SOLUTION IN 21 TO 30

21.       4500 x X= 3375  X = 3375      =3

                                    4500         4   

                       45) 3375  (75

                           315  

                            225

                              225

                                  x

22.       1400 x X =     1050 X = 1050      =   3

                                                1400           4

   

23.       Given exp. (1000)⁹ = (10³)⁹  =   10²⁷  = 10³ = 1000.

                         10²⁴     10²⁴          10²⁴       

        

24.       Given exp. 8988 x 1/8 x 1/4 = 2247/8    = 280.875

25.       Given exp. = 666 x 1/6 x 1/3 = 37.

                                 ²¹⁶   ³⁶ ⁹

26.       Given  300  x  1296        = 450

                                     64 ₄         8 ₆ ₄  

27.       Given exp. = (12³) x 6⁴ = (12)² x 6⁴   = (12)² x 6² = (72)² = 70.          

                          432               12 x 6²

28.       Given exp. = 35 + 15 x 3/2 = 35 + 45/2 = 35 + 22.5 = 57.5.

29.       5358 x 51 = 5358 x (50 + 1)      267900    

                       = 5358 x 50 + 5358 x 1                     + 5358           

                      =2679900 + 5358 = 27358.             273258

30.    587 x 999 = 587 x (1000 – 1)

                   =587 x 1000 – 587 – 1 = 587000 – 587 = 586413

SOLUTION IN 11 TO 20.

11.         7429                   let 8597 – X = 3071

-                                  4558              then,   X= 8597 – 3071             8579

                        3071                                                                   -3071

                                                                                                       5526

12.       3251                             let 4207 –X =3007

                                       Then, X = 4207 – 3007 = 1200.

                     +587

                      +369

                                       4207

13.       Let 4300731 – X =2535618

                                Then, X =4300731 – 2535618

                    4300731

                  -2535618

                    1765618

14.       19657                              let X -53651 =9999

                               33994                                         then, X = 9999 + 53651 + 9999 + 1+ 53650

                           53651                                                 =10000 + 53650 = 63650

                                      

15.           3

                             +   33

                                 + 333

                             +      3.33

                                    372.33

16.       Given sum = 9+ 3/4+ 7 + 2/17 (9+1/15)

                            = (9+ 7 -9) + (3/4+ 2/17 + 1/15)

                                  = 7+ 765 + 120 – 68        = 7 817

                                                                 1020                       1020

17.       Given exp. =-84 x (30 – 1) + 365

                                      = - (84 x 30) +84 + 365

                                       = - 2520 + 449 = -2071

                                         -2520

                                          + 449

                                         -2071

                                        = -2071

18.       35423   317 x 89 =317 x (90 – 1)

                                      +7164 = (317 x 90 – 317)

                                                     +41720 = (28530 – 317) = 28213

                                                     84307

                                                    -28213

                                                    54094

19.       9548 16862 =8362 + X X = 16862 – 8362 = 8500.

                                          +7314

                                                   16862

20.   X + 3699 + 1985 – 2047 = 31111

                         X + 3699 + 1985 = 31111 + 2047

                            X + 5684 = 33158                                                             33158

                                              X = 33158 – 5684 =27474.                                            -5684

                                                                                                                                 27474

EXERCISE MARK AGAINST THE CORRECT ANSWER IN EACH OF THE FOLLOWING: IN 131 TO 140:

130.(51 + 52 + 53 + ….   +100) =?

a)      2525

b)      2975

c)       3225

d)      3775

131.(1 – 1/n) + ( 1 – 2/n) + (1 – 3/n) + …. Up to n terms =?

a)      1/2n

b)      ½ (n-1)

c)       ½ n(n-1)

d)      None of these

132.How many natural numbers are there between 23 and 100 which are exactly divisible by 6?

a)      8

b)      11

c)       12

d)      13

e)      None of these

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

a)      1035

b)      1245

c)        1230

d)      945

e)      None o f these

134.The sum of how many terms of the series s 6+ 12 +18 +  24 …. Is 1800?

a)      16

b)      24

c)       20

d)      18

e)      2

135.How many terms are there in the G.P. 3, 6, 12 24, 384?

