these
9. If the lines 3x + 4y + 1 = 0, 5x + λy + 3 = 0 and 2x + y – 1 = 0 are concurrent, then λ is equal to
(a) −8
(b) 8
(c) 4
(d) −4
10. The line 3x – 2y = k, meets the circle x2 + y2 = 4r2 at only one point, if k2 is
(a) 20 r2
(b) 52 r2
(c) 
(d) 
11. The value of 
is
(a) 2
(b) π
(c) π/4
(d) 2π
12. Solution of the equation 
is
(a) 
(b) 
(c) 
(d) 
13. 
(a) 
(b) 
(c) 
(d) 
14. 
is equal to
(a) 1/2
(b) 0
(c) 1
(d) None of these
15. In an ellipse, the distance between its foci is 6 and its minor axis is 8, the eccentricity of the ellipse is
(a) 4/5
(b) 3/5
(c) 1/√52
(d) 1/2
16. 
(a) 
(b) 
(c) 
(d) 
17. If the number of diagonals of a polygon of n sides is 54, then n is equal to
(a) 9
(b) 10
(c) 11
(d) 12
18. If the vectors 
represents the sides of a triangle, then the triangle is
(a) isosceles
(b) equilateral
(c) right angled
(d) scalene
19. If (α + β) = π/4, then the value of (1 + tan α) (1 + tan β) is
(a) 1
(b) −1
(c) 2
(d) −2
20. In a ∆ ABC, if a = 13, b = 14 and c = 15, then its circumradius is
(a) 65/4
(b) 65/3
(c) 65/8
(d) None of these
21. If tan θ + cot θ = 2, then general solution of θ is
(a) 
(b) 
(c) 
(d) None of these
22. If 
then 
is
(a) 
(b) 
(c) 
(d) None of these
23. The sum of all integers between 200 and 400 divisible by 9 is
(a) 3366
(b) 6633
(c) 6336
(d) 6363
24. On simplification of 
, we get
(a) 1.0
(b) 0.1
(c) 0.01
(d) 0.11
25. The HCF of two numbers is 12 ad their difference is 12. The numbers are
(a) 66, 78
(b) 70, 82
(c) 94, 106
(d) 84, 96
26. If x : y = 8 : 9, then 5x – 4y ; 3x + 2y is equal to
(a) 3 : 2
(b) 2 : 3
(c) 3 : 4
(d) 2 : 21
27. Ages of ‘A’ and ‘B’ are in the ratio of 2 : 3 respectively. Six years hence the ratio of their ages will become 8 : 11 respectively. What is B’s present age?
(a) 18 yr
(b) 24 yr
(c) 27 yr
(d) None of these
28.A, B and C rent a pasture, A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs 175. How much must C pay or his share of rent?
(a) 80
(b) 60
(c) 50
(d) 40
29. If 35% of a number is 12 less than 50% of that number, then the number is
(a) 80
(b) 60
(c) 50
(d) 40
30. A single discount equivalent of a discount series of 40% and 20% is
(a) 50%
(b) 52%
(c) 55%
(d) 60%
31. What sum of money will amounts to Rs 520 in 5 yr and to Rs 568 in 7 yr at simple interest ?
(a) Rs 400
(b) Rs 120
(c) Rs 510
(d) Rs 220
32. In what time will Rs 1000 amount to Rs 1331 at 20% per annum, compounded half-yearly ?
(a) 
(b) 2 yr
(c) 1 yr
(d) 
33. A can finish a piece of work in 6 days and B in 9 days; they work at it together, but A is called of 4 days before the work is actually completed, find what time the work was finished.
(a) 5 days
(b) 12 days
(c) 9 days
(d) 6 days
34. A train takes 18 s to pass completely through a station 162 m long and 15 s through another station 120 m long. The length o the train is
(a) 70 m
(b) 80 m
(c) 90 m
(d) 100 m
35. Between a square of perimeter 44 cm and a circle of circumference 44 cm which figure has larger area and by how much ?
