Q1. X can do a piece of work in 24 days. When he had worked for 4 days, Y joined him. If complete work was finished in 16 days, Y can alone finish that work in how many days? (a) 18 days (b) 27 days (c) 36 days (d) 42 days Q2. If 6 men and 8 boys can do a piece of work in 10 days and, 26 men and 48 boys can do the same in 2 days. Then, the time taken by 15 men and 20 boys to do the same type of work will be? (a) 5 days (b) 4 days (c) 6 days (d) 7 days Q3. In an election between two candidates, 75% of voters casted there votes, out of which 2% votes were declared invalid. A candidate got 9261 votes which were 75% of the valid votes. The total number of voters enrolled in that election was ? (a) 16000 (b) 16800 (c) 16400 (d) 18000

Q4. A sells an article to B making a profit of 1

5 of his outlay. B sells it to C, gaining

20%. If C sells it for Rs. 600 and incurs a loss of 1

6 of his outlay, the cost price of A

is? (a) Rs. 600 (b) Rs. 500 (c) Rs. 720 (d) Rs. 800

Q5. A traders allows a trade discount of 20% and a cash discount of 61

4%, on the

marked price of the goods and gets a net gain of 20% of the cost. By how much above the cost should the goods be marked for the sale? (a) 40%

(b) 50% (c) 60% (d) 70% Q6. A person lent Rs. 5000 partly at the rate of 4% and partly at the rate of 5% p.a. at simple interest. The total interest after 2 years is Rs. 440. The sum of money lent at each of the above rates is to be divided in the ratio? (a) 4 : 5 (b) 3 : 2 (c) 5 : 4 (d) 2 : 3 Q7. Vessels A & B contain mixtures of milk & water in the ratios 4 : 5 & 5 : 1 respectively. In what ratio should quantities of mixture be taken from A & B to form a mixtures in which milk to water is in the ratio 5 : 4? (a) 2 : 5 (b) 4 : 3 (c) 5 : 2 (d) 2 : 3 Q8. 200 litres of mixture contains milk and water in the ratio 17 : 3. After the addition of some more milk to it, The ratio of milk to water in the resultant mixture becomes 7 : 1. The quantity of milk added to it was? (a) 20 L (b) 40 L (c) 60 L (d) 80 L Q9. A contractor was engaged to construct a road is 16 days. After 12 days with 20

labors it was found that only 5

8th of the road had been constructed. To complete

the work in stipulated time the number of extra labours required are? (a) 16 (b) 12 (c) 10 (d) 18

Q10. A tank has a leak which would empty the filled tank in 10 hours. If the tank is full of water and a tap is opened which admits 4 litres of water per minute in the tank, the leak takes 15 hours to empty the tank. How many litres of water does the tank hold? (a) 2400 L (b) 4500 L (c) 1200 L (d) 7200 L Q11. A man goes downstream with a boat to some destination and returns upstream to his original place in 5 hours. If the speed of boat in still water & stream are 10 km/hour & 4 km/hour, respectively the distance of destination from the starting place is ? (a) 16 km (b) 18 km (c) 21 km (d) 25 km Q12. A number being divided by 52 gives remainder 45. If the number is divided by 13, the remainder will be? (a) 5 (b) 6 (c) 12 (d) 7

Q13. If x4 +1

x4 = 119 and x > 1, then the value of x3 +

1

x3 is?

(a) 6√13

(b) 8√13

(c) 13√13

(d) 10√13

Q14. If x = 4√15

√5 + √3, the value of

x+√20

x−√20+

x+√12

x−√12 is?

(a) 1 (b) 2

(c) √3

(d) √5

Q15. There is a small island in the middle of a 100 metres wide river and a tall tree stands on the island. P and Q are points directly opposite to each other on two banks and in line with the tree. If the angles of elevation of the top of tree from P and Q are respectively 30° and 45°, find the height of the tree? (a) 35.6 metres (b) 36.6 metres (c) 37.6 metres (d) 46.6 metres Q16. Two circles with centres A and B of radii 3 cm and 4 cm respectively intersect at two points C and D such that AC and BC are tangents to the two circles. Find the length of common chord CD? (a) 4.4 cm (b) 4.3 cm (c) 4.5 cm (d) 4.8 cm Q17. The value of 3(𝑠𝑖𝑛 𝑥 – 𝑐𝑜𝑠 𝑥)4 + 6(sin 𝑥 + cos 𝑥)2 + 4(sin6 𝑥 + cos6 𝑥) is? (a) 13 (b) 24 (c) 0 (d) 9

Q18. sin 18°

cos 72°+ √3 (tan 10°.tan 30°.tan 40°.tan 50°.tan 80°) =?

