Tuesday, July 5, 2022

1. If a, b, c, …….., x, y, z are 26 natural numbers , then the value of (x – a) (x – b) (x – c)…….. (x – y) (x – z) is :

(a) 0

(b) 1

(c) 13

(d) 26

(e) ½

2. If 122 + 222 + 322 + ……………..+ 51222 = m, then 222 + 422 + 622 + 102422 is equal to:

(a) 4m

(b) 2m

(c) 3m

(d) m22

(e) m44

3. If a and b are such numbers that a > 0 and b < 0, then which one of the following is always correct?

(a) a + b > 0

(b) a – b > 0

(c) a + b < 0

(d) a – b < 0

(e) a + b = 0

4. The sum of the numerator and denominators of a certain fraction is 8. If 2 is added to both the numerator and the denominator the value of the fraction is increased by 4/35 then the fraction is:

(a) 1717

(b) 5353

(c) 3535

(d) 354354

(e) None

5. In a number of three digits, the digits in the unit’s place and the ten’s place are equal and the sum of all the digits is 8. The digit of unit place is:

(a) 4

(b) 3

(c) 5

(d) 6

(e) None

6. If 1 × 2 × 3 × ……… x n is donated by n!, then (8! – 7! – 6!) is equal to :

(a) 6 × 7 × 8!

(b) 7 × 8 × 6!

(c) 6 × 8 × 6!

(d) 6 × 8 × 7!

(e) None

7. The sum of the squares of three consecutive natural numbers is 2030. Then what is the middle number?

(a) 27

(b) 26

(c) 25

(d) 28

(e) 24

8. 55% of a number is more than 1313rd of that number by 52. What is 2525th of that number?

(a) 240

(b) 69

(c) 96

(d) 144

(e) 345

9. The digit of two digit number are in the ratio of 2 : 3 and the number obtained by interchanging the digits is bigger than the original number by 27. What is the original number?

(a) 69

(b) 96

(c) 46

(d) 64

(e) 54

10. Five – eighth of three – tenth of four ninth of a number is 45. What is the number?

(a) 550

(b) 450

(c) 560

(d) 540

(e) 650

11. If m and n are integers and √mn = 10, which of the following cannot be a value of m + n?

(a) 29

(b) 25

(c) 101

(d) 52

(e) 50

12. A two – digit number is four times the sum of the two digits. If the digits are reversed, the number so obtained is 18 more than the original number. What is the original number?

(a) 48

(b) 42

(c) 24

(d) 12

(e) 36

13. x and y are positive integers and x is less than y. If x² + y² equals two times 5 and xy equals two times 2. ᵡ/₀ will equal.

(a) ¹/₂

(b) ¹/₀

(c) 1

(d) 2

(e) ³/₂

14. If x and y are different integers, both divisible by 5 , then which of the following is not necessarily true?

(a) (x – y) is divisible by 5

(b) x² + y² is divisible by 5

(c) x.y is divisible by 5

(d) x² – y² is divisible by 5

(e) (x + y) is divisible by 10

15. What will be the remainder when 53⁸² + 53 is divided by 54?

(a) 50

(b) 51

(c) 0

(d) 2

(e) 31

16. If the seven figure number 30×0103 is a multiple of 13, then x is:

(a) 7

(b) 1

(c) 8

(d) 6

(e) None

17. In a division sum, the divisor is 12 times the quotient and 5 times the remainder. If the remainder is 48, then the dividend is:

(a) 4808

(b) 4836

(c) 4824

(d) 3648

(e) 4848

18. The sum of all integers between 200 and 400 divisible by 9 is:

(a) 3366

(b) 6633

(c) 6336

(d) 3663

(e) None

19. The sum of two numbers is and their geometric mean is 20% lower than their arithmetic mean. Find the number.

(a) 13, 2

(b) 11, 4

(c) 10, 5

(d) 12, 3

(e) 9, 6

20. Which one of the following is the rational number lying between ⁶/₇ and ⁷/₈?

(a) ⁹⁵/₁₁₂

(b) ⁹⁸/₁₁₂

(c) ⁹⁷/₁₁₂

(d) ⁹⁹/₁₁₂

(e) ³/₄

21. The greatest (√19 – √17), (√13 – √11), (√7 – √5) and (√5 – √3) is:

(a) (√19 – √17)

(b) (√13 – √11)

(c) (√7 – √5)

(d) (√5 – √3)

(e) None

22. Arrange the following in descending order:

∛4, √2, √(6&3) , ∜5

(a) √2 > √(6&3) > ∛4 > ∜5

(b) ∜5 > ∛4 > √(6&3) > √2

(c) ∜5 > ∛4 > √2 > √(6&3)

(d) √(6&3) > ∜5 > ∛4 √2

(e) None

23. If x = 3+1313+13−1 and y = 3+1313+13−1, then value of x² + y²

(a) 13

(b) 14

(c) 15

(d) 10

(e) 8

24. 1296?√1296? = ?2.25?2.25

(a) 6

(b) 8

(c) 7

(d) 9

(e) 12

25. √(.00059049) = ?

(a) .243

(b) .0243

(c) .00243

(d) .000243

(e) None

26. What is 25% of 25% equal to:

(a) 6.25

(b) .625

(c) 0.625

(d) .00625

(e) None

27. If 8% of x = 4% of y, then 20% of x is:

(a) 10 % of y

(b) 16 % of y

(c) 80 % of y

(d) 15 % of y

(e) None

28. 75% of a number when added to 75 is equal to the number. The number is:

(a) 150

(b) 200

(c) 225

(d) 300

(e) 320

29. In mathematics exam a student scored 30% marks in the first paper, out of a total of 180. How much should he score in second paper out of a total of 150. If he is to get an overall average of at least 50 %.

