Gurudwara Road Model Town, Hisar SSC CGL Tier 2

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1 Gurudwara Road Model Town, Hisar SSC CGL Tier 2 Math Paper code: No. of Questions: 100 Max. Marks : 200 Time: 2 Hours Negative Marking : 0.5 Each question carries 2 marks Please use OMR Sheet At simple interest a sum of Rs. 64 becomes Rs in 2 years. What will Rs. 86 becomes in 4 years at the same rate? (a) Rs (b) Rs (c) Rs (d) Rs A merchant sold one-third of his goods at 10% loss. At what profit should he sell the remaining goods so as to gain 20% on selling the whole goods? (a) 5% (b)10% (c) 30% (d) 35% 3. A reduction in the price of apples enables a person to purchase 3 apples for Rs. 1 instead of for Rs What is the % reduction in price? (a) 20 (b) 25 (c) 30 (d) 4. A briefcase was sold at a profit of 10%. If its cost price was 5% less and it was sold for Rs. 7 more, the gain would have been 20%. Find the cost price of the briefcase (a) Rs. 175 (b) Rs. 200 (c) Rs. 225 (d) Rs A, B and C undertake to do a work for Rs 480. A and B together do of the work and rest is done by C alone. How much should C get? a) Rs360 b)rs 120 c)rs240 d)rs180 Pinnacle SSC CGL Coaching Centre, Gurudwara Road, Model Town, Hisar Page 1

2 6. For which of the following values of x the inequality 3(x 2 4x + 4) < x gets satisfied? (a) x > 3, x < 3 4 (b) x > 3, x < 3 4 (c) 3 4 < x < 3 (d) 3 4 x 3 7. If the incentre of an equilateral triangle lies inside the triangle and its radius is 3 cm, then the side of the equilateral triangle is a) 9 3 cm b) 6 3 cm c) 3 3 cm d) 6 cm 8. Two circles intersect at A and B. P is a point on the common chord AB extended. PS and PT are tangents from P to the two circles. Then: (a) PS = PT (b) SP 2 = PA.PB (c) Triangles SPA and PTA are similar (d) Both (a) and (b) 9. Oranges are bought at 16 for a rupee and an equal number more at 14 for a rupee. If these are sold at 20 for a rupee, find the loss or gain percent. a)25% loss b)25.3%profit c)25.6%loss d) 25.3% loss 10. A man buys 3 tables and 12 chairs for Rs He sells the tables at a profit of 20% and chairs at a profit of 10% and makes a total profit of Rs 300. At what price did he buy tables and chairs? a)rs600,rs1800 b)rs200,rs350 c) Rs800, Rs 1400 d) Can t be determined 11. Present age of Anand is 47 years and his wife's age is just 38 years. When they were married, Anand was exactly one and half as old as his wife. How many years ago they were married? (a) 15 (b) 20 (c) 25 (d) The roots of the equation (x + 3) (x 3) = 160 are: (a) ± 13 (b) 13, 13 (c) ± 12 (d) 12, A cricket player and some average for his runs made in 64 innings. In 65 th inning he could not make any score and he is out. Thus, his average decreases by 2 runs. What is his new average score? (a) 130 runs (b) 128 runs (c) 70 runs (d) 68 runs 14. If x 2 + 5y 2 + z 2 = 2y(2x + z) then which of the following statements(s) is/are necessarily true? Pinnacle SSC CGL Coaching Centre, Gurudwara Road, Model Town, Hisar Page 2

