PAR Mathematics Paper 1 for 2007

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1. In a division sum, the divisor is 10 times the quotient and 5 times the remainder. If the remainder is 46, the dividend is:

(1) 4236

(2) 4306

(3) 4336

(4) 5336

2. If 1.5 x = 0.04 y, then the value of (y-x) (y + x) is:

(1) 730/77

(2) 73/77

(3) 7.3/77

(4) 703/77

3. An employee may claim ₹ 7.00 for each km when he travels by taxi and ₹ 6.00 for each km if he drives his own car. If in one week he claimed ₹ 595 for traveling km. How many kms did he travel by taxi? (1) 55

(2) 65

(3) 62

(4) 70

4. The square root of 3 + √ 5 is:

(1) √ 3/2 + 1/ √ 2

(2) √ 3/2 – 1/ √ 2

(3) √ 5/2 – 1/ √ 2

(4) √ (5/2) + √ (1/2)

5. The mean temperature of Monday to Wednesday was 370C and of Tuesday to Thursday was 340C, if the temperature on Thursday was 4/ 5th that of Monday, then what was the temperature on Thursday?

(1) 36.50C

(2) 360C

(3) 35.50C

(4) 340C

6. A certain number of two digits is three times the sum of its digits. If 45 be added to it, the digits are reversed. The number is:

(1) 72

(2) 32

(3) 27

(4) 23

7. Three years ago the average age of A and B was 18 years. While C joining them now, the average becomes 22 years. How old (in years) is C now?

(1) 24

(2) 27

(3) 28

(4) 30

8. If 2 ^ (2x-1) = 8 ^ (3-x) , then the value of x is:

(1) -1

(2) -2

(3) 2

(4) 3

9. A man ′ s basic pay for a 40 hours ′ week is ₹ 200. Overtimes is paid at 25 % above the basic rate. In a certain week, he worked overtime and his total was ₹ 300. He therefore, worked for a total of (in hours) :

(1) 52

(2) 56

(3) 58

(4) 62

10. On a ₹ 10,000 payment order, a person has choice between 3 successive discounts of 10 % , 10 % and 30 % and 3 successive discounts of 40 % , 5 % and 5 % . By choosing the better one he can save (in Rupees) :

(1) 200

(2) 255

(3) 400

(4) 433

11. ₹ 600 are divided among A, B, C so that ₹ 40 more than 2/5th of A՚s share, ₹ 20 more than 2/7th of B՚s share and ₹ 10 more than 9/17th of C՚s may all be equal. What is A՚s share (in Rupees) ?

(1) 150

(2) 170

(3) 200

(4) 280

12. A, B, C started a business with their investment in the ratio 1: 3: 5. After 4 months, A invested the same amount as before and B as well as C withdrew half of their investments. The ratio of their profits at the end of the year was:

(1) 5: 6: 10

(2) 6: 5: 10

(3) 10: 5: 6

(4) 4: 3: 5

13. If 9 men working 71/2 hours a day can finish a piece of work in 20 days, then how many days will be taken by 12 men, working 6 hours a day to finish the work? It is being given that 2 men of latter type work as much as 3 men of the former type?

(1) 91/2

(2) 11

(3) 121/2

(4) 13

14. Three pipes A, B and C can fill a cistern in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 7 hours. The number of hours taken by C alone to fill the cistern is:

(1) 12

(2) 14

(3) 16

(4) 18

15. A train B speeding with 120 kmph crosses another train C running in the same direction, in 2 minutes. If the lengths of the trains B and C be 100 m and 200 m respectively, what is the speed (in kmph) of the train C?

(1) 111

(2) 123

(3) 127

(4) 129

16. River is running at 2 kmph. It took a man twice as long to row up as to row down the river. The rate (in km/hr) of the man in still water is:

(1) 8

(2) 10

(3) 4

(4) 6

17. A merchant has 1000 kg of sugar, part of which he sells at 8 % profit and the rest at 18 % profit. He gains 14 % on the whole. The quantity (in kg.) sold at 18 % profit is:

(1) 560

(2) 600

(3) 400

(4) 640

18. A sum of money becomes ₹ 13,380 after 3 years and ₹ 20,070 after 6 years on compound interest. The sum (in Rupees) is: (1) 8800

(2) 8890

(3) 8920

(4) 9040

19. A well with 14 m inside diameter is dug 10 m deep. Earth taken out of it, has been evenly spread all around it to a width of 21m to form an embankment. The height (in meters) of the embankment is: (1) 1/2

(2) 2/3

(3) 3/4

(4) 3/5

20. A rectangular carpet has an area of 120 sq meters and a perimeter of 46 meters. The length of its diagonal (in meters) is: (1) 11

(2) 13

(3) 15

(4) 17

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