a)      8

b)      9

c)       10

d)      11

e)      7

136.2 +2 ²+ 2³ + ….2⁹ =?

a)      2044

b)      1022

c)       1056

d)      None of these

137.(1² + 2² + 3² + ….+ 10²) =?

a)      330

b)      345

c)       365

d)      385

138.(2²+ 4²+ 6²+ ….+ 20²)=?

a)      770

b)      1155

c)       1540

d)      385 x 385

139.(11² +12² + 13²+ …..+ 20²) =?

a)      385

b)      2485

c)       2870

d)      3255

                       ANSWERS

EXERCISE MARK AGAINST THE CORRECT ANSWER IN EACH OF THE FOLLOWING: IN 121 TO 130.

121.A number when divided by 196 leaves 75 as remainder. When the same number is divided by 37, the remainder will be:

a)      1

b)      2

c)       8

d)      11

122.A boy multiplied 987 by a certain number and obtained 559981 as his answer. If in the answer both 98 are wrong and the other digits are correct, then the correct answer would be:

a)      553681

b)      555181

c)       555681

d)      556581

123.How many of the following numbers are completely divisible by 132?

 264,396,462,792,968,2178,5184,6336

a)      4

b)      5

c)       6

d)      7

124.How many 3-digit numbers are completely divisible by 6?

a)      149

b)      150

c)       151

d)      166

125.The sum of first 45 natural numbers is:

a)      1035

b)      1280

c)       2070

d)      2140

130.The sum of all even natural numbers between 1 and 31 is

a)      16

b)      128

c)       240

d)      512

ANSWERS:

EXERCISE: MARK AGAINST THE CORRECT ANSWER IN EACH OF THE FOLLOWING: IN 111 TO 120

  111.Which one of the following numbers will completely divide (3²⁵ + 3²⁶ +3²⁷ +3²⁸)?

a)      11

b)      16

c)       25

d)      30

112.A 3-digit number 4a3 is added to another 3-digit number 984 to give a 4-digit number 13b7, which is divisible by 11. Then (a + b) =?

a)      10

b)      11

c)       12

d)      15

113.If X and y are positive integer such that (3X+ 7y) is a multiple of 11, then which of the following will be divisible by 11?

a)      4X + 6Y

                                  b)     X + y + 4

                                  c)      9X+ 4 Y

                                  d)      4X – 9Y

    116. If the number 653 Xy is divisible y 90, then (X + Y) =?

a)      2

b)      3

c)       4

d)      6

117.How many of the following numbers are divisible by 3 but not by 9?

 2133, 2343, 3474, 4131, 5286, 5430, 6336, 7347, 8115, 9276

a)      5

b)      6

c)       7

d)      None of these

118.Which of the following numbers is divisible by each one of 3, 7, 9 and 11?

a)      639

b)      2076

c)       3791

d)      37911

e)      None of these

119.How many of the following numbers are divisible by 132?

 264, 396, 462, 792, 968, 2178, 5184, 6336

a)      4

b)       5

c)       6

d)      7

120.A number when divided by 6 leaves a remainder 3. When the square of the number is divided by 6, the remainder is:

a)      0

b)      1

c)       2

d)      3

ANSWERS:

EXERCISE: MARK AGAINST THE CORRECT ANSWER IN EACH OF THE FOLLOWING: IN 101 TO 110.

101.  On    multiplying a number by 7, the product is a number each of whose digits is 3. the smallest such number is:   a)      47619

b)      47719

c)       48619

d)      47649

102. The difference of the squares of two consecutive even integers is divisible by which of the following integers?

a)      3

b)      4

c)       6

d)      7

 103. The difference of the squares of two consecutive odd integers is divisible by which of   the following integers?

a)      3

b)      6

c)       7

d)      8

 104. If n is a natural number, then (6n² + 6ṇ) is always divisible by:

a)      6 only

b)      6 and 12 both

c)       12 only

d)      By 18 only

105.N is a whole number which when divided by 4 given 3 as remainder. what will be the remainder when 2n is divided by 4?