(a) 1 (b) 2

(c) 1

2

(d) 3√3

Q19. If √3 + 𝑥 + √3 − 𝑥

√3 + 𝑥 – √3 − 𝑥 = 2, then the value of x is equal to ?

(a) 5/12 (b) 12/5 (c) 5/7 (d) 7/5

Q20. The internal bisector of ∠ABC & ∠ACB of ∆ABC meet each other at O. If ∠BOC = 110°, then ∠BAC is equal to? (a) 40° (b) 80° (c) 110° (d) 55° Q21. A took 15 secs to cross a rectangular field diagonally walking at the speed of 52 m/min & B took the same time to cross the same field along its sides walking at the speed of 68 m/min. The area of the field is? (a) 30 m² (b) 40 m² (c) 80 m² (d) 60 m² Q22. A solid metallic cone of height 10 cm, radius of base 20 cm is melted to make spherical balls each of 4 cm diameter. How many such balls can be made? (a) 25 (b) 75 (c) 50 (d) 125 Q23. Four runners started running simultaneously from a point on a circular track. They took 200 seconds, 300 second, 360 seconds & 450 seconds to complete one round. After how much time do they meet at the starting point for the 1st time? (a) 1800 sec (b) 3600 sec (c) 2400 sec (d) 4800 sec Q24. A cooker is sold at a gain of 16%. If it had been sold for Rs. 20 more, 20% would have been gained. The cost price of the cooker is? (a) 350 Rs. (b) 400 Rs. (c) 500 Rs.

(d) 600 Rs. Q25. A train passes a man standing on a platform in 8 seconds and crosses the platform which is 264 meters long in 20 seconds. The length of the train is? (a) 188 (b) 176 (c) 175 (d) 96 Q26. If a certain sum of money at the rate of interest compounded annually becomes 4 times in 6 years. In how much time it will become 256 times? (a) 48 (b) 24 (c) 36 (d) 60 Q27. If a certain amount of money becomes 64000 in 2 years and Rs. 125000 in 5 years. Find the principal & rate of interest being compounded yearly? (a) 50%, 40900 (b) 25%, 40960 (c) 35%, 40970 (d) None of these Q28. S.I & C.I on a certain sum of money is 600 Rs. & 610 Rs. respectively. Find the principal if time is 2 years? (a) 9000 (b) 8000 (c) 7000 (d) 12000 Q29. A man wants to invest Rs. 16850 in bank account of his 2 sons, whose ages are 12 years & 16 years in such a way so that they will get equal amount at an age

of 120 years at the rate of 331

3% compounded annually. Find the share of younger

son? (a) 4050 (b) 4080 (c) 4090

(d) 4085 Q30. The compound interest on a certain sum of money at a certain rate per annum for 2 years is Rs. 2050, and the simple interest on the same amount of money at the same rate for 3 years is Rs. 3000. Find the sum of money is? (a) Rs. 20,000 (b) Rs. 18,000 (c) Rs. 21,000 (d) Rs. 25,000

Q31. If x = 2√24

√3+√2 then

𝑥+√8

𝑥−√8+

𝑥+√12

𝑥−√12 will be?

(a) 1 (b) 2 (c) 0 (d) –2

Q32. If a = 2+√3

2−√3 & b =

2−√3

2+√3 , then the value of a² + b² + ab will be?

(a) 185 (b) 195 (c) 200 (d) 175

Q33. If 2a – 2

𝑎 + 3 = 0 , then a³ –

1

𝑎3 + 2 is?

(a) −40

7

(b) −47

8

(c) 5

(d) −35

8

Q34. If x³ + y³ = 56 & x + y = 8. Find the value of 1

𝑥+

1

𝑦 ?

