## WBCS MAIN PAPER VI : MATHEMATICS - NUMBER SYSTEM WITH SIMPLIFICATION

- WBCS Main Examination Paper - VI : 2022
- WBCS Main Examination Paper - VI : 2021
- WBCS Main Examination Paper - VI : 2020
- WBCS Main Examination Paper - VI : 2019
- WBCS Main Examination Paper - VI : 2018
- WBCS Main Examination Paper - VI : 2017
- WBCS Main Examination Paper - VI : 2016
- WBCS Main Examination Paper - VI : 2015
- WBCS Main Examination Paper - VI : 2014

1. The smallest number by which 6400 must be multiplied to make a perfect cube is

(A) 4 (B) 8 (C) 2 **(D) 10**

2. Which of the following numbers has the maximum number of divisors?

**(A) 154 (B) 44 (C) 108** (D) 99

3. If a glass holds 275 ml, how many of these glasses can be filled from a 2-liter drink of lemonade?

**(A) 7 full glasses **(B) 9 full glasses (C) 8 full glasses (D) 6 full glasses

4. A 2-digit number is such that the unit's digit is four times the ten's digit and if 54 is added to the number, the digits are reversed. Then the number is

(A) 14 **(A) 28** (C) 82 (C) 41

5. A can with 30 marbles weighed 120 gm. The same can with 15 marbles weighed 95 gm. Then the weight of the can is

(A) 50 gm (A) 60 gm **(C) 70 gm** (C) 80 gm

6. The product of the digits of a two-digit number is 24. If its unit's digit exceeds twice its ten's digit t 2, then the number is

(A) 64 (8) 46 **(C) 38** (C) 83

7. A shopkeeper buys a number of books for 280. If he had bought 4 more books for the same amount, each book would have cost K1 less. How many books did he buy?

**(A) 16** (8) 20 (C) 18 (C) 22

8. At the time of wedding the bride's age was % of the groom's age. After 8 years her age is of her husband's age. Then the age of the bride at the time of her wedding is

(A) 18 years (B) 19 years **(C) 24 years **(D) 26 years

9. If the first and the third terms of a G.P. are 2 and 8 respectively, then its second term is

(A) 4 (B) 0 (C) -4 **(A) ±4**

10. In a multiple choice exam of 30 questions, a correct answer earns 2 marks, an incorrect answer loses 3 marks and an unanswered question scores 0 marks. If Raj left out 6 questions and his score was 28, then number of questions he gets correct is

(A) 22 **(A) 20** (C) 25 (C) 15

11. If the number 472573* is completely divisible by 72, then which number should replace the star?

(A) 4 (A) 5 (C) 6 (C) 7

12. The sum of first 102 positive integers is

(A) 5250 (A) 5251 (C) 5252 **(C) 5253 **

13. The difference between the squares of two consecutive numbers is 65. The greatest number is

(A) 34 (B) 35 (C) 36 **(D) 33**

14. The difference between the greatest and least numbers formed out of the digits 8, 9, 0, 7 is

(A) 2407 **(B) 2781 **(C) 9081 (D) 1809

15. A survey in a city showed that the probability that a person smokes is 36. If 40 people in a certain sample smoke, then number of people in the sample is

(A) 240 (B) 120 **(C) 180 **(D) 200

16. The hundreds digit of the square root of the square number 3,15,844 is

**(A) 5** (B) 6 (C) 3 (D) 4** **

17. Which of the following numbers is divisible by 3, 4, 5 and 7?

** (A) 2940** (B) 3570 (C) 3150 (D) 1400

18. The smallest number which is being divided by 8, 9, 12 and 15 always leaves 1 as a remainder is** **

**(A) 181 (B) 197 (C) 361 **(D) 359

19. If one-third of one-fourth of a number is 20, then one-tenth of that number is

(A) 45 (B) 54 (C) 24 (D) 36

20. When & is expressed in decimal form, the digit in the 19th decimal place is

**(C)7 **(C) 1 (A) 5 (A) 8

21. A hotel bill for a number of people for overnight is 24,800. If there were 4 more people, the bill each person had to pay, would have reduced by 200. Then the number of people staying overnight is

**(A) 6 (B) 10 (C) 12 (D) 8**

22. A student was asked to multiply a number by 3/2 but he divided the number by 3/2. His result was therefore 10 less than the correct answer Find the number.

