1. Mr Murmu walked 6 km to reach the station | 1 from his house, then he boarded a train whose average speed was 60 km/hr and thus reached his destination. In this way he took total 3 hours. If the average speed of the entire journey was 32 km/hr then the average speed of walking is:
(A) 3 km/hr
(B) 4.5 km/hr
(C) 4 km/hr
(D) none of the above
2. The sum of the curved surface area and total surface area of a solid cylinder is 2068 cm. If radius of its base is 7 cm, then what is the volume of this cylinder? (use pi = 22/7 )
(A) 3080 cm³
(B) 2080 cm³
(C) 2075 cm³
(D) none of the above
3. If x = sec(theta) + tan theta y = sec(theta) - tan theta then the relation between x and y is:
(A) x ^ 2 + y ^ 2 = 0
(B) x ^ 2 = y ^ 2
(C) x ^ 2 = y
(D) xy = 1
4. Two circles each of radius 36 cm are intersecting each other such that each circle is passing through the center of the other circle. What is the length of common chord to the two circles?
(A) 35sqrt(3) cm
(B) 34sqrt(3) cm
(C) 36sqrt(3) cm
(D) none of the above
5. A, B and C started a business with initial investments of Rs. 20000, Rs. 25000and Rs. 10000, respectively. After 5 months from start, A invested Rs. 4000more. After 6 months from start, C invested Rs. 8000 more. After 4 months from start, B withdrew Rs. 8000. At the end of the year, they will receive a profit of Rs. ' x' In what ratio they will share the profit?
(A) 42: 67:59
(B) 67:59:42
(C) 67: 42:59
(D) None of the above
6. What is the value of 5sin^2 (60 deg) + 7sin^2 (45 deg) +8 cos^ 2 45^ ?
(A) 45/4
(B) 4/45
(C) 49/4
(D) 4/49
7. Two train start simultaneously from two stations Ranchi and Giridih respectively towards each other on the same track. The distance between the two station is 560 km and the speed of trains are 30 and 40 km/h respectively. Simultaneously with the train, a sparrow sitting on the top of one of the train starts towards the other and reverse its direction on reaching the other train and so on. If the speed of the sparrow is 80 km/h then the distance that the sparrow flies before being crushed between the train is:
(A) 70 km
(B) 560 km
(C) 640 km
(D) 650 km
8. 3 men and 5 women together can finish a job in 3 days. Working on the same job 3 women take 5 days more than the time required by 2 men. What is the ratio of efficiency of man to a woman?
(A) 2:1
(C) 5:2
(B) 3:2
(D) 4:1
9. The ratio of milk to water in a 100 litres mixture is 2: 3. if 10 litres of this mixture are withdrawn and replaced with milk. This process is repeated 2 more times, what is the percentage of milk in final mixture?
(A) 56.26
(C) 57.27
(B) 56.86
(D) 57.86
10. ABC is an equilateral triangle. If the area of the triangle is 36√3, then what is the radius of circle circumscribing the triangle ABC?
(A) 2√(3)
(C) 4√(3)
(B) 3√(3)
(D) 6√3
11. ABC is a right-angle triangle and angle ABC = 90 degrees. BD is a perpendicular on the side AC. What is the value of BD?
(A) AD×DC
(B) BC×AB
(C) BC×CD
(D) AD×AC
12. An article is sold at 25 percent loss. If its cost price is doubled and selling price is increased by Rs. 660, then there is a profit of 20 percent. What is the original cost price of the article?
(A) Rs. 480
(C) Rs. 400
(B) Rs. 500
(D) Rs. 360
13. Average age of 7 students of a class is 28 years. Average age of first three students is 30 years. Age of fourth student is 4 years less than the age of fifth student. Ages of last two students is same and is 5 more than the average age of first three students. What is the average age of fourth and fifth student?
(A) 20 years
(C) 16 years
(B) 36 years
(D) 18 years
14. The compound interest (compounding annually) on a certain sum at the rate of 8 percent per annum for two years is Rs. 6656. What would be the simple interest on the same sum at the same rate of interest for two years?
(A) Rs 6200
(B) Rs 5200
(C) Rs 6400
(D) Rs 5400
15. Salaries of B, C, D and E are in the ratio of 2:3:4:5 respectively. Their salaries are increased by 20 percent, 30 percent, 40 percent and 50percent respectively. If the increased salary of D is Rs. 560, then what is the sum of the original salaries of B, C, D and E?