(a) 5

6

(b) 8

19

(c) 4

7

(d) 3

8

Q35. If a = 2 + √3,then 𝑎6 + 𝑎4 + 𝑎2 + 1

𝑎3 is ?

(a) 56 (b) 68 (c) 70 (d) 72

Q36. If (a – b) = 6, (b – c) = 8, (c – a) = 3, then find the value of 𝑎3 + 𝑏3 + 𝑐3 − 3𝑎𝑏𝑐

𝑎 + 𝑏 + 𝑐?

(a) 17.5 (b) 15.5 (c) 20.5 (d) 54.5

Q37. If (𝑥 +1

𝑥)

2= 3, then the value of 𝑥206 + 𝑥200 + 𝑥90 + 𝑥84 + 𝑥18 + 𝑥12 +

𝑥6 + 1 ? (a) 84 (b) 206 (c) 0 (d) 1

Q38. If (r cos θ − √3)2

+ (r sin θ − 1)2 = 0 then r tan θ+sec θ

r sec θ+tan θ will be equal to

which of the following?

(a) 4

5

(b) 5

4

(c) √3

4

(d) √5

4

Q39. The value of sin θ−2 sin3 θ

2 cos3 θ−cos θ is equal to ?

(a) sin θ (b) cos θ (c) tan θ (d) cot θ

Q40. If cos x + cos² x = 1, then the value of sin12 x + 3 sin10 x + 3 sin8 x + sin6 x −2 ? (a) 0 (b) 1 (c) –1 (d) 2

Q41. 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? (a) 48000 (b) 50000 (c) 51000 (d) 45000

Q42. A man spends 40% of his monthly salary on food and one-third of the remaining on transport. If he saves Rs. 4,500 per month, which is equal to half the balance after spending on food and transport, his monthly salary is ? (a) Rs. 11,250 (b) Rs. 22,500 (c) Rs. 25,000 (d) Rs. 45,000 Q43. Rama’s expenditures and savings are in the ratio 5 : 3. If her income increases by 12% and expenditure by 15%, then by how much percent do her savings increase? (a) 12% (b) 7% (c) 8% (d) 13% Q44. One type of liquid contains 20% water and the second type of liquid contains 35% of water. A glass is filled with 10 parts of first liquid and 4 parts of second liquid. The water in the new mixture in the glass is? (a) 37%

(b) 46%

(c) 121

7%

(d) 242

7%

Q45. In an examination 80% of the boys passed in English and 85% passed in Mathematics, while 75% passed in both. If 45 boys failed in both, the number of boys who sat for the examination was? (a) 400 (b) 450 (c) 200 (d) 150 Q46. A candidate who gets 20% marks in an examination, fails by 30 marks. But if he gets 32% marks, he gets 42 marks more than the minimum pass marks. Find the pass percentage of marks.? (a) 52% (b) 20% (c) 25% (d) 12% Q47. A reduction of 20% in the price of sugar enables a purchaser to obtain 8 kg more for Rs. 160. Then the price per kg before reduction was? (a) Rs. 5 (b) Rs. 6 (c) Rs. 10 (d) Rs. 4 Q48. A man had a certain amount with him. He spent 20% of that to buy an article and 5% of the remaining on transport. Then he gifted Rs. 120. If he is left with Rs. 1,400, the amount he spent on transport is? (a) Rs. 76 (b) Rs. 61 (c) Rs. 95 (d) Rs. 80

Q49. The population of a town is 6000, if males are increased by 5% & females by 9%. Then the population will become 6500 after 1 year. Find the no. of males & females? (a) 1000, 5000 (b) 3000, 3000 (c) 2000, 4000 (d) 4000, 2000 Q50. A family consumes, 25 kg rice & 9 kg wheat per month & spends Rs. 350. The price of rice is 20% of the price of wheat. If the price of wheat is increased by 20%. Then find the percentage reduction in the consumption of rice, if it has the same amount to spend, the price of rice is constant? (a) 36% (b) 25% (c) 30% (d) 35%

Q51. The marked price of an article is 50% above cost price. When marked price is increased by 20% and selling price is increased by 20%, the profit doubles. If original marked price is Rs. 300, then original selling price is? (a) Rs. 200 (b) Rs. 250 (c) Rs. 240 (d) Rs. 275 Q52. Krishna purchased a number of articles at Rs. 10 for each and the same number for Rs. 14 each. He mixed them together and sold them for Rs. 13 each. Then his gain or loss percent is?

