SSC CGL 2013 MATH MAINS EXAM ANS KEY TEST FORM NO 223 MN 4 Due to lack of time there may be some error sign and other so neglect it. 1. Find the value of √30+√30+√30+……….. ANS. 6 2. The odd term in the sequence. 0,7,26,63,124,217, is Ans. 217 3. If men can do a piece of work in x days, then the number of days in which y men can do the same work is Ans. X2/Y days 4. Three perons undertake to complete a piece of work for Rs. 1200. The first person can complete the work in 8 days, second person in 12 days and third person in 16 days. They complete the work with the help of a fourth person in 3 days. What does the fourth person get ? Ans. 225 5. Two workers A and B working together completed a job in 5 days. If A worked twice as efficiently as he actually did and B worked 1/3 as efficiently as he actually did, the work would have been completed in 3 days. To complete the job alone, A would require 25/4 days 6. A can do a piece of work in 20 days and B in 30 days. They work together for 7 days and then both leave the work. Then C alone finishes the remaining work in 10 days. In how many days will C finish the full work? Ans.24 days 7. When 335 is added to 547, the result is 8B2. 8B2 is divisible by 3. What is the largest possible value of A? Ans.4 8. The greatest 4-digit number exactly divisible by 10,15,20 is Ans. 9960 9. Which one of the numbers is divisible by 25 ? Ans. 303375 10. Find the sum of (1- 1/n+1) + (1- 2/n+1) + (1- 3/n+1)……… (1 – n /n+1) Ans ½ n . 11.In a class there are ‘z’ students. Out of them ‘x’ are boys. What part of the class is composed of girls? Ans. 1 – x / z 12. If the students of 9th class are arranged in rows of 6,8,12 or 16, no student is left behind. Then the possible number of students in the class is Ans. 96 13. The unit digit in 3*38*537*1256 is Ans. 8 14. If a clock strikes appropriate number of times at each hour, how many times will it strike in a day? Ans.156 15. The third proportional of 12 and 18 is Ans. 27 16. Ram got twice as many marks in English as in Science. His total marks in English Science and Maths are 180. If ratio of his marks in English and Maths is 2:3, what are his marks in Science? Ans. 30 17. Three number are in the ratio 2:3: 4. If the sum of their squares is 1856, then the numbers are Ans. 16,14and 32 18. If x runs are scored by A, y runs by B and z runs by C, then x : y = y : z = 3 : 2. If total number of runs scored by A,B and C is 342, the runs scored by each would be respectively Ans. 162, 108, 72 19. Rs. 900 is divided among A, B, C; the division is such that ½ of A’s money = 1/3rd Of B’s money = 1/4th of C’s money. Find the amount received by A, B, C. Ans 200, 300, 400 20. If Rs. 126.50 is divided among A, B, and C in the ratio of 2 : 5 : 4, the share of B exceeds that of A by Ans. Rs. 34.50 21 The average of first three numbers is double of the fourth number. If the average of all the four numbers is 12, find the 4th number. Ans. 48/7 22. Sunil comletes a work in 4 days, whereas Dinesh completes the work in 6 days. Ramesh works 3/2 times as fact as Sunil. The three together can complete the work in Ans.. 23/9 days 23. A farmer can plough a field working 6 hours per day in 18 days. The worker has to work how many hours per day to finish the same work in 12 days? Ans. 9 24. Two successive discounts of a% and b% on the marked price of an article are equivalent to the single discount of Ans. (a + b - ab/100)% 25. A tradesman marks his goods 30% more than the cost price. If he allows a discount of 25/4 % then his gain percent is Ans. 21 7/8 % 26. A shopkeeper purcheased a chair marked at Rs. 600 at two successive discounts of 15% and 20% respectively. He spend Rs. 28 on transportation and sold the chair for Rs. 545. His gain percent was Ans. 25 % 27. The marked price of a piano was Rs. 15000. At the time of sale, there were successive discounts of 20%, 10% and 10% respectively on it. The sale price was Ans Rs. 9720 28. Gita buys a plot of land for Rs. 96000. She sells 2/5 of it at a loss of 6%. She wants to make a profit of 10% on the whole transaction by selling land. The gain % on the remaining land is Ans. 20 2/3 29. An article is sold at a gain of 15%. Had it been sold for Rs. 27 more, the profit would have been 20%. The cost price of the article is Ans. Rs. 540 30. On selling 17 balls at Rs 720, there is a loss equal to the cost price of 5 balls. The cost price (in Rs) of a ball is Ans Rs.60 31. Sourav purchased 30 Kg of rice at the rate of Rs 10 per kg and 35 kg at the rate of Rs 11 per kg. He mixed the two. At what price per kg (in Rs) should he sell the mixture to make a 30% profit in the transaction ? Ans 13.7 32. A number increased by 22 ½ % gives 98. The number is Ans 80 33.Two items A