(a) square, 33 cm2
(b) Circle, 33 cm2
(c) Both have equal area
(d) square, 495 cm2
36. The curved surface of a right circular cone of height 15 cm and base diameter 16 cm is
(a) 120π cm2
(b) 60π cm2
(c) 136π cm2
(d) 68π cm2
37. The straight line x + y = a will be a tangent to the ellipse 
if a is
(a) 8
(b) ±5
(c) ±10
(d) ±6
38. The centre of hyperbola 9x2 – 16y2 + 18x + 32y – 151 = 0 is
(a) (2, −2)
(b) (−1, 1)
(c) (−3, −3)
(d) (1, 1)
39. The area of the parallelogram whose diagonals are given by the vectors 
and 
is
(a) 10√3
(b) 5√3
(c) 8
(d) 4
40. Vector moment of the force 
acting at the point (1, −1, 2) about the point (2, −1, 3) is
(a) 
(b) 
(c) 
(d) 
41. For any event A,
(a) 
(b) 
(c) P(A) > 2
(d) 
42. 
is equal to
(a) 0
(b) 4
(c) 2/3
(d) None of these
43. The range of the function f(x) = x – [x] is
(a) [0, 1]
(b) [0, 1)
(c) (0, 1)
(d) None of these
44. If α, β are the roots of the quadratic equation 4x2 – 4x + 1 = 0, then α3 + β3 is
(a) 1/4
(b) 1/8
(c) 16
(d) 32
45. 
is equal to
(a) sec x(tan x + sec x)
(b) sec x(sec x – tan x)
(c) sec x( tan x – sec x)
(d) tan(sec x + tan x)
46. Two numbers are in the ratio of 9 : 7. If the difference of their square is 288, then the smaller of the numbers is
(a) 21
(b) 24
(c) 27
(d) 28
47. A cistern has 3 pipes, A to supply and B and C to draw off. A can fill it in 10 h, while B and C can empty it in 15 h and 20 h respectively. If the cistern is 7/10 full when they are all opened at once, in what time will it be empty?
(a) 36 h
(b) 42 h
(c) 48 h
(d) 52 h
48. If x = a cos3 θ, y = a sin3 θ, then 
is equal to
(a) tan2 θ
(b) sec2 θ
(c) sec θ
(d) |sec θ|
49. The average temperature of 1st 2nd and 3rd December was 24.4° The average temperature of the first two days was 24°C. The temperature on the 3rd of December was
(a) 20°C
(b) 25°C
(c) 25.2°C
(d) None of these
50. Shyam bought 2 articles for Rs 5.50 each, and 3 articles for Rs 3.50 each and 3 articles for Rs 5.50 each and 5 articles for Rs .50 each. The average price for one article is
(a) Rs 3
(b) Rs 3.10
(c) Rs 3.50
(d) Rs 2
51. ‘Heart’ is related to ‘Blood’ in the same way as ‘Lung’ is related to
(a) Oxygen
(b) Chest
(c) Purification
(d) Air
52. ‘Face’ is related to ‘Expression’ in the same way as ‘Hand’ is related to
(a) Gesture
(b) Work
(c) Handshake
(d) Pointing
Directions (Q. 53-54) : The following questions consist of two words each that have a certain relationship to each other, followed by four pair of words. Select the pair that has the same relationship as the original pair of words.
53. Inspiration : Poetry
(a) Music : Notes
(b) Dirt : Disease
(c) Brush : Painting
(d) Mind : Thought
54. Poverty : Prosperity
(a) Intelligence : Stupidity
(b) Rain : Flood
(c) Train : Cart
(d) Love : Sorrow
55. A man goes towards East 5 km, then he takes a turn to South-West and goes 5 km. He again takes a turn towards North-West and goes 5 km with respect to the point from where he started, where is he now?
(a) At the starting point
(b) In the West
(c) In the East
(d) In the North-East
56. Vijayan started walking towards South. After walking 15 m, he turned to the left and walked 15 m. He again turned to his left and walked 15 m. How far is he from his original position and in which direction?
(a) 15 m, North
(b) 15 m, South
(c) 30 m, East
(d) None of these
57. If the first half of the above alphabets is written in the reverse order, which letter will be exactly middle between the 9th letter from the left and the 10 letter from the right end?
(a) B
(b) A
(c) N
(d) D
58. If the second half of the following alphabets is written in the reverse order, which will be the 10th letter to the left of 9th letter counting from the right end ?
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
(a) I
(b) C
(c) J
(d) H
Directions (Q. 59-68) : In each of the following letters series, some of the letters are missing, which are given in that order as one of the alternatives below it. Choose the correct alternative.