(A) Rs 1400
(B) Rs 1500
(C) Rs 1600
(D) Rs 1700
16. The slant height of a cone is 20 cm. If area of its base is 616c * m ^ 2 then what is the curved surface area of this cone? (use pi = 22/7 )
(A) 870c * m ^ 2
(B) 880c * m ^ 2
(C) 900c * m ^ 2
(D) 920c * m ^ 2
17. Which of the following is equal to sec(A) - cos A ?
(A) sin A^ * cot A
(B) cot A^ * cos A
(C) tan A^ * sin A
(D) cos A^ * sin A
18. a + b = 6 and ab = 5 then what is the value of a ^ 3 + b ^ 3 ?
(A) 116
(B) 106
(C) 136
(D) 126
19. What is the sum of all the common terms between the given series S1 and S2? S * 1 = 2, 9, 16 ,...........,632 S * 2 = 7, 11, 15 ,...........,743
(A) 7140
(B) 6750
(C) 6860
(D) 6974
20. A alone can do 2/5 of a work in 12 days. B is 25 percent more efficient than A. C alone can do the same work in 12 days less than B. D is 25 percent less efficient than C. If they all work together, then the work will be completed in how many days?
(A) 300/47
(B) 180/43
(C) 200/51
(D) 240/53
21. Select the combination of letters that when sequentially placed in the given letter series will complete the series.
db_cbd_ba_bd_bac_d
(A) adbcd
(B) bdcbd
(C) adcdb
(D) dacdb
22. Which number will replace the question mark (?) in the following series?
5, 12, 26, 54, ?
(A) 110
(B) 112
(C) 98
(D) 92
23. Three of the following four numbers are alike in a certain way and one is different. Pick the number that is different from the rest.
(A) 43
(B) 57
(C) 39
(D) 63
24. Three of the following four letter-clusters are alike in a certain way and one is different. Pick the odd one out.
(A) PQUR
(B) HLIO
(C) DBFA
(D) RSTY
25. If ABC DEED-ABCABC; where A, B, C, D & E are different digits. What are the values of D & E?
(A) D = 2 , E = 0
(B) D = 0 E = 1
(C) D = 1 E = 0
(D) D = 1 E = 2
26. Usha runs faster than Kamla, Preeti runs slower than Swati, Swati runs slower than Kamla. Who is the slowest?
(A) Kamla
(B) Preeti
(C) Usha
(D) Swati
27. Two different positions of the same dice are shown. Which number will be at the top if 6 is at the bottom?
(A) 5
(B) 2
(C) 3
(D) 4
28. Showing the women in the park, Neha said "she is the daughter of my grandfather's only son". how is Neha is related to that woman?
(A) Sister
(B) Cousin
(C) Father
(D) Uncle
29. Arrange the following words in a logical and meaningful order.
- Learn
- College
- Degree
- Admission
- Assessment
- Class
(A) 2, 1, 4, 5, 6, 3
(B) 4, 2, 1, 6, 3, 5
(C) 4, 2, 6, 1, 5, 3
(D) 5, 4, 2, 1, 6, 3
30. Two statements are given, followed by three conclusions numbered I, II and III. Assuming the statements to be true even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
Some roads are streets.
Some streets are lanes.
Conclusions:
I. No road is a lane.
II. All streets are lanes.
III. Some lanes are roads.
(A) Only conclusions II and III follow.
(B) Only conclusion I follows.
(C) Only conclusion II follows.
(D) Either conclusions I or III follows.
31. The ratio of the present age of Mitali to that of Shabnam is 4: 7. If the difference between the present age of Shabnam and the age of Mitali after 5 years will be 13 years, then what is the sum of the present ages of Mitali and Shabnam?
(A) 64 years
(B) 60 years
(C) 66 years
(D) 74 years
32. Which two signs should be changed in the following equation to make it correct? 9-3+12x8+4=11
(A) + and x
(B) + and +
(C) + and -
(D) - and +
33. In a code language, REGULAR is written as GERTRAL. How will BROTHER be written as in that language?
(A) ORBEHTS
(B) ROBSERH
(C) ORBUREH
(D) ORBSREH
34. In a parking area the total number of wheels of all the cars and motorcycle is 100 more than twice the number of parked vehicles. The number of cars parked is?
(A) 35
(B) 45
(C) 50
(D) 55
35. Select the set in which the numbers are related in the same way as are the numbers of the following set.
(8, 15, 9)
(A) (9, 12, 16)
(B) (5, 17, 11)
(C) (4, 16, 12)
(D) (7, 13, 14)