(a) Loss 81

3%

(b) Gain 82

3%

(c) Loss 82

3%

(d) Gain 81

3%

Q53. There are three containers of equal capacity. The ratio of Sulphuric acid to water in the first container is 3 : 2, that in the second container is 7 : 3 and in the third container it is 11 : 4. If all the liquids are mixed together, then the ratio of Sulphuric acid to water in the mixture will be? (a) 61 : 29 (b) 61 : 28 (c) 60 : 29 (d) 59 : 29 Q54. A Can contains a mixture of two liquids A and B in the ratio 7 : 5. When 9 liters of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7 : 9. Liters of liquid A contained by the can initially was? (a) 10 (b) 20 (c) 21 (d) 25 Q55. Two alloys are both made up of copper and tin. The ratio of copper and tin in the first alloy is 1 : 3 and in the second alloy is 2 : 5. In what ratio should the two alloys be mixed to obtain a new alloy in which the ratio of tin and copper be 8 : 3? (a) 3 : 5 (b) 4 : 7 (c) 3 : 8 (d) 5 : 11 Q56. In two alloys A and B, the ratio of zinc to tin is 5 : 2 and 3 : 4 respectively. Seven kg of the alloy A and 21 kg of the alloy B are mixed together to form a new alloy. What will be the ratio of zinc and tin in the new alloy? (a) 2 : 1 (b) 1 : 2 (c) 2 : 3 (d) 1 : 1 Q57. A mixture contains wine and water in the ratio 3 : 2 and another mixture contains them in the ratio 4 : 5. How many liters of the later must be mixed with 3 liters of the former so that the resulting mixture may contain equal quantities of wine and water?

(a) 52

5 litres

(b) 52

3 litres

(c) 41

2 litres

(d) 33

4 litres

Q58. A vessel contains 20 liters of acid. 4 liters of acid is taken out of the vessel and replaced by the same quantity of water. Next 4 liters of the mixture are withdrawn, and again the vessel is filled with the same quantity of water ,ratio of acid left in the vessel with the quantity of acid initially in the vessel is? (a) 4 : 5 (b) 4 : 25 (c) 16 : 25 (d) 1 : 5 Q59. Four horses are tethered each at four different corners of a square grass field

with side measuring 63 m, in such a way that they don’t reach to one another

completely. The area of the field not grazed by the horses is?

(a) 675.5 m²

(b) 780.6 m²

(c) 758.8 m²

(d) 850.5 m²

Q60. The radii of two right circular cylinders are in the ratio 2 : 3. Their heights are

in the ratio 5 : 4. The ratio of their curved surface areas is?

(a) 5 : 6

(b) 3 : 4

(c) 4 : 5

(d) 2 : 3

Q61. A 6 m tall man finds that the angle of elevation of the top of a 24 m high tower and the angle of depression of its base are complementary angles. The distance of the man from the pillar is? (a) 2√3 m (b) 8√3 m

(c) 6√3 m (d) None of these Q62. Two pillars of equal height stand on either side of a road. At a point on the road between the pillars the elevation of the tops of the pillars are 60° and 30°. Find the height of the pillars if it is given that the width of the road is 150 m? (a) 64.87 (b) 62.34 (c) 78 (d) 66 Q63. One year ago, the ratio between Mahesh’s and Suresh’s salaries was 3 : 5.

The ratio of their individual salaries of last year and present year are 2 : 3 and 4 : 5

respectively. If their total salaries for the present year are Rs. 43000, what is the

present salary of Mahesh ?

(a) Rs. 19000

(b) Rs. 18000

(c) Rs. 16000

(d) Rs. 15500

Q64. Rashi calculates her profit percentage on the selling price whereas Rishi

calculates his profit percentage on the cost price. They find that the difference of

their profits is Rs. 275. If the selling price of both are the same and Rashi gets 25%

profit and Rishi gets 15% profit, then find their selling price?