59. aab_ab-cabcca_bcab_c
(a) bbc
(b) bbab
(c) cabc
(d) cbab
60. ccbab_caa_bccc_a_
(a) babb
(b) bbba
(c) baab
(d) babc
61. ba_b_aabb_a_a_bb
(a) bbaabb
(b) ababba
(c) ababab
(d) bababa
62. a_c_abb_a_bc_ab_ca
(a) cbcaaa
(b) bccab
(c) bccaac
(d) bccacb
63. cab_a_c_bc_bc_b_ab
(a) bcbbab
(b) bcbbbc
(c) acacab
(d) cbaaac
64. cccbb_aa_cc_bbbaa_c
(a) acbc
(b) baca
(c) baba
(d) acba
65. _abb_bb_a_bbab_ba
(a) bababa
(b) bbabbb
(c) ababaa
(d) aaaabb
66. ccb_c_bbc_b_cc_ccbb
(a) bccbbb
(b) bcccbb
(c) aaaaba
(d) bbbbbb
67. abca_bcaab_aa_caa_ca
(a) bbac
(b) bbaa
(c) acbb
(d) acac
68. b_b_bb_bbb_bb_b
(a) bbbbba
(b) bbaaab
(c) ababab
(d) aabaab
Directions (Q. 69-72) : These questions are based on the information given below.
Six persons, P, Q, R, S, T and U are sitting in a circle facing one another front to front. P is sitting in front of Q. Q is sitting to the right of T and left of R. P is to the left of U and right of S.
69. Who is sitting opposite to R ?
(a) P
(b) Q
(c) S
(d) U
70. Who is sitting opposite to S?
(a) U
(b) T
(c) R
(d) Cannot be determined
71. Who is sitting between P and R?
(a) S
(b) T
(c) U
(d) Q
72. If the position of P and R are changed, who will be sitting between S and U?
(a) P
(b) R
(c) Q
(d) T
73. If HINDU is coded as 61257 and MAN is coded as 924, then INDIRA will be coded as
(a) 454626
(b) 594921
(c) 452787
(d) 884572
74. If NOCIE is written as $ @ # ? % and SCENT is written as # % 8 ^ @, the COIN will be written as
(a) #?$Q
(b) #?@%
(c) @^?$
(d) None of these
Directions (Q. 75-78) : In each of the following question, five groups of letters are given, four of them are alike in a certain way while one is different. Choose the odd one.
75.
(a) MNW
(b) OPY
(c) JKT
(d) GHO
76.
(a) PRW
(b) CDJ
(c) EFG
(d) LMH
77.
(a) ACCUSE
(b) OPAQUE
(c) ASSUME
(d) ANIMAL
78.
(a) FRY
(b) HAN
(c) CUT
(d) DOT
Directions (Q. 79-84) : Read the following data and answer the questions that follow Six compounds are being tested for possible use in a new anti-poison, “Sweet ‘N’ Deadly”.
(i) U is sweeter than V and more deadly than Z.
(ii) V is sweeter than Y and less deadly than Z.
(iii) W is less sweet than X and less deadly than U.
(iv) X is less sweet an more deadly than Y.
(v) Y is less sweet and more deadly than U.
(vi) Z is sweeter than U and less deadly than W.
79. Which is the sweetest?
(a) U
(b) W
(c) X
(d) Y
80. Which of the following is/are both sweeter and more deadly than V?
(a) U only
(b) W only
(c) Z only
(d) U and Z only
81. Which of the following adds no new information about sweetness to the statements that precede it ?
(a) (i)
(b) (iii)
(c) (iv)
(d) (v)
82. Which of the following is/are sweeter than Y and more deadly than W?
(a) U only
(b) V only
(c) Z only
(d) U and V only
83. Which is the last deadly ?
(a) U
(b) V
(c) W
(d) Y
84. Which is the most deadly ?
(a) Z
(b) W
(c) U
(d) X
85. In a row of trees, one tree is fifth from either end of the row. How many trees are there in the row ?
(a) 6
(b) 7
(c) 8
(d) 9
Directions (Q. 86-91) : In the following passage, there are blanks which have been numbered. For each blank, four words have been suggested against the number below the passage. Choose the most appropriate word for each blank.
I want to avoid violence. Non-violence …(86)… the first article of my faith. It is also the …(87)… article of my creed. But I had to …(88)… my choice. I had either to submit …(89)… a system which I considered …(90)… done irreparable harm to my country, …(91)… incur the risk of the mad fury of my people bursting forth, when they get the truth from my lips.
86.
(a) was
(b) be
(c) is
(d) being
87.
(a) last
(b) common
(c) simple
(d) unique
88.
(a) make
(b) select
(c) prepare
(d) do
89.
(a) over
(b) in
(c) against
(d) to
90.
(a) is
(b) was
(c) had
(d) has
91.
(a) nor
(b) but
(c) or
(d) and
Directions (Q. 92-94) : Find out the part which has an error in the following sentences. If there is no error, the answer is (d).
92. A series of lectures (a) / of Indian philosophy (b)/ are arranged by the University. (c) / No error (d)
93. The house with all its (a) / furniture and exotic plants (b) / were sold for Rs 50000. (c) / No error (d)
94. The teacher asked the students (a) / if everyone of them were interested in (b) / going on an excursion. (c) / No error (d)
Directions (Q. 95-97) : Choose the alternative which best express the meaning of the given idiom/ phrase.
