QUANTITATIVE APTITUDE ( SSC CAPFs SI & CISF ASI EXAM, 23-06-2013 - Previous Year Paper )




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QUANTITATIVE APTITUDE

 

  1. The ratio of two numbers is 3 : 4 and their HCF is 5. Their LCM is :
    (1) 10
    (2) 60
    (3) 15
    (4) 12

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    Solution:2



  2. The value of tan 1° tan2° tan3° ...tan 89° is:
    (1) 1
    (2) 2
    (3) undefined
    (4) 0

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    Solution:1



  3. A man sold 250 chairs and had a gain equal to selling price of 50 chairs. His profit per cent is :
    (1) 20%
    (2) 25%
    (3) 50%
    (4) 15%

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    Solution:2



  4. A can do as much work as B and C together can do. A and B can together do a piece of work in 9 hours 36 minutes and C can do it in 48 hours. The time (in hours) that B needs to do the work alone, is :
    (1) 18
    (2) 24
    (3) 30
    (4) 12

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    Solution:2



  5. A solid right circular cylinder and a solid hemisphere stand on equal bases and have the same height. The ratio of their whole surface areas is:
    (1) 3 : 2
    (2) 3 : 4
    (3) 4 : 3
    (4) 2 : 3

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    Solution:3



  6. If area of an equilateral triangle is a and height b, then value of  b2/a is:

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    Solution:3


  7. The batting average for 30 finings of a cricket player is 40 runs. His highest score exceeds his lowest score by 100 runs. If these two innings are not included, the average of the remaining 28 innings is 38 runs. The lowest score of the player is :
    (1) 15
    (2) 18
    (3) 20
    (4) 12

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    Solution:2


  8. An article was sold at 16% gain. Had it been sold for 2200 more, the gain would have been 20%. Then the cost price of the article is :
    (1) 5000
    (2) 4800
    (3) 4500
    (4) 5200

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    Solution:1



  9. From the top of a hill 200 m high, the angle of depression of the top and the bottom of a tower are observed to be 30° and 60°. The height of the tower is (in m) :

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    Solution:3



  10. A copper sphere of diameter 18 cm is drawn into a wire of diameter 4 mm. The length of the wire, in metre, is :
    (1) 2.43
    (2) 243
    (3) 2430
    (4) 24.3

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    Solution:2



  11. Triangle PQR circumscribes a circle with centre 0 and radius r cm such that LPQR = 90°. If PQ = 3 cm, QR = 4 cm, then the value of r is :
    (1) 2
    (2) 1.5
    (3) 2.5
    (4) 1

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    Solution:4




  12. Show Answer

    Solution:3



  13. Water flows at the rate of 10 metres per minute from a cylindrical pipe 5 mm in diameter. How long it lake to fill up a conical vessel whose diameter at the base is 30 cm and depth 24 cm ?
    (1) 28 minutes 48 seconds
    (2) 51 minutes 12 seconds
    (3) 51 minutes 24 seconds
    (4) 28 minutes 36 seconds

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    Solution:1



  14. Three circles of equal radius 'a' cm touch each other. The area of the shaded region is :


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    Solution:4



  15. If x = a- b, y = b- c, z = c- a, then the numerical value of the algebraic expression x3 + y3+ z3 - 3xyz will be
    (1) a+ b + c
    (2) 0
    (3) 4 (a + b+ c)
    (4) 3 abc

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    Solution:2



  16. The linear equation such that each point on its graph has an ordinate four times its abscissa is :
    (1) y+ 4x= 0
    (2) y= 4x
    (3) x = 4y
    (4) x + 4y = 0

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    Solution:2



  17. A godown is 15 m long and 12 m broad. The sum of the areas of the floor and the ceiling is equal to the sum of areas of the four walls. The volume (in m3) of the godown is:
    (1) 900
    (2) 1200
    (3) 1800
    (4) 720