3 (A) x = 2y (B) x = 2z (C) 2x = z (a) only (A) (b) only (B) and (C) (c) only (A) and (B) (d) None of these 15. A shopkeeper purchased 25 kg. of sugar at Rs. 5 per kg. and 75 kg. of sugar at Rs. 9 per kg. He mixed the two varieties and sells the mixture at Rs. 10 per kg., find his profit percentage. (a) 11.11% (b)25% (c) 33.33% (d)100% 16. Out of a group of swans, 2 7 times the square root of the number are swimming in water while two remaining are playing on the shore. The total number of swans is: (a) 4 (b) 8 (c) 12 (d) The length of a chord of a circle is equal to the radius of the circle. The angle which this chord subtends in the major segment of the circle is equal to (a) 30 (b) 45 (b) 60 (d) The average marks obtained by 24 students of a class is 64. If the average marks of the first 6 students is 72 and that of the next 17 students is 62, find the marks obtained by the last student. (a) 50 (b)58 (c)67 (d) An article is sold for Rs. 500 and hence lost something. Had the article is sold for Rs. 700, the merchant would have gained three times the former loss. Find the cost price of the article. (a) Rs. 525 (b)rs.550 (c)rs.600 (d)rs A man sold an article at 10% loss. Had he bought it for 10% more and sold it for Rs. 20 less, he would have lost 20%. Original cost price of the article is: (a) Rs. 200 (b) Rs. 500 (c) Rs (d) Rs A merchant sold 80 dozen oranges. He sold some at 4% loss and rest at the cost price and thus losing 3 % on the whole. What is the quantity sold at loss? (a)20 dozen (b) 40 dozen (c) 50 dozen (d) 60 dozen 22. If = = then is equal to (a) 0 (b) 1 (c) 2 (d) A class of 60 students contributed Rs for a charity. If each boy has contributed Rs. 94 and each girl contributed Rs. 73, find the number of boys in the class. (a) 20 (b)30 (c)40 (d) 45 Pinnacle SSC CGL Coaching Centre, Gurudwara Road, Model Town, Hisar Page 3

4 24. If the area of a rectangle be ( ), h h a) (4 + 14) cm b) ) cm c) ( + 14) cm d) (2 + 7) cm 25. On replacing an old member of a group with a younger member, the average age of 10 members of the group remains same as it was 2 years ago. How much is the new member younger than the old one? (a) 10 years (b) 12 years (c) 15 years (d) 20 years 26. A shopkeeper allows two successive discounts on an article whose marked price is Rs.150 and selling price is Rs.105. What is first discount if second discount is 12.5%? (a) 16.67% (b)17.5% (c)20% (d)25% 27. If n is a whole number greater than 1, then ( 1) : a) 16 b) 12 c) 10 d) If + = 1, a 0 the value of a 3 + b 3 is (a) 0 (b) 1 (c) -1 (d) The length of each edge of a regular tetrahedral is 12 cm. The area (in sq.cm) of the total surface of the tetrahedron is a) b) c) d) If = =, h a) 3:2:1 b) 1:2:6 c) 1:3:6 d) 2 :4 :6 31. A sum of money is divided among 160 males and some females, in the ratio 16 : 21. Individually each male gets Rs. 4 and each female Rs. 3. The number of females is: (a) 280 (b) 198 (c) 284 (d) A sum of money placed at compound interest doubles itself in 5 years. It will amount to eight times it self in (a) 10 years (b) 12 years (c) 15 years (d) 20 years 33. A man spends of his income on food and on clothing. If he still saves Rs. 100, what is his total income? (a) Rs.20 (b) Rs. 80 (c) Rs. 400 (d)rs The simple interest and compound interest on a certain sum compounded annually for 2 years are Rs. 900 and Rs. 954 respectively. The sum is: Pinnacle SSC CGL Coaching Centre, Gurudwara Road, Model Town, Hisar Page 4

5 (a) Rs (b) Rs (c) Rs (d) Rs A person who spends 66 % of his income is able to save Rs per month. His monthly expenses are 3 (a) Rs (b) Rs (c) Rs (d) Rs The simplification of gives: (a) 0.01 (b) (c) 0.1 (d) If 8% of x is the same as 4% of y, then 20% of x is the same as: (a) 10% of y (b) 16% of y (c) 80% of y (d) 50% of y 38. Arrange the following in descending order : 4, 2, 3, 5 (a) 4 > 5 > 2 > 3 (b) 5 > 4 > 3 > 2 (c ) 2 > 3 > 4 > 5 (d) 3 > 5 > 4 > There are 81 litres pure milk in a container. One-third of milk is replaced by water in the container. Again onethird of mixture is extracted and equal amount of water is added. What is the ratio of milk to water in the new mixture? (a) 1: 2 (b) 1: 1 (c) 2: 1 (d) 4: Find the value of + + 3xy, if x+ y = 1 (a) 1 (b) 0 (c)1 (d) The daily wage is decreased by 19% and a person now gets Rs 27 per day. What was his daily wage before the decrease?. a)rs33 b)rs34 c)rs 33 d) Rs An equation whose graph passes through the origin, out of the origin, out of the given equations 2x + 3y = 2, 2x 3y = 3, -2x +3y = 5 and 2x + 3y = 0 is : (a) 2x-3y = 3 (b) -2x--+3y=5 (c) 2x+3y=0 (d) 2x+3y=2 43. An electrical contractor purchases a certain amount of wire, 10% of which was stolen. After using 85% of the Pinnacle SSC CGL Coaching Centre, Gurudwara Road, Model Town, Hisar Page 5