95. To case pearls before a swine
(a) To spend recklessly
(b) To spend a lot of money on the unkeep of domestic hogs
(c) To waste money over trifles
(d) To offer to a person a thing which he cannot appreciate
96. A chip off the old block
(a) A piece of wood
(b) An old friend
(c) Characteristics f one’s ancestors
(d) A good bargain
97. To smell a rat
(a) To detect bad smell
(b) To misunderstand
(c) To suspect a trick or deceit
(d) To see hidden meaning
Directions (Q. 98-100) : Choose the alternative which is most nearly similar in meaning to the word given in capitals.
98. IDENTIFY
(a) Picture
(b) Envision
(c) Notice
(d) Recognize
99. RETICENCE
(a) Reserve
(b) Sincerity
(c) Frankness
(d) Generosity
100. CONCEAL
(a) Steal
(b) Hide
(c) Avoid
(d) Keep
101. Which state has smallest land area ?
(a) Goa
(b) Nagaland
(c) Sikkim
(d) Tripura
102. The climate of India is mainly tropical because
(a) of the locate of the Himalayas in its North
(b) major part of India lies within the tropics
(c) of the overpowering influence of India Ocean
(d) of the seasonal influence of jet streams
103. The Chief Minister of Union Territory where such a set up exists, is appointed by the
(a) President
(b) Prime Minister
(c) Lt. Governor
(d) Majority party in Legislature
104. Which one of the following does not constitute the electoral college for electing the President of India?
(a) Elected members of Rajya Sabha
(b) Elected members of Lok Sabha
(c) Elected members of the Legislative Assembly of each state
(d) Elected members of the Legislative Council
105. Who was known as the ‘Liberator of the Press’?
(a) Bentick
(b) Hastings
(c) Metcalfe
(d) Macaulay
106. Who was responsible for the Introduction of English as the official language in India?
(a) Lord William Bentinck
(b) Sir Charles Wood
(c) Marquess of Dalhousie
(d) Allan Octavian Hume
107. Ram Prasad Bismil was associated with
(a) Kakori Conspiracy Case
(b) Alipore Bomb Case
(c) Meerut Conspiracy Case
(d) Kanpur Conspiracy Case
108. Who wrote Tughluqnamah ?
(a) Raskhan
(b) Amir Khusrau
(c) Isami
(d) Malik Mohammad Jaisi
109. Among the following which planet takes maximum time for one revolution around the Sun ?
(a) Earth
(b) Jupiter
(c) Mars
(d) Venus
110. Which of the following is not a provision of the Charter Act of 1853 ?
(a) Under this Act, a Legislative Council for India was created
(b) Governor General was given the power to veto the Bills passed by the Legislative Council
(c) A provision was made for an open competitive examination for recruitment to Indian Civil Services
(d) None of the above
111. The shortest day I Australia will be on
(a) June 21
(b) December 22
(c) September 23
(d) March 21
112. The sun reaches its maximum angular distance from the equator at the
(a) zenith
(b) solstice
(c) equinox
(d) noontime
113. Which of the following gases is most predominant in the Sun ?
(a) Helium
(b) Hydrogen
(c) Nitrogen
(d) Ozone
114. Who among the following was the first woman minister of a state ?
(a) Vijayalakshmi Pandit
(b) Sarojini Naidu
(c) Rajkumari Amrit Kaur
(d) Indira Gandhi
115. The first woman film star nominated to the Rajya Sabha was
(a) Nargis Dutt
(b) Shabana Azmi
(c) Madhubala
(d) Meena Kumari
116. Which of the following pairs is not correctly matched?
(a) Reinhold Messner Computer Technology
(b) Harlow Shapley Astronomy
(c) Gregor Mendel Hereditary Theory
(d) Godfrey Hounsfield CT Scan
117. Who is the first Air Chief to receive the honour of “Marshal” ?
(a) Arjun Singh
(b) Satish Kumar Srin
(c) S. K. Mehra
(d) Yashwant Tipnis
118. Who was known as ‘Lady with Lamp’?
(a) Sarojini Naidu
(b) Joan of Arc
(c) Mother Teresa
(d) Florence Nightingale
119. The first woman to climb Mount Everest was
(a) Marie Jose Perec
(b) Florence Griffith Joyner
(c) Junko Tabei
(d) Jackie Joyner Kersee
120. Which of the following altitudes passes through India?
(a) Equator
(b) Arctic Circle
(c) Tropic of Capricorn
(d) Tropic of Cancer
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