**(A) 12 **(B) 15 (C) 10 (D) 20

23. Rima has %1000 in denominations of 5 and %2 coins. If the number of two-rupee coins Rima has is five-eighths of the number of five-rupee coins, then five-rupee coins Rima has

**(A) 160 **(B) 200 (C) 100 (D) 120

24. The value of

(A) 1 (B) 1/3 **(C) 2/9** (D) 2/3

(A) 5 (B) 3 **(C) 1 **(D) 0

26. Find the value of

27. In a certain positive fraction, the denominator is greater than the numerator by 3. If 1 is subtracted from the numerator and denominator both, the fraction reduces by 4. Then the fraction is

(A) 3/14 (B) 7/20 **(C) 4/7** (D) 8/14

28. What is the value of

(A) 6 (B) 2 **(C) 4** (D) 3

29. Find the value of x from the following equation.

30. Value of

(A) 9 (B) 5 (C) 4 (D) 18

then the value of x

(A) 1** (B) 2 ** (C) 3 (D) 4

(A) 1860 (C) 186 (A) 18.6 (C) 1.86

35. The value of

(C) 54 (C) 56 (A) 52 (A) 53

1.The difference between the squares of two consecutive even integers is always divisible by (A) 3 **(B) 4 **(C) 6 (0) 7

2.It has been seen in a survey of a region that 70 persons read English newspaper, 73 persons read Bengali newspaper and 64 persons read both the papers. If 63 persons do not read any paper on how many people the survey has been done?

(A) 79 **(B) 142** (C) 207 (D) 143

3.The least number which when diminished by 5 is divisible by each of 21, 28, 36, 45 is

(A) 425 (B) 1260 **(C) 1265** (D) 1259

4.If the product of two successive positive integers is 7482. Which is the greatest integer? (A) **87** (B) 82 (C) 84 (D) 89

5.Find the largest possible number that may divide each of two numbers sum of which is 1394, when none of the component numbers is zero or equal to each other.

(A) 17 (8) 34 (C) 41 **(D) 82 **

6.There are five positive observations. Average of the first three observations is 8 and that of the last three observations is 6. If the average of all five observations is 6, what is the third observation?

(A) 10 (8) 8 **(C) 12** (D) 14

7.Find the largest possible 4 digit number divisible by 45. 18 and 35. (A) 9540 **(B) 9450** (C) 9460 (0) 9350

8.A farmer has some hens and some rabbits. If the total number of the feet of the hens and the rabbits is 160 and their total number of heads is 50, the numbers of hens the farmer have

(A) 20 (8) 18 (C) 10 (D) 15

9.stands for division, stands for multiplication, x' stands for subtraction and stands for addition. Which of the following equations is correct?

(A) 18+6-7+5x2 = 20 **(B) 18+6+7x5-2 = 18** (C) 18x6+7+5-2 = 16 (D) 18+6x7+5-2 = 22

10.The sum of the first five multiples of 3 is

**(A) 45** (8) 55 (C) 65 (D) 75

11.If & + 2& + && + 1&&= 2 & 4 then & stands for

(A) 5 **(B) 6** (C) 7 (D) 8

12.A lift carrying 50 passengers from the ground floor of a 100 storied building is moving upward. The lift stops at 1st, 2nd, 3rd floor then skips 4th floor, again stops at 5th, 6th and 7th then skips 8th floor and so on. Passengers get discharged in a pattern. 2, 3, 3, 2, 3, 3, In which floor the lift becomes empty?

(A) 16 (8) 24 **(C) 25** (D) 26

13.The smallest number which when divided by 12, 15, 20 or 54 leaves a remainder of 4 in each case, is (A) 454 (8) 564 **(C) 544** (0) 464

14.If ROOT529 = 23 then the value of N0.000529 is (A) 2.3 (8) 0.23 **(C) 0.023** (0) 0.0023

15.In a two digit number, the unit's digit exceeds ten's digit by 2 and the product of the sum of the digits and the number is 144, then what is the number?