and B are sold at a profit of 10% and 15% respectively. If the amount of profit received is the same, then the cost price of A and B may be Ans Rs 3,000, Rs 2,000 34. In an examination A got 25% marks more than B, B got 10% less than C and C got 25% more than D. If D got 320 marks out of 500, the marks obtained by A were Ans 450 35. If the average of 6 consecutive even numbers is 25, the difference between the largest and the smallest number is Ans 10 36. A train goes from Ballygunge to Sealdah at an average speed of 20 km/hour and comes back at an average speed of 30 km/hour. The average speed of the train for the whole journey is Ans 24 km/hr 37. The arithmetic mean of 100 observations is 24, 6 is added to each of the observations and then each of them is multiplied by 2.5. Find the new arithmetic mean. Ans 75 38. Sachin Tendulkar has a certain average for 11 innings. In the 12th innings he scores 120 runs and thereby increases his average by 5 runs. His new average is 65 Ans 65 39. The average of 11 results is 50. If the average of the first six results is 49 and that of the last six is 52 the sixth result is Ans 56 By selling 25 metres of cloth a trader gains the selling price of 5 metres of cloth. The gain of the trader in % is Ans 25 41. A sells a suitcase to B at 10% profit. B sells it to C at 30% profit. If C pays Rs 2,860 for it, then the price at which A brought it is Ans Rs 2,000 42.What sum will give Rs 244 as the difference between simple interest and compound interest at 10% in 1 ½ years compounded half yearly ? Ans Rs 32,000 43. A sum of Rs 3,200 invested at 10% p.a. compounded quarterly amounts to Rs 3,362. Compute the time period. Ans ½ years 44. If a sum of money compounded annually becomes 1.44 times of itself in 2 years, then the rate of interest per annum is Ans 20% 45. A lawn is in the form of a rectangle having its breadth and length in the ratio 3:4 . The area of the lawn is 1/12 hectare. The breadth of the lawn is Ans 25 metres 46. A right circular cone is 3.6 cm high and radius of its base is 1.6 cm. It is melted and recast into a right circular cone with radius of its base as 1.2 cm. Then the height of the cone (in cm) is Ans 6.4 47. The area of a rectangle is thrice that of a square. The length of the rectangle is 20 cm and the breadth of the rectangle is 3/2 times that of the side of the square. The side of the square, in cm, is Ans 10 48. Three sets of 40,50 and 60 students appeared for an examination and the pass percentage was 100,90 and 80 respectively. The pass percentage of the whole set is Ans 88 2/3 49. A certain distance is covered by a cyclist at a certain speed. If a jogger covers half the distance in double the time, the ratio of the speed of the jogger to that of the cyclist is Ans 1:4 50. The distance between places A and B is 999 km. An express train leaves place. A at 6 am and runs at a speed of 55.5 km/hr. The train stops on the way for 1 hour 20 minutes. It reaches B at Ans 1.20 am 51. If a walks from his house to school at the rate of 4 km per hour, he reaches the school 10 minutes earlier than the scheduled time, However, if he walks at the rate of 3 km per hour, he reaches 10 minutes late. Find the distance of his school from his house. Ans 4 km 52.Two trains are running 40 km/hr and 20 kn/hr respectively in the same direction. The fast train completely passes a man sitting in the slow train in 5 seconds. The length of the fast train is Ans 27 7/9 m 53. The compound interest on Rs 5,000 for 3 years at 10% p.a. will amount to Ans Rs 1,655 54. If a right circular cone of height 24 cm has a volume of 1232 cm3, then the area (in cm2) of curved surface is Ans 550 55. The diameter of a circular wheel is 7 m. How many revolutions will it make in travelling 22 km? Ans 1000 56. The area of an equilateral triangle is 9√3 m2 . The length (in m) of the median is ……………… Ans 3√3 57. If each edge of a cube is inread by 50%, the percentage increase in surface area is Ans 125 % 58. How many tiles, each 4 decimeter square, will be required to cover the floor of a room 8 m long and 6 m broad ? Ans 300 59. If the surface area of two speres are in the ratio 4 : 9, then the ratio of their volumes will be Ans. 8 : 27 60. If x = y = 333 and z = 334, then the values of x3 + y3 z3 – 3xyz is Ans. 1000 61. If x-a2 / b+c) + (x-b2 /c+a) + (x-c2/a+b ) = 4 (a+b+c), then x is equal to Ans. (a+b+c)2 62. If h, c, v are respectively the height, cured surface area and volume of a right circular cone, then the value of 3pievh3 c2h2 + 9v2 is Ans is 0 63. The volume of the conical tents is 1232 cu. M and the area of its base is 154 sq. m Find the length of the canvass required to build the tent, if the canvass is 2 m in width. Ans . 