6 remainder, he had 47m 25cm of wire left How much wire did he purchase? a)350m b)320m c)300m d)370m 44. Two vessels A and B contain acid and water mixed in the ratio 2: 3 and 4: 3. In what ratio must these mixtures be mixed to form a new mixture containing half acid and half water? (a) 5: 7 (b) 1: 2 (c) 2: 1 (d) 7: Find the effective annual rate of 5 per cent per annum compound interest paid half yearly. a) 1.025% b)6.0625% c)5.0625% d) None of these 46. A, B, C are three points on the circumference of a circle and if = = 5 2 cm and <BAC = 90, find the radius. (a) 10 cm (b) 5 cm (c) 20 cm (d) 15 cm 47. Find the compound interest on Rs for 3 years if the rate of interest is 5% for the first year, 6% for the second year and 10% for the third year. a)rs b)rs c)rs d)rs Two circles touch each other externally at point A and PQ is a direct common tangent which touches the circles at P and Q respectively. Then <PAQ = (a) 45 (b) 90 (c) 80 (d) A and B can do a piece of work in 12 days, B and C in I5 days, A and C in 20 days. In how many days they working together will finish the work. (a) 5 days (b) 10 days (c) 12 days (d) 18 days 50. DE is a tangent to the circumcircle of ABC at the vertex A such that DE BC. If AB = 17 cm, then the length of AC is equal to (a) 16.0 cm (b) 16.8 cm (c) 17.3 cm (d) 17 cm men can complete a work in 18 days. After 6 days, 5 more men joined. In how many days the remaining work would be completed? (a) 6 days (b) 12 days (c) 8 days (d) 10 days 52. The length of radius of a circumcircle of a triangle having sides 3 cm, 4 cm and 5 cm is: (a) 2 cm (b) 2.5 cm (c) 3 cm (d) 1.5 cm 53. Find the remainder on dividing by 18. (a) 0 (b) 1 (c) 16 (d) 17 Pinnacle SSC CGL Coaching Centre, Gurudwara Road, Model Town, Hisar Page 6

7 54. If 12 men and 16 boys can do a piece of work in 5 days and 13 men and 24 boys can do it in 4 days, compare the daily work done by a man with that done by a boy? (a) 1 : 2 (b) 1 : 3 (c) 2 : 1 (d) 3 : Find the least number which when divided by 2,3,4,5 and 6 leaves remainder I in each case, but when divided by 7 leaves no remainder. (a) 60 (b)293 (c)300 (d) P and Q are centre of two circles with radii 9 cm and 2 cm respectively, where PQ = 17 cm. R is the centre of another circle of radius x cm, which touches each of the above two circles externally. If PRQ = 90, then the value of x is (a) 4 cm (b) 6 cm (c) 7 cm (d) 8 cm 57. Pipe A fills the cistern in half an hour and pipe B in 40 minutes, but owing to a crack in the bottom of the cistern it is found that pipe A now takes 40 minutes to fill the cistern. How long will B take now to fill it and how long will the crack take to empty it? a)the leak empties in 1 hour and B fills in 2 hours. b) B fills in an hour and the leak empties in 2 hours c) B fills in an hour and the leak empties in an hour d) Data inadequate 58. A box is made of 1 cm thick wood. If outer dimensions of box are 12 cm by 10 cm by 7 cm, find volume of wood used. (a) 246 cm 3 (b) 440 cm 3 (c) 616 cm 3 (d) 729 cm A tank is fitted with two taps. The first tap can fill the tank completely in 45 minutes and the second tap can empty the full tank in one hour. If both the taps are opened alternatively for one minute, then in how many hours the empty tank will be filled completely? a) 2 hours 55 minutes b) 3 hours 40 minutes c) 4 hours 48 minutes d) 5 hours 53 minutes 60. If each side of a cube is increased by 30%, then its surface area will be increased by: (a) 50% (b)51% (c) 60% (d) 69% 61. The product of two whole number is 37. The square root of the difference of numbers is: (a) 8 (b) 7.5 (c) 6 (d) 4.5 Pinnacle SSC CGL Coaching Centre, Gurudwara Road, Model Town, Hisar Page 7