**(A) 24** (8) 02 (C) 68 (D) 46

16.Which term of the A.P. 3, 8, 13, 18, is 78? (A) 12th (13) 13th (C) 15th **(D) 16th **

17.Total price of 6 shirts and 7 trousers is Rs.4,130 while that of 4 shirts and 9 trousers is Rs.4.270. Find out the price of 3 shirts.

(A) Rs 850 **(B) Rs.840** (C) Rs.860 (D) Rs.810

18.The maximum number of students among whom 910 pens and 1001 pencils can be distributed in such a way that each student gets same number of pens and pendls. is (A) 1911 (8) 910 (C) 1001 **(D) 91 **

19.If 17th term of an A.P. exceeds its 10th term by 7. The common difference is **(A) 1** (B) 2 (C) 3 (D) 4

20.The least number which when divided by 15. 27, 35 and 42 leaves a remainder of 7 in each division is (A) 1883 (8) 2007 (**C) 1897 **(0) 1987

21.If an amount of Rs.84,105 is distributed equally amongst 35 children. Now much amount would each child get? (A) Rs.2.430 (B) Rs.2.043 **(C) Rs.2,403** (0) None of the above

22.Gold is 19 times as heavy as water and copper is 9 times as heavy as water. The ratio in which these two metals are to be mixed so that the mixed alloy becomes 15 times as heavy as water is (A) 2:3 (8) 1:2 **(C) 3:2** (ID) 19:135

23.The least number that is to be subtracted from 5629 to make the result a perfect square is

**(A) 4 **(3) 1 (C) 2 (0) 3

24.Which of the following is the value of

(256 x 256 -144x144)/ 112

(A) 360 (B) **400 **(C) 380 (ID) 420

25.The sum of first 16 terms of the AP.: 10, 6, 2,... is

**(A) -320** (13) 320 (C) -352 (D) -400

26.The value of

(A) 2 (B) 4 (C) N2 (D) 8

27.Total expenses of

a hostel are partly constant and partly vary directly as the number of boarders. When the number of boarders are 120 and 100 the total expenses are Rs.2000 and Rs.1700 respectively. Find the total number of boarders if the total expense is Rs.1880.

(A) 200 **(B) 112** (C) 138 (D) 115

28.The missing terms in AR , 13_ 3 are (A) 11 and 9 (B) 17 and 9 **(C) 18 and 8** (D) 18 and 9

29.Find the least possible 5 digit number dividing which by each of 12, 10, 16 and 18 leaves a remainder of 5. (A) 10105 (5) 10055 (C) **10085 **(D) 10155

30.The number of multiples of 4 between 10 and 250 is (A) 50 (B) 40 (C) **60 **(0) 30

31.In a class of 150 students 70 passed in mathematics, 60 students passed in statistics and 20 in both subjects. Then number of students failed in both subjects is

(A) 30 (B) **40 **(C) 50

32The difference of a proper fraction and its reciprocal is 7/12. Find the fraction. (A)-413** (B) 3/4 **(G) 315 (D) 1/2

33.102 +1/100 + 0.0001 equals to (A) 1.000101 (6) 10.00101 **(C) 100.0101** (D) None of the above

34.Five bells ring at intervals of 3, 5, 6, 8, and 9 seconds. If all the bells ring once, after how long a period the b

ells would ring together again?

(A) 12 minutes **(B) 6 minutes** (C) 18 minutes (D) 24 minutes

1.Rs. 6000 is divided among 40 boys and some girls so that each boy gets Rs. 100 and each girl gets Rs. 250, then the number of girls is

(A) 20 (B) 15 **(C) 8** (D) 9

2.The mean of five observations x, x + 2, x + 6, x + 4, x + 8 is 11. The mean of last three observations is

(A) 9 (B) 9.33 **(C) 13** (D) 9.66

3.What fraction of 4/7 must be added to itself to make the sum 15/14 ?

(A) 1/2 (B) 4/7 **(C) 7/8 ** (D) 15/14

4.How many numbers between 400 and 600 begin with or end with the digit 5 ?

(A) 40 (B) 100 **(C) 110** (D) 120

5.A problem is given to three students whose chances of solving it are 1/2, 1/3 and 1/4 respectively. What is the probability that the problem will be solved ?