(a) Rs. 2100

(b) Rs. 2350

(c) Rs. 2250

(d) Rs. 2300

Q65. Find the unit digit of the expression (55)725 + 735810 + 22853 ?

(a) 4 (b) 0 (c) 6 (d) 5

Q66. In ∆ABC internal angle bisector of ∠C cuts AB at point D. In this AB ≠ AC and E

is a point on CD such that AE = AD. If ∠ABC = 50° then ∠CAE is equal to ?

(a) 40°

(b) 50°

(c) 30°

(d) 25°

Q67. The base of a right prism is a trapezium whose parallel sides are 8 cm and

14 cm long and the distance between them is 8 cm. If the volume of the prism is

1056 cm³, its height is?

(a) 44 cm

(b) 16.5 cm

(c) 12 cm

(d) 10.56 cm

Q68. A play ground is rectangular in shape. In order to make this ground fit for

games, Rs 1000 was spent at the rate of 25 paise per m². The width of the field is

50 m. If the length of the ground is increased by 20 m, the cost of making it

suitable for game at the same rate in rupee will be?

(a) 1,250

(b) 1,000

(c) 1,500

(d) 2,250

Q69. It has rained 2 cm at the land measuring one square kilometer. Considering

that by collecting 50% of rain drops in a pond of dimension 100 m × 10 m, water

level in the pond would have risen by?

(a) 1 km

(b) 10 m

(c) 10 cm

(d) 1 m

Q70. The medians of a triangle are 9 cm, 12 cm and 15 cm long. The area of the

triangle in cm² is?

(a) 24

(b) 72

(c) 48

(d) 144

Q71. P and Q are the mid points of two chords (not diameter) AB and AC of a circle

with center O. OP and OQ lines are extended to points S and R respectively, to

touch the circle. In major arc T is another point between R and S. Then if ∠BAC =

32° then ∠RTS = ?

(a) 32°

(b) 74°

(c) 106°

(d) 64°

Q72. The angle bisector of ∠A of a triangle ABC cuts BC at D and D meets

circumcircle of ∆ABC at E. Then it is always true that AB.AC + DE.AE =?

(a) AD²

(b) AE²

(c) CE²

(d) CD²

Q73. 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? (a) 2 : 1 (b) 1 : 4 (c) 1 : 2 (d) 4 : 1

Q74.Two cars started simultaneously toward each other from town A and B, that are 480 km apart. It took the first car travelling from A to B 8 hours to cover the distance and the second car travelling from B to A 12 hours. Determine at what distance from A the two cars meet? (a) 288 km (b) 200 km (c) 300 km (d) 196 km

Q75. Find the remainder of 7688

400 ?

(a) 1 (b) 0 (c) 5 (d) 4

Q76. Find the remainder of 448

33 ?

(a) 30 (b) 31 (c) 29 (d) 28

Q77. Find the remainder of (96)115+12

97 ?

(a) 21 (b) 31 (c) 11 (d) 41

Q78. Find the maximum value of 27sin 𝜃 × 81cos 𝜃 ? (a) 35 (b) 36 (c) 39 (d) 37 Q79. Find the maximum value of 10sin θ.cos θ + 1 – 2sin² θ ?

(a) √27

(b) √26

(c) √24

(d) √28

Q80. The denominator of a fraction is 3 more than its numerator. If the numerator

is increased by 7 and the denominator is decreased by 2, we obtain 2. The sum of

numerator and denominator of the fraction ?

(a) 5

(b) 13

(c) 17

(d) 19

Q81. The value of 1

20+

1

30+

1

42+

1

56+

1

72+

1

90 is?

(a) 1

10

(b) 3

5

(c) 3

20

(d) 7

20

Q82. Find the largest number of 4 digits such that on dividing by 15, 18, 21 and 24

the remainders are 11, 14, 17 and 20 respectively ?

(a) 6557

(b) 7556

(c) 5675

(d) 7664

Q83. Which is the least number which when doubled will be exactly divisible by 12,

18, 21 and 30 ?

(a) 2520

(b) 1260

(c) 630

(d) 196

Q84. If the students of a class can be grouped exactly into 6 or 8 or 10, then the

minimum number of students in the class must be ?