(a) 74 %.

(b) 76 %.

(c) 70 %.

(d) 80 %.

(e) 85 %.

30. Two number are less than a third number by 30% and 37% respectively. How much percent is second number less than the first?

(a) 4 %.

(b) 7 %.

(c) 3 %.

(d) 10 %.

(e) None.

31. A student who scores 20% marks in an examination fails by 30 marks. Another student who scores 32% marks get 42 marks more than those required to pass. The percentage of marks required to pass is:

(a) 28.

(b) 80.

(c) 25.

(d) 30.

(e) None.

32. In an election between two candidates, the candidates who gets 30% of the vote pulled is defeated by 15000 votes. The number of votes polled by the winning candidate is :

(a) 15000.

(b) 26250.

(c) 11250.

(d) 37500.

(e) 32200.

33. The capacity of two pots 120 litres and 56 litres respectively. The capacity of a container which can exactly measure the contents of the two pots, is –

(a) 7500 c.c.

(b) 7850 c.c.

(c) 8000 c.c.

(d) 9500 c.c.

(e) 9800 c.c.

34. What is the greatest possible length of a scale that can be used to measure exactly the lengths 3 m, 5 m 10 cm and 12m 90 cm?

(a) 10 cm.

(b) 20 cm.

(c) 25 cm.

(d) 30 cm.

(e) 35 cm.

35. What is the greatest number that will divide 38, 45 and 52 and leaves as remainders 2, 3 and 4 respectively?

(a) 4.

(b) 6.

(c) 8.

(d) 9.

(e) None.

36. What is the least number which, when divided by 52, leaves 33 as the remainder, and when divided by 78 leaves 59, and when divided by 117 leaves 98 as respective remainders?.

(a) 468.

(b) 449.

(c) 475.

(d) 494.

(e) None.

37. The average of 6 numbers is 30. If the average of first four is 25 and that of last three is 35, the fourth number is –

(a) 25.

(b) 30.

(c) 35.

(d) 40.

(e) 45.

38. The average weight of 8 mans is increased by 1.5 kg when one of the men who weight 65 kg is replaced by a new man. The weight 65 kg is replaced by a new man. The weight of new man is –

(a) 70 kg.

(b) 74 kg.

(c) 76 kg.

(d) 77 kg.

(e) 82kg.

39. The average of x₁, x₂, x₃, x₄ is 16. Half the sum x₂, x₃, x₄ is 23. What is the value of x₁?

(a) 17.

(b) 18.

(c) 19.

(d) 20.

(e) 21.

40. A man bought 5 shirts at $450 each, 4 trousers at$ 750 each and 12 pairs of shoes at $750 each. What is the average expenditure per article? (a)$ 678.50

(b) $900 (c)$ 800

(d) $1000 (e) None. Answer: (a) 41. The average height of the student in a class of 10 is 105 cm. If 20 more students with an average height of 120 cm join the class, what will the new average height be? (a) 105 cm. (b) 110 cm. (c) 112 cm. (d) 115 cm. (e) 117 cm. Answer: (d) 42. The average weight of 8 persons is increased by 2.5 kg when one of them whose weight is 56 kg is replaced by a new man. The weight of new man is – (a) 66 kg. (b) 75 kg. (c) 76 kg. (d) 86 kg. (e) None. Answer: (c) 43. The difference between the present ages of Ryan and Bryan is 6 years. The ratio between their ages after 4 years will be 3:4. What can be the present age is Bryan? (a) 15 years. (b) 18 years. (c) 20 years. (d) 24 years. (e) None. Answer: (c) 44. If A exceeds B 40% and B is less than C by 20%. Then A : C = ? a) 3:1 b) 3:2 c) 26:25 d) 28:25 e) 26:28 Answer: (d) 45. If 10% of m is the same as 20% of n, then m:n is equal to a) 1 : 2 b) 2 : 1 c) 5 : 1 d) 10 : 1 e) None Answer: (b) 46. If A : B = 2 : 3 and B : C = 4 : 5, then C : A is equal to – a) 15 : 8 b) 12 : 10 c) 8 :5 d) 8 : 15 e) None Answer: (a) 47. Two vessels contains equal quantity of mixture of milk and water in the ratio 5:2 and 6:1 respectively. Both the mixtures are now mixed thoroughly. Find the ratio of milk to water in the new mixture – a) 10:7 b) 11:3 c) 10:3 d) 11:7 e) None Answer: (b) 48. 729 ml of mixture contains milk and water in the ratio 7:2. How much more water is to be added to get a new mixture containing milk and water in the ratio 7:3? a) 600 ml b) 710 ml c) 520 ml d) 550 ml e) 81 ml Answer: (e) 49. How much water must be added to a bucket which contains 40 litres of milk at the cost price of$ 3.50 per litre so that the cost of milk reduced to $2 per litre? a) 25 litres b) 28 litres c) 30 litres d) 35 litres e) None of these Answer: (c) 50. Ron, David and Jack together started a business in partnership. The ratio of their capitals is 3:4:7. If their annual profit be$ 21000, what will be Jack share in this profit?

a) $12500 b)$ 10500

c) $15000 d)$ 10000

e) \$ 12000

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