(A) 1/4 (B) 1/2 **(C) 3/4** (D) 7/12

6.A whole number *n* which when divided by 4 gives 3 as remainder. What will be the remainder when 2*n* is divided by 4 ?

(A) 0 (B) 1 (C) 4 **(D) 2**

7.If one-third of one-fourth of a number is 15, then three-tenth of that number is

(A) 35 (B) 36 (C) 45 **(D) 54**

8.The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number ?

(A) 3 **(B) 4** (c) 9 (D) Cannot be determined

9.If [4.5] = [4+0.5] = 4, then [- 4.5] will be

(A) - 4 (B) 4 (C) 5 **(D) - 5**

10.The unit's digit present in the product 274 x 318 x 577 x 313 is

**(A) 2** (B) 3 (C) 4 (D) 5

11.When a ball bounces, it rises to 3/4 of the height from which it fell. If the ball is dropped from a height of 32 m, how high will it rise at the third bounce ?

(A) 13 m **(B) 13.5 m** (C) 14.5 m (D) None of the above

12.What is the smallest number which when decreased by 8 is divisible by 21, 27, 33 and 55 ?

(A) 1490 (B) 10405 (C) 15490 **(D) None of the above**

13.The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?

(A) 4 **(B) 8** (C) 16 (D) None of the above

14.A sum of Rs. 312 was divided among 100 boys and girls in such a way that each boy gets Rs. 3.60 and each girl Rs. 2.40. The number of girls is

**(A) 40** (B) 45 (C) 35 (D) 30

15.A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is

(A) 18 **(B) 24** (C) 42 (D) 81

16.The digit in unit's place of the product 81 x 82 x ... x 89 is

**(A) 0** (B) 2 (C) 6 (D) 8

1.What least number must be added to 8275 to make the sum a perfect square ?

(A) 4 (B) 8 (C) 5 **(D) 6**

2.What least number must subtracted from 732 to make the remainder a perfect square ?

**(A) 3** (B) 4 (C) 5 (D) 6

3.By what number must 192 be multiplied, so that the product may be a perfect square ?

(A) 5 (B) 4 **(C) 3** (D) 2

4.By what least number must 1260 be divided to make the quotient a perfect square ?

**(A) 35** (B) 30 (C) 40 (D) 45

5.The boys of a school can be arranged in 15, 18 or 24 equal rows and also into a solid square. Find the least number of boys in the school.

(A) 3800 (B) 4000 **(C) 3600** (D) 1000

6.The ratio of two numbers is 5 : 8 and their difference is 69. Find the numbers.

(A) 120, 131 (B) 150, 163 **(C) 115, 184** (D) 118, 173

7.In a group of cows and hens, the number of legs are 14 more than twice the number of heads. The number of cows is

(A) 5 **(B) 7 **(C) 10 (D) 12

1.The sum of all two digit numbers divisible by 5 is

(A) 1035 (B) 1245 (C) 1230 **(D) 945**

2.The number 0 is

(A) whole number but not integer.

(B) integer but not rational.

(C) rational but not real number.

**(D) whole number, integer, rational and real number**.

3.Two equations 3x + 6y = 15 and 6x + 12y = 30 have

(A) only one solution (B) infinite number of solution **(C) no solution **(D) None of the above

4.If the length of shadow on the ground of a post is √3 times of its height, the angle of elevation of the Sun is

**(A) 30°** (B) 45° (C) 60° (D) None of the above

5.If the numerical values of total surface area and volume of a cube are equal, then the length of its diagonal is

**(A)** 6√3 (B) 6 (C) 6√2 (D) 3√6

6.If we subtract 5√5 from √125, the value is

**(A)** √80 (B) √120 (C) √100 (D) None of the above

7.A boy recorded the weight of some of his friends as 32kg, 30kg, 40kg, 65kg, 54kg, 38kg, 36kg, 45kg, 50kg, 52kg, 40kg. What is the median ?

(A) 38 kg **(B) 40 kg** (C) 45 kg (D) 43.8 kg

8.The number of coconuts plucked from each tree is 1 more than the number of coconut trees in Anil's garden. The total number of coconut plucked is 132. The total number of coconut trees in the garden is

(A) 12 (B) 22 **(C) 11** (D) 33

9.It has been seen in a survey of a region that 70 persons read English newspaper, 73 persons read Bengali newspaper and 64 persons read both the papers. If 63 persons do not read any paper on how many people the survey has been done ?