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    Solution:2



  18. 3 men and 7 women can do a job in 5 days, while 4 men and 6 women can do it in 4 days. The number of days required for a group of 10 women working together, at the same rate as before, to finish the same job is :
    (1) 30
    (2) 36
    (3) 40
    (4) 20

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    Solution:4


  19. The value of

    (1) 4.8484
    (2) 4.8694
    (3) 4.8884
    (4) 4.8234

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    Solution:3



  20. A shopkeeper marked the selling price of his goods in such a way that after giving a discount of 10% he gains 17%. How much per cent above the cost price is the marked price?
    (1) 36%
    (2) 27%
    (3) 30%
    (4) 40%

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    Solution:3



  21. One of the factors of the expression

    (1) 4x+ √3
    (2) 4x+ 3
    (3) 4x - 3
    (4) 4x - √3

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    Solution:4



  22. On a journey across Kolkata, a taxi averages 50 km per hour for 50% of the distance, 40 km per hour for 40% of it and 20 km per hour for the remaining. The average speed, in km/hour, for the whole journey is :
    (1) 42
    (2) 40
    (3) 35
    (4) 45

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    Solution:2



  23. A man ordered 4 pairs of black socks and some pairs of brown socks. The price of a black socks is double that of a brown pair. While preparing the bill the clerk interchanged the number of black and brown pairs by mistake which increased the bill by 50%. The ratio of the number of black and brown pairs of socks in the original order was :
    (1) 2 : 1
    (2) 1 : 4
    (3) 1 : 2
    (4) 4 : 1

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    Solution:2



  24. In the following figure, AB be diameter of a circle whose centre is 0. If ∠AOE = 150°, ∠DAO = 51° then the measure of ∠CBE is :

    (1) 115°
    (2) 110°
    (3) 105°
    (4) 120°

    Show Answer

    Solution:3
    (3)



  25. If the square of the sum of two numbers is equal to 4 times of their product, then the ratio of these numbers is :
    (1) 2 : 1
    (2) 1 : 3
    (3) 1 : 1
    (4) 1 : 2

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    Solution:3



  26. If a2 + b2 = 5ab, then the value of

    (1) 32
    (2) 16
    (3) 23
    (4) -23

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    Solution:3



  27. In a big garden 60% of the trees are coconut trees, 25% of the number of coconut trees are mango trees and 20% of the number of mango trees are apple trees. If the number of apple trees are 1500, then the number of trees in the garden is :
    (1) 48000
    (2) 50000
    (3) 51000
    (4) 45000

    Show Answer

    Solution:2



  28. A sum of money placed at compound interest doubles itself in 5 years. It will amount to eight times of itself in :
    (1) 15 years
    (2) 12 years
    (3) 10 years
    (4) 20 years

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    Solution:1



  29. Minimum value of 4tan2θ + 9cot2θ is :
    (1) 12
    (2) 1
    (3) 6
    (4) 13

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    Solution:1



  30. If 50% of (P - Q) = 30% of (P + Q) and 9 = x% of P, then the value of x is :
    (1) 30
    (2) 25
    (3) 20
    (4) 50

    Show Answer

    Solution:2



  31. If sinθ - cosθ = 1/2 the value of sinθ + cosθ is :
    (1) - 2
    (2) ±2
    (3) √7/2
    (4) 2

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    Solution:3



  32. If cosecθ - cotθ = 7/2 , the value of cosecθ is :

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    Solution:3



  33. (1) 950
    (2) 730
    (3) 650
    (4) 970

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    Solution:4



  34. A single discount equivalent to the following three successive discounts of 30%, 20% and 10% is given by :
    (1) 49.6%
    (2) 50.60%
    (3) 49.40%
    (4) 50.40%

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    Solution:1



  35. The greatest among the following numbers

    is :