275 m 64. Assume that a drop of water is spherical and its diameter is one-tenth of a cm. A conical glass has a height equal to the diameter of its rim. If 32,000 drops of water fill the glass completely, then the height of the glass, in cm, is Ans. 4 65. The total number of spherical bullets, each of diameter 5 decimeter, that can be made by utilizing the maximum of a rectanglular block of lead with 11 metre length, 10 meter breadth and 5 metre width is Ans. Equal to 8400 66. The diagonals of a rhombus are 12 cm and 16 m respectively. The length of once side is Ans. 10 cm 67. A rectangular block of metal has dimensions 21 cm, 77 cm and 24 cm. The block has been melted into a sphere. The radius of the sphere is …… Ans . 21 cm. 68. If x = 3√5 + 2, then the value of x3 – 6 x2 + 12 x – 13 is Ans 0 69. A tower standing on a horizontal plane subtends a certain angle at a point 160 m apart from the foot of the tower. On advacing 100 m towards it, the tower is found to subtend an angle twice as before. The height of the tower is Ans 80 m 70. Angles A, B, C are three angles of a triangle. If A-B = 15, B-C = 30 , then Angle A, B, C, are Ans 80, 65, 35, 71. If ABC is an equilateral triangle and D is a point on BC such that AD┴BC, then Ans. AB : BD = 2 : 1 72. Triangle ABC is an isosceles triangle and AB = AC = 2a unit, BC = a unit. Draw AD┴BC, and find the length of AD. Ans. √15 / 2 a unit 73. All sides of a quadrilateral ABCD touch a circle. If AB = 6 cm, BC = 7.5 cm, CD = 3 cm, then DA is Ans. 1.5 cm. 74. If (x – a) (x – b) = 1 and a – b + 5 = 0 , then the value of (x-a)3 - 1 / (x – a)3 is Ans. 140 75. If √ x = √3 - √5, then the value of x2-16x + 6 is Ans 2 76. The value of √2 3√4 √2 3√4 √2 3√4…………. Ans 2 77. The value of { 3√2 / (√3 + √6) - 4√3 / √6 +√2) + √6 / (√2 + √3) } is Ans 0 78. If a2 + b2 + c2 = 2 (a –b –c) – 3, then the value of 4a – 3b + 5 a is Ans 2 79. If 2x + 2/x = 3 , then the value of x3 + 1/x3 + 2 is Ans 7 /8 80. Out of the given responses, one of the factors of (a2 – b2)3 + ( b2 – c2)3 + (c2 – a2)3 is Ans. (a + b) (a – b) 81. An isosceles triangle ABC is right-angled at B.D is a point inside the triangle ABC. P and Q are the feet of the perpendiculars drawn from D on the sides AB and AC respectively of triangle ABC. If AP = a cm, AQ = b cm and angle BAD = 15 , sin 75 = Ans √3a / 2 b 82. Each interior angle of a regular octagon in radians is Ans 3 pie /4 83. D and E are two points on the sides AC and BC respectively of triangle ABC such that DE = 18 cm, CE = 5 and Angle DEC = 90 . If Tan angle ABC = 3.6, then AC : CD = Ans . ***** 84. D is a point on the side BC of a triangle ABC such that AD ┴ BC. E is a point on AD for which AE : ED = 5 : 1. If angle BAD = 30 and tan ( angle ACD) = 6 tan ( angle DBE), then Angle ACB = Ans. 45 degree 85. If sin x + cos x = √2 cos x, then the value of (cos x – sin x) is Ans. √2 sin x 86. In a right-angled triangle, the product of two sides is equal to half of the square of the third side, i.e., hypotenuse. One of the acute angles must be Ans. 45 degree 87. If two concentric circles are of radii 5 cam and 3 cm, then the length of the chord of the larger circle which touches the smaller circle is Ans. 8 cm 88. Inside a square ABCD, triangle BEC is an equilateral triangle. If CE and BD interest at O, then angle BOC is equal to Ans 75 degree 89. A point D is taken from the side BC is a right-angled triangle ABC, where AB is hypotenuse. Then Ans. AB2 + CD2 = BC2 + AD2 90. Let C be a point on a straight line AB. Circles are drawn with diameters AC and AB. Let P be any point on the circumference of the circle with diameter AB. If AP meets the other circle at Q then Ans. QC║PB 91. Sin A / 1 + cos A + sinA / 1-cos A is ( 0 < A < 90) Ans. 2 cosec A 92. If r sin x = 1, r cos = √3, then the value of (√3 tan x +1) is Ans. 2 93. In a frequency distribution, ogives are graphical representation of Ans. Cumulative frequency 94. If x sin 45 = y cosec 30, then x4 / y4 is equal to Ans. 43 95. The Angle of elevation of a tower from a distance 50 m from its foot is 30 degree. The height of the tower is Ans. 50 / √3 m 96. ABCD is a rectangle where the ratio of the lengths of AB and BC is 3 : 2. If P is the mid-point of AB, then the value of sin angle CPB is Ans 4/5 97. What is the annual production of wheat ? Ans 2750 tonnes 98 The average Kharif production of the given years is Ans. 4 million tonnnes 99. Averge number of men per interval who participated in this survey is Ans. 214 100. Given is a line graph showing the number of accident in a city during the first 6 months of 1999. The decrease % of accidents from May to June is Ans. 15 5/8%
Posted on: Mon, 30 Sep 2013 06:20:12 +0000
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