(A) 79 **(B) 142** (C) 207 (D) 143

10.The sum of digits of a two-digit number is 12. When the digits are interchanged, the resulting number is 36 more than original number. What is the original two-digit number ?

(A) 93 **(B) 48** (C) 39 (D) 84

11.The sum of three consecutive multiples of 3 is 72. What is the largest number ?

(A) 21 (B) 24 (C) 27 **(D) 36**

12.What is the smallest number to be subtracted from 549162 in order to make it a perfect square ?

(A) 28 (B) 36 (C) 62 **(D) 81**

13.0.04 x X = 0.000016, X = ?

**(A) 0.0004** (B) 0.04 (C) 4 (D) None of the above

14.If the number 97251*6 is completely divisible by 11, then the smallest whole number in place of * will be

**(A) 6** (B) 2 (C) 1 (D) 5

15.A river 1.5 m deep and 36 m wide is flowing at the rate of 3.5 km per hour. The amount of water that runs into the sea per minute (in cubic meter) is

**(A) 3150** (B) 31500 (C) 6300 (D) 63000

16.When the numerator of a fraction increases by 4, the fraction increases by ⅔. The denominator of the fraction is

(A) 2 (B) 3 (C) 4 **(D) 6**

17.Ram was asked to find ⅞ of a fraction but he mistakenly divided the fraction by ⅞ . As a result the difference between the answers was 75 / 784. What should be the Ram's correct answer ?

(A) 13/32 (B) 9/14 **(C) **5/16 (D) 5/14

18.The area of a circle is 2464 square meters. What will be its circumference ?

(A) 132 m **(B) 176 m** (C) 231 m (D) 272 m

19.The square of a number is 48 more than 22 times of itself. Find the number.

(A) 25 (B) 22 **(C) 24** (D) 28

20.What will come in place of question mark ?

12, 18, 36, 90, 270, ?

**(A) 945** (B) 960 (C) 845 (D) None of the above

21.4 + 0.4 + 0.04 + 0.004 - 0.23 = ?

(A) 4.226 (B) 4.224 (C) 4.414 **(D) 4.214**

22.Total price of 6 shirts and 7 trousers is Rs. 4,130 while that of 4 shirts and 9 trousers is Rs.4,270. Find out the price of 3 shirts.

(A) Rs.850 **(B) Rs.840** (C) Rs.860 (D) Rs.810

23.If the product of two successive positive integers is 7482. which is the greatest integer ?

**(A) 87** (B) 82 (C) 8.4 (D) 89

24.Rohan appeared for the Global Talent Search Examination wherein 4 marks are awarded for every correct answer and 1 mark is deducted for every wrong answer. Rohan attempted all the 60 questions and secured 130 marks. What would have been his score if there was no negative marking ?

(A) 140 **(B) 152** (C) 160 (D) 168

25.If it is possible to form a number with the second. the fifth and the eighth digits of the number 31549786, which is the perfect square of a two digit even number, which of the following will be the second digit of that even number ?

(A) 1 **(B) 4** (C) 6 (D) None of the above

26.Free books were distributed equally among children of a class. The number of books each child got was one-eighth of the number of children. Had the number of children been half, each child would have got 16 books. How many books were distributed in total ?

(A) 256 (B) 432 **(C) 512** (D) 640

27.If (0,0), (4, -3) and (x, y) are collinear then

(A) x = 8, y = - 6 (B) x = 8, y = 6 (C) x = 4, y = - 6 **(D) x = - 8, y = 6**

28.A single person takes 6 minutes to fill a bottle. If from 11 am to 12.30 pm 1845 bottles are to be filled, how many persons should be employed on this job ?

(A) 121 (B) 127 **(C) 123** (D) 139

29.If an amount of Rs.84,105 is distributed equally amongst 35 children. How much amount would each child get ?

(A) Rs.2,430 (B) Rs.2,043 **(C) Rs.2,403** (D) None of the above

1.a, b, c, d are four consecutive odd integers and their average is 42. What is the product of a and c ?