8 62. In a parallelogram two adjacent sides are 33 cm and 56 cm and one diagonal is 65 cm. What is its area? (a)824 cm 2 (b)924 cm 2 (c) 1648cm 2 (d) 1848cm A spherical shell of metal has an outer radius of 9cm and inner radius of 8cm. If the metal costs Rs 1.80 per cu cm, find the cost of shell. a)rs b)rs l c)rs d)rs A jar contained a mixture of two liquids A and B in the ratio 4: 1. When 10 litres of the mixture was taken out and 10 litres of liquid B was poured into the jar, this ratio became 2: 3. The quantity of liquid A contained in the jar initially was (a) 4 litres (B) 8 litres (c) 16 litres (d) 40 litres 65. 8% of the voters in an election did not cast their votes. In this election, there were only two candidates. The winner by obtaining 48% of the total votes defeated his contestant by 1100 votes. The total number of voters in the election was: (a) (b) (c) (d) A person standing on the bank of a river finds that the angle of elevation of the top of a tower on the opposite bank is 45º. Then which of the following statements is correct? (a) Breadth of the river is twice the height of the tower (b) Breadth of the river and the height of the tower are the same (c) Breadth of the river is half of the height of the tower (d) None of these 67. The price of an article was increased by r%. Later the new price was decreased by r%. If the latest price was Re. 1, then the original price was: (a) Re. 1 b) Rs. (c) Rs. (d) 68. The numerical value of ( + ) ( ) a) 0 b) -1 c) +1 d) `If in a ABC, the medians CD and BE intersect each other at O, then the ratio of the areas of Pinnacle SSC CGL Coaching Centre, Gurudwara Road, Model Town, Hisar Page 8

9 a) 1 :6 b) 6 :1 c) 1 :12 d) 12 : Find the number in the unit place in (958) 116. a)4 b)2 c)8 d)6 71. A cube of edge 5 cm is cut into cubes each of edge of 1 cm. The ratio of the total surface area of one of the small cubes to that of the large cube is equal to : a) 1 : 125 b) 1 : 5 c) 1 : 625 d) 1 : If the volume of surface area of a sphere are numerically the same, then its radius is: a) 1 unit b) 2 units c)3untis. d) 4 units 73. Two trains 105 m and 90 m long run the speeds of 45 km/h and 72 km/h respectively in opposite directions on parallel tracks. How much time do they take to cross each other? (a) 5 sec (b) 6 sec (c) 7 sec (d) 8 sec 74. A motorboat whose speed in still water in 15 km/h goes 30 km downstream and comes back in a total 4 hours 30 min. Determine the speed of the stream. (a) 2 km/h (b) 3 km/h (c) 4 km/h (d) 5 km/h 75. The cost of ploughing trapezoid field at the rate of Rs 1.35 per square metre is Rs The difference between the parallel sides is 8 metres and the perpendicular distance between them is 24 metres. Find the length of parallel sides., a) 17m,9m b)28m,20m c)34m,26m d)can t be determined 76. Ramesh leaves his house daily at a particular time to go to his office. If he travels at 50 km/h, he reaches 5 minutes late and if travel at 60 km/h, he reaches 5 minutes early. At what speed should he travel to reach office on time? (a) km/h (b) 55 km/h (c) km/h (d)57.5 km/h 77. The curved surface area of a cylindrical pillar is 264 m 2 and its volume is 924 m 3. The ratio between its diameter and height is: (a) 7 : 6 (b) 6 : 7 (c) 3 : 7 (d) 7 : The ratio of the radius and height of a cone is 5 : 12. Its volume is cm 3. Its slant height is : 7 (a) 13 cm (b) 14 cm (c) 17 cm (d) 26 cm Pinnacle SSC CGL Coaching Centre, Gurudwara Road, Model Town, Hisar Page 9

10 79. A theft is reported to a policeman. The thief starts running and the policeman chases him. When the policeman starts chasing, the thief was at a distance of 250 metre. The thief and the policeman run at the speed of 8 km/h and 9 km/h respectively. Find the time the policeman will take to catch the thief. (a) 10 minutes (b) 15 minutes (c) 30 minutes (d) 60 minutes 80. If D, E and F are the mid-points of the sides of are equilateral triangle ABC, then the ratio of the area of triangles DEF and DCE is: (a) 1. 1 : 1 (b) 1 : 1. 1 (c) 0. 9 : 1 (d) 1 : In the given fig., which is the longest side? (a) BC (b) AB (c) AC (d) AB and AC 82. In the given fig. the value of x is (a) 10º (b) 20º c) 15º (d) 12º 83. A starts from X towards Y at 10 a.m. B starts from Y towards X at 11 a.m. If they reach their destinations at 2 p.m. and 5 p.m. respectively, at what time will they meet? Pinnacle SSC CGL Coaching Centre, Gurudwara Road, Model Town, Hisar Page 10

11 (a) p.m. (b) p.m. (c) 1.48 p.m. (d) 2.24 p.m 84. ABC is a triangle and O is the centre of its circumcircle and OBC = 22º, then BAC will be (a) 22º (b) 44º (c) 68º (d) 46º 85. A man leaves a point P and reaches the point Q in 3 hours. Another man leaves the point Q. 1 hour earlier And reaches the point P in 3 hours. Find the time in which the first man meets to the second man. a) 1 hr b)2hrs c)30 min d)can t be determined 86. In the given figure, if PQ RS, then LNM is equal to: (a) 35º (b) 40º (c) 75º (d) 80º 5 cos 5 cot 87. If cos =, 0 < <, then the value of will be: 13 2 cos ec cos 169 (a) (b) (c) (d) If 4 sin = 3 cos, then 2 sec is: 2 4(1 tan ) (a) 25/16 (b) 25/28 (c) 1/4 (d) If one of the interior angles of a regular polygon is found to be equal to (9/8) times of one of the interior angles of a regular hexagon, then the number of sides of the polygon is: Pinnacle SSC CGL Coaching Centre, Gurudwara Road, Model Town, Hisar Page 11

12 (a) 4 (b) 5 (c) 7 (d) An aeroplane when flying at a height of 3125 m from the ground passes vertically below another plane at an instant when the angles of elevation of the two planes from the same point on the ground are 30 and 60 respectively. The distance between the two planes at that instant is a) 6520 m b) 6000 m c) 5000 m d) 6250 m 91. The simplified value of ( + ) ( + tan sec ) is a) -1 b) 0 c) d) Spheres A and B have their radii 40 cm and 10 cm respectively. Ratio of surface area of A to the surface area of B is : (a) 1 : 16 (b) 4 : 1 (c) 1 : 4 (d) 16 : If one angle of a triangle is greater than each of the two remaining angles by 30º, then the angles of the traingle are: (a) 40º. 40º, 100º (b) 50º. 50º, 80º (c) 30º. 30º, 120º (d) 35º. 35º, 110º 94. A rectangular reservoir contains litres of water. If its length of breadth be 6 m and 3.5 m respectively, what is the depth of water in it? (a) 2 m (b) 5 m (c) 6 m (d) 8 m 95. PQR and LMN are similar. If 3 PQ = LM and MN = 9 cm, then QR is equal to: (a) 3 cm (b) 6 cm (c) 9 cm (d) 12 cm Pinnacle SSC CGL Coaching Centre, Gurudwara Road, Model Town, Hisar Page 12

13 Directions (96 100): Study the following information and answer the following questions: Company Year In which of the following years was the difference between the highest and the lowest sales the maximum? (a) 2004 (b) 2006 (c) (d) In the year 2008, the sales of company 2 were what percent of the sales of company 5? (a) 171 (b) 213 (c) 47 (d) In which of the following years do the sales of company 3 show the highest increase over that of the previous year? (a) 2005 (b) 2006 (c) 2007 (d) The sales of which company in 2007 show the highest increase over that in 2004? (a) 1 (b) 2 (c) 3 (d) In the year 2006, the sales of company 4 were approximately what percent of the average sales of the five companies for the year? (a) 66 (b) 94 (c) 101 (d) 104 Pinnacle SSC CGL Coaching Centre, Gurudwara Road, Model Town, Hisar Page 13