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61. A does half as much work as B in three-fourths of the time. If together they take 18 days to complete a work, how much time shall B take to do it?
(a) 30 days
(b) 66 days
(c) 40 days
(d) 35 days
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62. Two trains A and B start simultaneously in the opposite direction from two points A and B and arrive at their destinations 9 and 4 hours respectively after their meeting each other. At what rate does the second train B travel if the first train travels at 80 km/hr.
(a) 120 Km./hour
(b) 60 Km./hour
(c) 80 Km./hour
(d) 100 Km./hour
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63. A mixture contains alcohol and water in the ratio of 12:5. On adding 14 litres of water, the ratio of alcohol to water becomes 4:3. The quantity of alcohol in the mixture is
(a) 18 liters
(b) 42 liters
(c) 26 liters
(d) 30 liters
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64. The most general solution of the equation tan 5θ = cot 2θ is:
(a)
(b)
(c)
(d)
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65. If a is a small and positive number, then the equation x – a = π/2 sin2x has:
(a) Two real roots
(b) Three real roots
(c) One real root
(d) No real root
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66. The base of a triangle is fixed. Then the locus of the vertex when one base angle is double the other is:
(a) y2 + 3x2 + 2ax + a2 = 0
(b) y2 – 3x2 – 2ax + a2 = 0
(c) y2 + 3x2 – 2ax + a = 0
(d) y2 – 3x2 + 2ax + a = 0
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67. ABCD is a square whose side is a. If AB and AD are taken as axes, then the equation of the circle circumscribing the square is:
(a) x2 + y2 = a(x -y)
(b) x2 + y2 = (x + y)
(c) x2 – y2 = a(x – y)
(d) x2 + y2 = a(x + y)
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68. The number of numbers that can be formed with the digits 1, 2, 3, 4, 3, 2 and 1 so that the odd digits always occupy the odd places is:
(a) 18
(b) 16
(c) 20
(d) 22
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69. Find three numbers in G.P., whose sum is 19 and whose product is 216.
(a) 4, 5, 7
(b) 4, 6, 9
(c) 4, 5, 10
(d) 47, 10 70
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70. In how many ways can 5 prizes be given away to 4 boys, when each boy is eligible for all the perizes?
(a) 625 ways
(d) 20 ways
(c) 81 ways
(d) 1024 ways
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71. Which of the following is not among the five Sustainable Development Goals (SDGs) that the Government of Himachal Pradesh seeks to achieve by 2022?
(a) To reduce infant mortality rate (IMR) from 35 to 20
(b) To reduce the drop out rate upto zero in primary and middle level schools
(c) To increase the ratio of girls from 909 to 940 per 1000 boys in the 0-6 years category
(d) To enhance the forest cover in the state to 30% of its geographical area
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72. The Government of Himachal Pradesh has launched ‘Doodh Ganga Scheme’ for dairy and related products in collaboration with which of the following?
(a) IDBI
(b) NABARD
(c) ADB
(d) IMF
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73. Which of the following combination is not correct?
(a) Pabbar Valley : Chanshal Range
(b) Baspa Valley : Chung Shakhago pass
(c) Kiarda Doon Valley : Dharti Range
(d) Saproon Valley : Bandla Range
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74. Match list – I and list – II and select the correct answer from the codes given below:
| List-I | List – II |
| (i) Gyephang | (A) Kinnaur |
| (ii) Zorkanden | (B) Chamba |
| (iii) Pir Panjal | (C) Shimla |
| (iv) Indrasan | (D) Lahaul & Spiti |
| (E) Kullu |
(a) B D E A
(b) C D B E
(c) D A B E
(d) D A B C
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75. Which of the following combination is correct?
(a) Bhaba Pass – Kinnaur
(b) Cheni Pass – Kullu
(c) Hamta Pass – Lahaul
(d) Shingor pass – Shimla
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76. Water Board, in which of the following valley the underground water is As per the study of Central Water Board, in which of the following valley being over exploited and is receding at a very fast rate?
(a) Kala Amb Valley Sirmaur
(b) Indora Valley, Kangra
(c) Hum Valley, Unal
(d) Balh Valley, Mandi
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77. The Shivalik hills are believed to have been inhabited by which of the following tribe during the prevedic period?
(a) Dasas
(b) Kinners
(c) Kiratas
(d) Nagas
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78. Which of the following is not the kind of marriage in Himachal Pradesh?
(a) Darosh, Dab Dhab
(b) Thagchod-pat
(c) Jhindphook
(d) Phaktun
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79. ‘Chiri’, ‘Balu’, ‘Chak’ and ‘Phuli’ are the kinds of which of the following?
(a) Dress
(b) Ornaments
(c) Traditional Songs
(d) Folk Dances
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80. Built in Shikhra style ‘Trilokinath’, ‘Panchvaktra’, ‘Bhutnath’ and ‘Ardhnarishwar’ are the most famous temples of which of the following town?
(a) Udaipur
(b) Bajaura
(c) Mandi
(d) Kangra
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