(a) 60

(b) 120

(c) 180

(d) 240

Q85. A salesman is allowed 12% commission on the total sales made by him and a

bonus of 1% on the sales over Rs 15000. It the total earning of the salesman is Rs

7650. Find the total sales?

(a) 72000

(b) 80000

(c) 60000

(d) 65000

Q86. ABCD is a square. Taking BC as base make a triangle QBC , point Q is on side AD and taking AC as base make a triangle PAC such that ∆QBC ~ ∆PAC. Now ar (∆QBC)

ar (∆PAC) will be equal to ?

(a) 2/1 (b) 1/3 (c) 2/3 (d) 1/2

Q87. From a solid cylinder whose height is 12 cm and diameter 10 cm, a conical

cavity of same height and same diameter of the base is hollowed out. The volume

of the remaining solid is approximately (𝜋 =22

7)?

(a) 942.86 cm3

(b) 314.29 cm3

(c) 628.57 cm3

(d) 450.76 cm3

Q88. The curved surface area and the total surface area of a cylinder are in the

ratio 1 : 2.If the total surface area of the right cylinder is 616 cm2, then its volume

is ?

(a) 1232 cm3

(b) 1848 cm3

(c) 1632 cm3

(d) 1078 cm3

Q89. The length and the breadth of a rectangular grass land are 55 m and 35 m respectively. Two roads each 4 m wide and one parallel to the length and other parallel to the width of the grass land have been made inside it. The cost of paving these roads by pebbles, at the rate of 75 paise per m² is? (a) Rs 254.50

(b) Rs 258

(c) Rs 262.50

(d) Rs 270

Q90. The lengths of perpendiculars drawn from any point in the interior of an equilateral triangle to the respective sides are 6cm, 8cm, and 10cm. The length of each side of the triangle is? (a) 20 cm (b) 21 cm

(c) 16√3 cm (d) 20 cm Q91. In a right angled ∆ABC, ∠ABC = 90°; BN ⊥ AC, AB = 6 cm, AC = 10 cm. Then AN : NC is? (a) 9 : 16 (b) 6 : 13 (c) 14 :19 (d) 20 : 21

Q92. In a ∆ABC a line DE is drawn parallel to BC. If 𝐴𝐷

𝐷𝐵=

2

3 then find the ratio of

area of ∆ADE & Area of DECB. (a) 4 : 21 (b) 21 : 3 (c) 21 : 25 (d) 4 : 19 Q93. Unit digit of (6732)170 × (6733)172 × (6734)174 × (6736)176 ? (a) 1 (b) 3 (c) 4 (d) 5 Q94. A 4 digit number is formed by repeating a 2-digit number such of 2525, 3232, etc. Any number of this form is always exactly divisible by ? (a) 7 (b) 11 (c) 13 (d) Smallest 3-digit prime number Q95. If the sum of first 11 terms of A.P. is equal to sum of first 19 terms of that A.P.

find the sum of first 30 terms of that A.P. ?

(a) 3

(b) 2

(c) 1

(d) 0

Q96. In the given figure, O is the centre of the circle and ∠AOB = 75°, then ∠AEB

will be ?

(a) 142.5

(b) 162.5

(c) 132.5

(d) 122.5

Q97. In a circle, center angle is 120°. Find the ratio of a major angle and minor

angle?

(a) 2:7

(b) 2:1

(c) 2:9

(d) 2:3

Q98. In the given, circle with centre O have two tangents PA, PB. CD is also

tangent, then?

(a) PC + PD = CD

(b) 3PB = PD + DC + PC

(c) 4PA = PD + CD + PC

(d) 2PB = PD + CD + PC

Q99. A, B & C are three points on a circle such that a tangent touches the circle at

A and intersects the extended part of chord BC at D. Find the central angle made

by chord BC. If ∠CAD = 39°, ∠CDA = 41°?

(a) 122

(b) 123

(c) 132

(d) 142

Q100. ABC is an isosceles triangle a circle is such that it passes through vertex C

and AB acts as a tangent at D for the same circle. AC and BC intersects the circle at

E and F respectively AC = BC = 4 cm and AB = 6 cm. Also, D is the mid-point of AB.

What is the ratio of EC : (AE + AD)?

(a) 9:7

(b) 3:4

(c) 4:3

(d) 1:3