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    Solution:4



  36. The areas of two similar triangles ABC and DEF are 20 cm2 and 45 cm2 respectively. If AB = 5 cm, then DE is equal to :
    (1) 6.5 cm
    (2) 7.5 cm
    (3) 8.5 cm
    (4) 5.5 cm

    Show Answer

    Solution:2



  37. In a triangle ABC, BC is produced to D so that CD = AC. If ∠BAD=111° and ∠ACB = 80°. then the measure of ∠ABC is :
    (1) 31°
    (2) 33°
    (3) 35°
    (4) 29°

    Show Answer

    Solution:4



  38. In ΔABC, ∠A + ∠B = 145° and ∠C + 2∠B = 180°, State which one of the following relations is true ?
    (1) CA = AB
    (2) CA < AB
    (3) BC > AB
    (4) CA > AB

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    Solution:4



  39. If the volumes of two right circular cones are in the ratio 4 : 1 and their diameters are in the ratio 5 : 4 then the ratio of their heights is :
    (1) 25 :16
    (2) 25 : 64
    (3) 64 : 25
    (4) 16 : 25

    Show Answer

    Solution:3



  40. The proportion of acid and water in three samples is 2 : 1, 3 : 2 and 5 : 3. A mixture containing equal quantities of all three samples is made. The ratio of water and acid in the mixture is :
    (1) 120: 133
    (2) 227: 133
    (3) 227: 120
    (4) 133 : 227

    Show Answer

    Solution:2



  41. A train 270 metre long is running at a speed of 36 km per hour, then it will cross a bridge of length 180 metres in :
    (1) 40 sec
    (2) 45 sec
    (3) 50 sec
    (4) 35 sec

    Show Answer

    Solution:2



    Directions (42-45) : The following table shows the productions of food-grains (in million tons) in a state for the period 1999 - 2000 to 2003 - 2004. Read the table and answer the questions.

  42. In 2002 - 2003, the percentage increase in the production of barley as compared to the previous year was :
    (1) 14.20
    (2) 17.85
    (3) 18.75
    (4) 7.90

    Show Answer

    Solution:3



  43. During the period 1999 - 2000 to 2003 - 2004, x per cent of the total production is production of wheat. The value of x is about :
    (1) 12.6
    (2) 37.4
    (3) 37.8
    (4) 20.2

    Show Answer

    Solution:2



  44. In the year 2003 - 2004, the increase in production was maximum over the previous year for :
    (1) Rice
    (2) Barley
    (3) Other cereals
    (4) Wheat

    Show Answer

    Solution:1



  45. The difference of average production of rice and the average production of barley over the years is :
    (1) 50
    (2) 60
    (3) 80
    (4) 40

    Show Answer

    Solution:4



    Directions (46-50) : Production of three different flavours soft drinks X, Y and Z for a period of six years has been expressed in the following graph. Study the graph and answer the questions.

  46. The approximate decline in the production of flavour Z in 2010 as compared to the production in 2008 is :
    (1) 33%
    (2) 22.5%
    (3) 42%
    (4) 25%

    Show Answer

    Solution:1



  47. The average annual production was maximum in the given period for the flavour:
    (1) Y only
    (2) Z only
    (3) X and Z
    (4) X only

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    Solution:1



  48. What percent of the total production of flavour X in 2005 and 2006 combined is the total production of flavour Z in 2007 and 2008 combined ?
    (1) 102.25
    (2) 115.57
    (3) 133.33
    (4) 96.67

    Show Answer

    Solution:3


  49. The percentage of rise/fall in production from the previous year is maximum for the flavour Y in this year :
    (1) 2007
    (2) 2008
    (3) 2009
    (4) 2006

    Show Answer

    Solution:1



  50. The difference (in lakh bottles) between the average production of flavour X in 2005, 2006, 2007 and the average production of flavour Y in 2008, 2009 and 2010 is :
    (1) 2.4
    (2) 0.5
    (3) 1.5
    (4) 5

    Show Answer

    Solution:4




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