(A) 1890 **(B) 1677** (C) 1860 (D) 1845

2.The difference between the squares of two consecutive even integers is always divisible by

(A) 3 (B) 7 (C) 6 **(D) 4**

3.The least number which when divided by 15, 27,35 and 42 leaves in each case a remainder 7, is

(A) 1883 (B) 1987 **(C) 1897** (D) 2007

4.If three-fifths of 60% of a number is 36, the number is

(A) 90 (B) 80 **(C) 100** (D) 75

5.{{25)25 - 25} is exactly divisible by

**(A) 25** (B) 24 (C) 50 (D) 26

6.A sum of Rs. 312 was divided among 60 boys and some girls in such a way that each boy gets Rs. 3.60 and each girl Rs. 2.40. The number of girls is

(A) 65 (B) 60 (C) 35 **(D) 40**

7.A boy was asked to multiply a number by 12. By mistake he multiplied the number by 21 and got his answer 63 more than the correct answer. The answer was

(A) 8 **(B) 7** (C) 12 (D) 9

8.How many digits are required for numbering the pages of a book having 300 pages ?

(A) 299 (B) 492 (C) 789 **(D) 792**

9.Price of 5 chairs and 2 tables is Rs. 1,350. Two chairs cost as much as one table. What is the price of one chair and one table ?

(A) Rs. 350 **(B) Rs. 450** (C) Rs. 500 (D) Rs. 550

10.A student was asked to divide a number by 3. But, instead of dividing it, he multiplied it by 3 and got 29.7. What was the correct answer ?

(A) 9.3 **(B) 3.3** (C) 9.8 (D) 9.9

11.In an examination, a student was asked to find 3/14 of a number. By mistake, he found ¾ of it. His answer was 150 more than the correct answer. The given number is

(A) 180 (B) 240 **(C) 280** (D) 290

12.The least number of 4 digits, which is a perfect square is

(A) 1000 (B) 1016 **(C) 1024** (D) 1089

13.The fraction for the recurring decimal 0.535353 ......... is

**(A) **53/99 (B) 28/53 (C) 26/53 (D) 27/ 53

14.A gardener plants 17956 trees in such a way that there are as many rows as there are trees in a row. The number of trees in a row are

(A) 136 **(B) 134** (C) 144 (D) 154

15.If numbers p, p + 2, p + 4 are all primes, then p equal to

(A) 5 (B) 29 **(C) 3** (D) 191

16.5, 2, 7, 9, 16, 25 ?

**(A) 41** (B) 45 (C) 48 (D) 52

17.The sum of first five prime number is

(A) 11 (B) 18 (C) 26 **(D) 28**

18.The least perfect square which is divisible by 3, 4, 5, 6, 8 is

**(A) 900** (B) 1200 (C) 2500 (D) 3600

19.Identify the wrong number in the series 69, 55, 26, 13, 5

(A) 13 (B) 5 (C) 26 **(D) 55**

20.4, 6, 12, 14, 28, 30, ?

(A) 32 **(B) 60** (C) 62 (D) 64

21. 4, 8, 28, 80, 244, ?

**(A) 728** (B) 278 (C) 428 (D) 628

22. 0, 6, 24, 60, 120, 210, ?

(A) 240 **(B) 336** (C) 290 (D) 504

23.A number is greater than 4 but less than 9; also the number is greater than 7 but less than 11. What is the number ?

(A) 6 (B) 7 **(C) 8** (D) 9

24.What is the next number in the following sequence ?

0, 7, 26, 63, 124, 215, .....

**(A) 342** (B) 372 (C) 296 (D) 409

1.If the sum of two numbers is 10 and the sum of their reciprocals is 5/12, the numbers would be-

(A) (8, 2) **(B) (6, 4)** (C) (7, 3) (D) (9, 1)

2.The product of two successive numbers is 1980. The smaller number is -

(A) 34 (B) 35 **(C) 44** (D) 45

3.⅘ of a certain number is 64. Half of the number-

(A) 32 **(B) 40** (C) 80 (D) 16

4.The number of digit of the square root of 0.00059049 is-

(A) 5 (B) 6 **(C) 4** (D) 3

5.7 x 0.7 x 0.07 x 7000 = ?