a)      3

b)      2

c)       1

d)      0

105.What will be the remainder when (67⁶⁷+67) is divided by 68?

a)      17

b)      16

c)       1

d)      2

106.Which of the following numbers will completely divide (49⁶⁷  - 1)

a)      8

b)      14

c)       48

d)      50

108  . (Xᶯ - aᶯ) is completely divisible by (X-a), when

a)      N is any natural number

b)      N is an even natural number

c)       N is an odd natural number

d)      N is prime

109.What will be the remainder when 17²⁰⁰is divided by 18?

a)      17

b)      16

c)       1

d)      2

110.Which one of the following is the common factor of (47⁴³ + 43⁴³) and (47⁴⁷ + 43⁴⁷)?

a)      (47- 43)

b)      (47 + 43)

c)       (47⁴³ + 43⁴³)

d)      None of these

                         ANSWERS:

EXERCISE: MARK AGAINST THE CORRECT ANSWER IN EACH OF THE FOLLOWING IN 91 TO 100:

91.   On dividing a number by 68, we get 269 as dividend and 0 as remainder. On dividing the same number by 67, what will be the remainder?

a)      0

b)      1

c)    2

d)      3

92.   On dividing a number by 56, we get 29 as remainder. On dividing the same number by 8, what will be the remainder?

a)      4

b)      5

c)6

d)      7

93.   On dividing a number by 357, we get 39 as remainder. One dividing the same number by 17, what will be the remainder?

a)      0

b)      3

c)    5

d)      11

94.   On dividing a number by 5, we get 3 as remainder. On dividing the same number by 17, what will be the remainder?

a)      0

b)      1

c)2

d)      4

95.   The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and 15 as remainder. What is the smaller number?

a)      240

b)      270

c)295

d)      360

96.   In a division sum, the remainder is 0. As student mistook the divisor by 12 instead of 21 and obtained 35 as quotient. What is the correct quotient?

a)      0

b)      12

c)    13

d)      20

97.   The sum of the two numbers is 12 and their product is 35. What is the sum of the reciprocals of these numbers?

a)      12/35

b)      1/35

c)    35/8

d)      7/32

98.   If 60% of 3/5 of a number is 36, then the number is:

a)      80

b)      100

c)75

d)      90

99.   The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is:

a)      3/5

b)      3/10

c)    4/5

d)      5/4

100.                                 On dividing 2272 as well as 875 by 3-digit number N, we get the same remainder. The sum of the digits of N is :

a)      10

b)      11

c)       12

d)      13

 ANSWER:

EXERCISE: MARK AGAINST THE CORRECT ANSWER IN EACH OF THE FOLLOWING IN 81 TO 90:

81.   What smallest number should be added to 4456 so that the sum is completely divisible by 6?

a)      4

b)      3

c)    2

d)      1

e)      None of these

82.   Which natural number is nearest to 9217, which completely divisible by 88?

a)      9152

b)      9240

c)9064

d)      9184

e)      None of these

83.   Which natural number is nearest to 8485, which is completely divisible by 88?

a)      8475

b)      8500

c)       8550

d)      8525

84.   The largest 4-digit number exactly divisible by 88 is

a)      9944

b)      9768

c)       9988

d)      8888

e)      None of these

85.   The largest 5-digit number exactly divisible by 91 is

a)      99921

b)      99918

c)       99981

d)      99971

e)      None of these

86.   What least number must be subtracted from 13601, so that the remainder is divisible by 87?

a)      23

b)      31

c)29

d)      37

e)      49

87.   What least number must be added to 1056, so that the sum is completely divisible by 23?

a) 2

b)3

c) 18

d)21

e)None of these

88.   The smallest 5-digit number exactly divisible by 41 is:

a) 10041

b)10004

c) 10045

d)10025

e)None of these

89.   The smallest 6-digit number exactly divisible by 111 is:

a)      111111

b)      110011

c)    100011

d)      110101

e)      None of these.

90.   In a division sum, the divisor is 10 times the quotient and 5 times the remainder. If the remainder is 46, what is the dividend?

a)      4236

b)      4306

c)    4336

d)      5336

e)      None of these

ANSWERS: