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: 00 Max. Marks : 200 Time: 2 Hours Negative Marking : 0.5 Each question carries 2 marks Please use OMR Sheet A certain number consists of two digits whose sum is 9. if the order of digits is reversed, the new number is 9 less than the original number. The original number is (a)45 b) 36 c)54 d)63 2. A number on being divided by 3 and 7 successively leaves the remainders 2 and 5 respectively. Find the sum of digits of the remainder when the same number is divided by 2. (a) 7 b) 7 c)8 d)6 3. A number being successively divided by 3,5 and 7 leaves remainders,2 and 3 respectively. What is the number? (a) 0 (6)46 (c) 57 (d) What is the greatest number that will exactly divide 48, 68,324 and 400? a) 4 b)4 c) 6 d)8 5. A man purchased a horse and a cow for Rs He sells the horse at 20% profit and the cow at 0% loss. If he gains 2% on the whole transaction, the cost price of the horse is : (a) Rs (b) Rs (c)rs.2800 (d)rs In what ratio a shopkeeper must add water to milk so that he gains 25% on selling it at cost price? (a)2:3 (b)3:2 (c)3: (d)4: 7. Two equal sums were lent at simple interest for 5 years and 4 years respectively. If interests on two sum are equal and rate of interest on the latter sum is 2% higher than the former, find the lower rate of interest. Pinnacle SSC CGL Coaching Centre, Gurudwara Road, Model Town, Hisar, Page

2 (a) 5% (b) 6% (c) 8% (d)0% 8. A can do a work in 5 days less than the time taken by B to do it. If both of them together take, h h h ( ) a) 5 b) 20 c) 25 d) In a group of 35 persons, 50% people contributed Rs. 40 each, 30% contributed Rs. 60 each and remaining persons Rs. 80 each. Find average contribution for the group. (a) Rs. 50 (b) Rs. 54 (c)rs.60 (d)rs A man bought 3 tins at Rs 50 each, 5 tins at Rs 60 each and 2 tins at Rs 65 each. What is the average price paid per tin? a)rs58 b)rs58.50 c)rs58.25 d)rs The average age of the boys in a class of 20 boys is 5.6 years. What will be the average age if 5 new boys come whose average is 5.4 years? a)5.56years b)3.36years c) 5 years d) 5.50 years 2. There are 8 litres pure milk in a container. One third of milk is replaced by water in the container. Again one third of mixture is extracted and equal amount of water is added. What is the ratio of milk to water in the new mixture? a) :2 b) : c) 2 : d) 4 : 5 3. The prices of a scooter and a television set are in the ratio 3:2. If a scooter costs Rs 6000 more than the television set, the price of the television set is: a)rs 8000 b)rs 2000 c)rs 0000 d)rs Two numbers ate respectively 37% and 30% less than a third number. What per cent is the first of the second? a)90% b)85% c)95% 3)80% 5. A man spends 50% of his income in board and lodging, 20% of the remainder in other personal necessities and 25% of the rest in charity, find his income, if he is left with Rs '. a) Rs 4000 b) Rs 8000 c) Rs 2000 d) Rs A grocer sells rice at a profit of 20% and uses a weight which is 25% less. Find his total percentage gain a)50% b)55% c)60% d) 65% 7. A cloth dealer professes to sell bed sheet at cost price, but uses a metre having a length of 80 cm only and charges for the metre. Find his gain per cent. a) 25% b)20% c) 6% d)30% Pinnacle SSC CGL Coaching Centre, Gurudwara Road, Model Town, Hisar, Page 2

3 8. A 25% hike in the price of tea forces a person to purchase 2 kg less for Rs 75. Find the original price of the tea. a)rs7 b)rs8 c)rs7.5 d)rs The true discount on a bill due 2 years hence at 5% per annum is Rs 5. Find the amount of the bill. a) Rs 85 b)rs 56 c)rs58 d)rs What price should a shopkeeper mark on an article costing him Rs 200 to gain 35% after allowing a discount of 25%? a) 270 b) 300 c) 330 d) The compound interest for two years on a capital in rupees two more than the simple interest for the same period. If the rate of interest is 5% per year, then the capital would be: (a) Rs. 800 (b) Rs. 840 (c) Rs. 880 (d) Rs A trader sells his goods at a discount of 20%. He still makes a profit of 25%. If he sells the goods at the marked price only, his profit will be a) 56.25% b) c) 50.25% d) 54.25% 23. How much will Rs amount to in 2 years at compound interest, if the rates for the successive years be 4 and 5 percent per years? (a) Rs (b) Rs (c) Rs (d) Rs A alone can do a piece of work in 90 days. He works at it for 5 days and then B alone finishes the remaining work in 50 days. Working together they will finish the work in: (a) 36 days (b)40, days (c) 60 days (d) 90 days 25. A garrison of 850 men has provision for 26 weeks. If at the end of 6 weeks, they are reinforced by 50 men, how long will the provisions last now? (a) 2 weeks (b) 5 weeks (c) 7 weeks (d) 22 weeks 26. A sum of money becomes 8 times of itself in 3 years at compound interest the rate of interest is (a) 00% (b) 8% (c) % (d) None of these 27. What sum of money at compound interest will amount to Rs. 480 at the end of first year and Rs. 576 at the end of second year? Pinnacle SSC CGL Coaching Centre, Gurudwara Road, Model Town, Hisar, Page 3

4 (a) Rs. 420 (b) Rs. 450 (c) Rs. 400 (d) Rs The marked price of a radio is Rs The shopkeeper allows a discount of 0% and gains 8%. If no discount is allowed, his gain percent will be a) 8 b) 20 c) 22 d) The simple interest on Rs at a certain rate of interest for 3 years is Rs What will be the compound interest on the same sum at the same rate and for the same time? (a) Rs (b) Rs (c) Rs (d) Rs A certain number of men can complete a job in 0 days. If 0 men are absent, the remaining man can do the work in 2 days. How many men were there originally? (a) 0 men (b) 20 men (c) 50 men (d) 60 men 3. There is a leak in the bottom of a cistern. When the cistern is thoroughly repaired, it would be filled in 3.5 hours. It now takes half an hour longer. If (he cistern is full, how long would the leak take to empty the cistern? a)28hours b)27hours c)32hours d)24hoars 32. A pipe can empty a tank in 40 minutes. A second pipe with diameter twice much as that of the first is also attached with the tank to empty it. The two tether can empty the tank in : a) 8 minutes b) 3 c) 30 minutes d) 38 minutes 33. A man rides at the rate of 20 kilometers an hour. But stops 0 minutes to change horses at the end of every 25th kilometer. How long will he take to go a distance of 75 kilometers? a) 9hrs 5min b) 9hrs 45min c)0hrs d) 8hrs45min 34. If (25) (625) = 5 h a) 3 b) 2 c) 0 d) 35. A dealer bought 80 fountain pens of two qualities for a total sum of Rs He paid Rs each for the better quality pen and Rs each for the ordinary quality one. The number of better quality pens bought by him is: (a) 25 (b) 32 (c) 48 (d) The value of cos º cos 2º cos 3º... cos 89º cos 90º is: Pinnacle SSC CGL Coaching Centre, Gurudwara Road, Model Town, Hisar, Page 4

5 (a) (b) 2 (c) 2 (d) A car completes a certain journey in 8 hours. it covers half the distance at 40 km/hr and the rest at 60 km/hr. The length of the journey in kilometers is: a) 92 b)384 c)400 d) The value of : a) is a) b) 2 c) 3 d) The distance between two stations A and B is 450 km. A train starts from A and moves towards B at an average speed of 5 km/hr. Another train starts from B, 20 minutes earlier than the train at A, and moves towards A at an average speed of 20 km/hr. How far from A will the two trains meet? a) 80km b)320 km c) 90km d)260km 40. If = 0 Then the value of a) 3 b) -3 c) d) 4. If x + =5, then is equal to (a) 5 (b) (c) 3 (d) 42. In a stream, B lies in between A and C such that it is equidistant from both A and C. A boat can go from A to B and back in 6 h 30 minutes while it goes from A to C in 9 h. How long would it take to go from C to A? (a) 3.75 h (b) 4 h (c) 4.25 h (d) 4.5 h 43. The value of ( ) ( 3.5) ( 2.5) a) b) c) 6 d) 5 Pinnacle SSC CGL Coaching Centre, Gurudwara Road, Model Town, Hisar, Page 5

6 44. If a + b = and =, h h a) b) 3 c) 5 d) An aeroplane started its flight 30 min later than the scheduled time. In order to reach his destination 500km away in time, it increased its speed by 250 km/hr. His normal speed is (a) 720 km/hr (b) 730 km/hr (c) 740 km/hr (d) 750 km/hr 46. If cos =, then the value of.. a) b) c) d) 47. If (2 + 3 )a =(2-3) = then the value of + a) b) 2 c) 2 3 d) What will be the cost of fencing a square field, whose side is 20 metre, if the cost of fencing is Rs. 0 per metre? (a) Rs. 200 (b)rs.400 (c)rs.800 (d)rs The length and breadth of a rectangle are in the ratio of 5:3. Find its area, if the perimeter is 64 cm. (a) 5 cm 2 (b) 60 cm 2 (c) 50 cm 2 (d) 240 cm A vertical stick 2 cm long casts a shadow 8 cm long on the ground. At the same time, a tower casts a shadow 40 m long on the ground. The height of the tower is a) 72 m b) 60 m c) 65 m d) 70 m 5. If = 0, then two value of x are (a),2 (b) 2, - (c) 0, (d), 52. Two men are on the opposite side of a tower. They measure the angles of elevation of the top of the tower 45º and 30º respectively. If the height of the tower is 40 m, find the distance between the men: (a) 40 m (b) 40 3 m (c) m (d) m Pinnacle SSC CGL Coaching Centre, Gurudwara Road, Model Town, Hisar, Page 6

7 53. A man from the top of a 00 metre high tower looks a car moving towards the tower at an angle of depression of 30º. After some time, the angle of depression becomes 60º. The distance (in metre) traveled by the car during this time is: (a) 00 3 (b) (c) (d) If A : B : C = 2 : 3 : 4, then is equal to : (a) 8 : 9 : 6 (b) 8 : 9 : 2 (c) 8 : 9 : 24 (d) 4 : 9 : In the given fig., which is the longest sides? (a) BC (b) AB (c) AC (d) AB and AC 56. If the length of a rectangle is increased by 30% and width by 20%, its area will increase by: (a) 50% (b)25% (c)56% (d) 60% 57. In a triangle, if three altitudes are equal, then the triangle is (a) Obtuse (c) Right (b) Equilateral (d) Isosceles 58. The area of the largest circle that can be drawn inside a square of side 28 cm is: (a) 7248 sq. cm (b) 784 sq. cm (c) 8624 sq. cm (d) 66 sq. cm 59. Find the curved surface area of a hemisphere whose diameter is 4 cm. Pinnacle SSC CGL Coaching Centre, Gurudwara Road, Model Town, Hisar, Page 7

8 (a) 54 cm 2 (b)308 cm 2 (c)462 cm 2' (d) 66 cm If a + b + c = 4 3 and a 2 + b 2 + c 2 = 6, then the ration a : b : c is (a) : : (c) : 2 : 3 (b) : 2 : 3 (d) None of these 6. If ABC is a triangle right angled at B and M, N are the mid points of AB and BC, then 4(AN 2 + CM 2 ) is equal to: (a) 4AC 2 (b) 5AC 2 (c) 4 5 AC 2 (d) 6AC The ratio of an interior angle to the exterior angle of a regular polygon is (7 : 2). The number of sides of the polygon is: (a) 6 (b) 9 (c) 7 (d) If y = x then x 4 + x 3 4x 2 + x + = 0 becomes: x (a) x 2 (y 2 + y 2) (b) x 2 (y 2 + y 4) = 0 (c) x 2 (y 2 + y 6) = 0 (d) None of these 64. D, E, F are the mid-points of BC, CA, AB of triangle ABC. If AD and BE intersect in G, then AG + BG + CG is equal to: (a) AD + BE + CF (b) 3 2 (AD + BE + CF) (c) 2 3 (AD + BE + CF) (d) 3 (AD + BE + CF) 65. Chords AB, BC, CD subtend angles of 80º, 60º and 70º respectively at the centre O of the circle then the acute angle between AC and BD is: (a) 60º (b) 75º (c) 65º (d) 80º 66. There are 576 boys and 448 girls in a school that are to be divided into equal sections of either boys or girls alone. Find the total number of sections thus formed. (a) 24 (b) 32 (c) 6 (d) None of these 67. In the given CD is parallel to AB then y is: Pinnacle SSC CGL Coaching Centre, Gurudwara Road, Model Town, Hisar, Page 8

9 (a) 40º (b) 60º (c) 80º (d) 00º 68. Measure of each interior angle of a regular polygon can never be: (a) 50 (b) 05 (c) 08 (d) =? (a) 5.27 (b) (c) 8.34 (d) What is the weight of water contained in a conical vessel of diameter 6 cm and height 2 cm? (a).256 kg (b).408 kg (c) kg (d) kg 7. From a right circular cylinder of radius 0 cm and height 2 cm a right circular cone of same base radius is removed. If the volume of the remaining proportion is 4400 cm 3 then, the height of the cone removed is : (a) 5 cm (b) 8 cm (c) 2 cm (d) 24 cm 72. The radius of the incircle of a triangle with sides 5 cm, 5 cm and 8 cm is: (a) 4 cm (b) 4.5 cm (c) 6 cm (d) If each of the radius of base nad the height of a cone be increased by 00%, how many times is the new volume of the original volume? (a) 2 times (b) 3 times (c) 6 times (d) 8 times 74. A wooden box without lid has external length, breadth and height cm, 9 cm and 7 cm respectively. If wood is 5 mm thick, find the volume of wood used in making the box. a) 73 cm 3 (b) 23 cm 3 (c) 273 cm 3 (d) 693 cm If AB is parallel to CD in the given figure, then x, y and z respectively are: Pinnacle SSC CGL Coaching Centre, Gurudwara Road, Model Town, Hisar, Page 9

10 (a) 60º, 50º, 70º (b) 50º, 60º, 70º (c) 60º, 60º, 60º (d) 70º, 50º, 60º 76. In ABC and DEF, if A = 50º, B= 70º, C=60º, D=60º, E=70º and F = 50º, then (a) ABC ~ DEF (b) ABC ~ EDF (c) ABC ~ DFE (d) ABC ~ FED 77. The ratio of the radius and height of a cone is 5 : 2. Its volume is 2 34 cm 3. Its slant height is : 7 (a) 3 cm (b) 4 cm (c) 7 cm (d) 26 cm 78. If the perimeter of an equilateral triangle is 36.9 m and the length of an altitude is 8 m, then the area of the triangle is: (a) 29.2 m 2 (b) 39.2 m 2 (c) 49.2 m 2 (d) 59.2 m If x, then x is equal to 44 2 (a) (b) 2 (c) 3 (d) If PQR = 90º, O is the centroid, PQ = 5 cm and QR = 2 cm, then OQ is: Pinnacle SSC CGL Coaching Centre, Gurudwara Road, Model Town, Hisar, Page 0

11 (a) 3 cm (b) 4 4 cm (c) 3 4 cm (d) 2 5 cm 3 8. What is the smallest number which when multiplied by 392, gives a perfect square? ` (a) 2 (b) 4 (c) 3 (d) A rectangle is cm longer than its breadth and its perimeter is 4 cm. The area of the rectangle is : (a) 6 cm 2 (b) 4 cm 2 (c) 2 cm 2 (d) 0 cm The value of is (a).5 (b) 0.5 (c).52 (d) A rectangular field is (25m 5m). Two mutually perpendicular passages of width 2 m have been left in its central part and grass has been grown in rest of the field. The area under the grass is (a) 295 m 2 (b) 299 m 2 (c) 300 m 2 (d) 375 m Find the average of first 9 prime numbers (a) 2.0 (b) 3.0 (c). (d) The number of iron rods, each of length 7 m and diameter 2 cm that can be made out of 0.88 cu m of iron is (use = 22/7) : (a) 300 (b) 400 (c) 500 (d) A train travels 8 km in the first quarter of an hour 6 km in the second quarter and 40 km in the third quarter. Find the average speed of the train per hour over the entire Journey. Pinnacle SSC CGL Coaching Centre, Gurudwara Road, Model Town, Hisar, Page

12 (a) 8 km/h (b) 72 km/h (c) 77 km/h (d) 78 km/h 88. 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) 30 runs (b) 28 runs (c) 70 runs (d) 68 runs 89. A started his business by investing Rs After one year, B joined with him by investing Rs, At the end of 3 years after the beginning of the business, they earned a profit of Rs How much more is received by B than A? (a) Rs (b) Rs (c) Rs (d) Rs There are some solid metallic right circular cones, each of radius 3 cm and height 4 cm. These melted and recast into a solid sphere of radius 6 cm. The number of these cones is : (a) 2 (b) 24 (c) 6 (d) 48 Directions (9 95): Refer to the graph below. The following graph gives Sales, Expense and Equity of company for a period of five years Rs Sales Expense Equility 9. What has been the simple annual growth rate of expense between 2000 and 2004? (a) 30% (b) 70% (c) 33% (d) 25% 92. In which year was the sales to expense ratio the lowest? Pinnacle SSC CGL Coaching Centre, Gurudwara Road, Model Town, Hisar, Page 2

13 (a) 2000 (b) 200 (c) 2002 (d) The % change in profit% for 200 over 2000 is: (a) 33.3% (b) 25% (c) 20% (d) -33.3% 94. In which year was the ratio of profits to equity the highest? (a) 2000 (b) 200 (c) both 2000 and 200 (d) both 200 and In which year was the ratio of sales to equity the lowest? (a) 2000 (b) 200 (c) 2002 (d) One-fourth of 60% of a number is equal to two-fifth of 20% of another number. What is the respective ratio of the first number to the second number? (a) 4 : 7 (b) 8 : 5 (c) 5 : 9 (d) Cannot be determined 97. What is the area of the largest circle inscribed in a rectangle 8 cm long and 4 cm wide? (a) 49 cm 2 (b) 54 cm 2 (c) 378 cm 2 (d) 078 cm The market price of an electric iron is Rs The shopkeeper allows a discount of 0% and gains 8%. If no discount is allowed, his gain per cent would be (a) 20% (b) 24% (c) 25% (d) 28% women can finish a piece of work in 8 days while 0 children can do it in 2 days. In how many days can 6 women and 3 children do it? (a) 7 days (b) 8 days (c) 9 days (d) 0 days 00. In an examination 70% of the candidates passed in English, 80% passed in Mathematics and 0% failed in both the subjects. If 44 candidates passed in both, the total number of candidates was: (a) 25 (b) 200 (c) 240 (d) 375 Pinnacle SSC CGL Coaching Centre, Gurudwara Road, Model Town, Hisar, Page 3