(A) 24.01 (B) 2.401 (C) 240.1 **(D) 2401**

6.The product of two numbers is 1575 and its division is 7/9 .Then the two numbers are

**(A) 45, 35** (C) 35, 27 (B) 81, 63 (D) 36, 35

7.By what least number must 21600 be multiplied to make it a perfect cube ?

(A) 6 **(B) 10** (C) 30 (D) 60

8.The sum 5 + 6 + 7 + 8 + ........... + 19 = ?

(A) 150 (B) 170 **(C) 180** (D) 190

9.What number should come next in the sequence 6, 11, 21, 36, 56, ___ ?

(A) 78 **(B) 81** (C) 82 (D) 86

10.What number should come next in the sequence 6, 11, 21, 36, 56, ___ ?

(A) 78 **(B) 81** (C) 82 (D) 86

11.The greatest possible length which can be used to measure exactly the length 7 m, 3 m 85 cm, 12 m 95 cm is -

(A) 15 cm (B) 25 cm **(C) 35 cm** (D) 42 cm

12.What number should come next in the sequence

4, 5, 7, 10, 11, 13, 16, — ?

**(A) 17** (B) 18 (C) 19 (D) 21

13.What number should come next in the sequence 3, 7, 13, 27, 53, — ?

(A) 105 (B) 106 **(C) 107** (D) 108

14.A student was asked to divide a number by 3, but instead of dividing it, he multiplied it by 3 and got 29.7. The correct answer was -

**(A) 3.3** (B) 9.3 (C) 9.8 (D) 9.9

15.How many digits are required for numbering the pages of a book having 300 pages ?

(A) 299 (B) 492 (C) 789 **(D) 792**

16.What comes next in the sequence 2, 5, 10, 17, 26, — ?

(A) 33 (B) 35 (C) 36 **(D) 37**

17.What decimal fraction is 40 ml of a litre ?

(A) 0.4 **(B) 0.04** (C) 0.004 (D) 0.0004

18.What number should come next in the sequence

6, 18, 72, 360, 2160, — ?

(A) 12120 (B) 13120 (C) 14120 **(D) 15120**

19.What comes next in the sequence 1, 3, 7, 15, 31, 63, — ?

**(A) 127** (B) 125 (C) 121 (D) 129

20.The least number of square tiles required to pave the ceiling of a room 15m 17cm long and 9m 2cm broad is -

(A) 656 (B) 738 **(C) 814** (D) 902

21.Look carefully for the pattern and then choose which pair of numbers comes next -

1, 10, 7, 20, 13, 30, 19,

(A) 25, 40 **(B) 40, 25** (C) 25, 31 (D) 40, 50

22.What comes next in the sequence 2, 6, 18, 54, — ?

(A) 108 (B) 148 **(C) 162** (D) 216

23.What number should come next in the sequence 3, 8, 15, 24, 35, — ?

(A) 44 **(B) 46** (C) 48 (D) 50

24.What number should come next in the sequence 20, 27, 23, 37, 26, — ?

(A) 44 **(B) 47** (C) 50 (D) 53

25.The least perfect square number which is divisible by 3, 4, 5, 6 and 8 is -

(A) 900 (B) 1200 (C) 1600 **(D) 3600**

26.What number should come next in the sequence 19, 2, 38, 3, 114, 4, — ?

(A) 228 (B) 256 (C) 356 **(D) 456**

27.What number should come next in the sequence

0, 2, 8, 14, 24, 34, — ?

**(A) 48** (B) 42 (C) 40 (D) 38

28.What comes next in the sequence 5.2, 4.8, 4.4, 4, — ?

(A) 3 (B) 3.3 (C) 3.5 **(D) 3.6**

29.What number should come next in the sequence 7, 14, 23, 34, 47, — ?

**(A) 62** (B) 60 (C) 64 (D) 66

30.There are three boxes. The first box contains 10 red balls, the second box contains 10 blue balls, and the third box contains 5 red and 5 blue balls. The boxes are wrongly labelled as red, blue and red-blue. You have to correctly lable each box.You are allowed to open one box, pick one ball at random, see its colour and put it back into the box, without seeing the color of the other balls.What is the smallest number of such operations necessary to correctly label the boxes ?

(A) 1 (B) 2 (C) 3 **(D) 4**

1.The boys of a school can be arranged in 15, 18 or 24 equal rows and also into a perfect square. The least number of boys in the school is

(A) 900 (B) 1600 (C) 2500 **(D) 3600**

2.No of Zeros in the product of natural numbers from 1 to 10 will be

(A) 4 (B) 3 **(C) 2** (D) 1

3.The least number of five digits which is multiple of 319 is

(A) 10,111 **(B) 10,208** (C) 10,319 (D) 10,357

4.Rs. 2610 is divided among A, B and C such that 0.5 of A = 0.6 of B = 0.75 of C. C gets

(A) Rs. 1044 (B) Rs. 1000 (C) Rs. 870 **(D) Rs. 690**

5.Find the largest natural number which exactly divides the product of any 4 consecutive natural numbers

(A) 36 **(B) 24** (C) 48 (D) 32

6.280 oranges are divided among 50 girls and boys so that each boy gets 5 oranges and each girl gets 7 oranges. How many girls are there ?

(A) 14 girls **(B) 15 girls** (C) 16 girls (D) 17 girls

7.254 x ? x 8 = 95504

**(A) 47** (B) 49 (C) 51 (D) 53

8.The number (6n2 + 6n) for natural number n is always divisible by

(A) 6 only (B) 12 only **(C) 6 and 12** (D) 18 only

9.A number is as much greater than 31 as is less than 55. The number is :

(A) 47 (B) 52 (C) 39 **(D) 43**

10.If the product of three consecutive integers is 120, then the sum of the integers is :

(A) 9 **(B) 15** (C) 12 (D) 14

11.The smallest number of 4 digits, which is a perfect square, is

(A) 1000 (B) 1016 **(C) 1024** (D) 1036

12.Akbar weighs 15 kg more than Rahim. Their combined weight is 135 kg. How much does Rahim weight ?

**(A) 60 kg** (B) 75 kg (C) 80 kg (D) None of the above

13.Bananas are bought at 3 for Rs. 2 and sold at 2 for Rs. 3. Find the gain percent.

(A) 110% (B) 115% (C) 120% **(D) 125%**

1.Which of the following numbers is not a perfect square ?

(A) 7056 (B) 3969 **(C) 5478** (D) 4624

2.What least number must be added to 15370 to make it a perfect square ?

(A) 4 **(B) 6** (C) 8 (D) 9

3.By what least number should 648 be multiplied to get it a perfect cube ?

(A) 3 (B) 6 **(C) 9** (D) 8

4.By what least number should 1536 be divided to get it perfect cube ?

**(A) 3** (B) 4 (C) 6 (D) 8

5.Which of the following numbers is divisible by 3 ?

(A) 24357806 (B) 35769812 **(C) 83479560** (D) 3336433

6.Which of the following numbers is divisible by 11 ?

(A) 3333333 (B) 1111111 **(C) 22222222** (D) none of the above

7.The greatest number which divides 134 and 167 leaving 2 as remainder in each case is

(A 14 (B) 17 (C) 19 **(D) 11**

8.The smallest number which when diminished by 3 is divisible by 11, 28, 36 and 45 is

(A) 1257 (B) 1260 (C) 1263 **(D) none of the above**

9.The number 5416*6 is a perfect square, the '*' marked digit is

(A) 5 (B) 6 (C) 4 **(D) 9**

10.Given set is (224, 15, 4) which is the similar set

(A) 10, 6, 5 (B) 24, 16, 0 **(C) 63, 8, 3** (D) none of the above

11.Given, set is (24, 21, 12) which is the similar set

**(A) 95, 90, 65** (B) 85, 80, 50 (C) 60, 70, 40 (D) 45, 55, 65

12.Find the missing number in the series 4, 5, 12, 39, 160, — ?

(A) 226 (B) 452 (C) 565 **(D) 805**

13.Identify the missing number in the series 2, 3, 12, 37, 86, 167 ?

(A) 204 (B) 258 **(C) 288** (D) 402

14.The missing number in the Series 225, 289, ? , 441 is

**(A) 361** (B) 383 (C) 375 (D) 386

15.Which is the odd number out in this series - 33792, 8448, 2148, 528, 132, 33, 825

**(A) 2148** (B) 8448 (C) 528 (D) 132