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Maths 2 Mark Question

Operations on Whole Numbers · Maharashtra Board STD 6 (MSBSHSE - English Medium). 37 questions.

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2 Mark Question

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37 questions · self-marked practice — reveal the answer and mark yourself.

Question 12 Marks
Using distributivity of multiplication over addition of whole numbers, find the following products:
736 × 103
Answer
736 × 103
= 736 × (100 + 3)
(Using distributivity of multiplication over addition of whole numbers)
= (736 × 100) + (736 × 3)
= 73600 + 2208
= 75808
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Question 22 Marks
Determine the sum by suitable rearrangements:
2359 + 1000 + 2641 + 9999
Answer
2359 + 10001 + 2641 + 9999
Therefore, 59 + 41 = 100
And, 99 + 01 = 100
Therefore, (2359 + 2641) + (10001 + 9999)
= (5000) + (20000)
= 25000
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Question 32 Marks
Find the number which when divided by 58 gives a quotient 40 and remainder 31.
Answer
Dividend = Divisor × Quotient + Remainder
Dividend = 58 × 40 + 31
= 2320 + 31
= 2351
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Question 42 Marks
Find the following products.
816 × 745
Answer
816 × 745
Since, 745 = (750 - 5)
Therefore, 816 × (750 - 5)
= (816 × 750) - (816 × 5)
(Using distributivity of multiplication over subtraction of whole numbers)
= 612000 - 4080
= 607920
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Question 52 Marks
Find the values of the following using properties:
24579 × 93 + 7 × 24579
Answer
24579 × 93 + 7 × 24579
= 24579 × (93 + 7)
(Using distributivity of multiplication over addition of whole numbers)
= 24579 × 100 = 2457900
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Question 62 Marks
Determine the sum by suitable rearrangements:
15409 + 178 + 591 + 322
Answer
15409 + 178 + 591 + 322
409 + 91 = 500
And,
78 + 22 = 100
Therefore, (15409 + 591) + (178 + 322) = (16000) + (500) = 16500
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Question 72 Marks
Find the values of the following using properties:
493 × 8 + 493 × 2
Answer
493 × 8 + 493 × 2
493 × (8 + 2)
(Using distributivity of multiplication over addition of whole numbers)
= 493 × 10 = 4930
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Question 82 Marks
Divide and check the quotient and remainder:
16135 ÷ 875
Answer
$\frac{16135}{875}$ gives quotient = 18 and remainder = 385.

Verification: [Dividend = Divisor × Quotient + Remainder]
16135 = 875 × 18 + 385
16135 = 15750 + 385
16135 = 16135
L.H.S = R.H.S
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Question 92 Marks
Determine the product of the greatest number of three digits and the smallest number of two digits.
Answer
Greatest 3-digit number = 999
Smallest 2-digit number = 10
Product = 999 × 10 = 9990
Hence, the required product is 9990
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Question 102 Marks
Find the values of the following using properties:
1568 × 184 - 1568 × 84
Answer
1568 × 184 - 1568 × 84
= 1568 × (184 - 84)
(Using distributivity of multiplication over subtraction of whole numbers)
= 1568 × 100 = 156800
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Question 112 Marks
A group housing society constructed 350 flats. If the cost of construction for each flat is Rs. 993570, what is the total cost of construction of all the flats.
Answer
Cost of construction of 1 flat = Rs. 993,570
Total number of flats constructed = 350
Total cost of construction of 350 flats,
= Rs. (993,570 × 350)
= Rs. 347,749,500
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Question 122 Marks
Find the following products.
2032 × 613
Answer
2032 × 613
Since, 613 = (600 + 13)
Therefore, 2032 × (600 + 13)
= (2032 × 600) + ( 2032 × 13)
= 1219200 + 26416
= 1245616
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Question 132 Marks
Find:
$\ \ \ 1\ 5\ 9 \ 0\ 8\\\underline{\times\ \ \ \ \ \ 5 \ 4 \ 2\ }\\ \overline{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }$
Answer
The product is shown beow:
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Question 142 Marks
Determine the product of:
The greatest number of four digits and the smallest number of three digits.
Answer
The largest four - digit number = 9999
The smallest three - digit number = 100
Therefore,
Product of the smallest three - digit number and the largest four - digit number
= 9999 × 100 = 999900
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Question 152 Marks
Using distributivity of multiplication over addition of whole numbers, find the following products:
816 × 745
Answer
258 × 1008
= 258 × (1000 + 8)
(Using distributivity of multiplication over addition of whole numbers)
= (258 × 1000) + (258 × 8)
= 258000 + 2064
= 260064
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Question 162 Marks
Find the difference between the largest number of 4 digits and the smallest number of 7 digits.
Answer
The largest four - digit number is 9999.
The smallest seven - digit number is 1000000.
Therefore, difference between them = 1000000 - 9999 = 990001
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Question 172 Marks
Study the following pattern:
$1 =\frac{1\times2}{2}$
$1+2=\frac{2\times3}{2}$
$1+2+3=\frac{3\times4}{2}$
$1+2+3+4=\frac{4\times5}{2}<$
By observing the above pattern, find:
2 + 4 + 6 + 8 + 10 + ............... + 100
Answer
2 + 4 + 6 + 8 + 10 +… + 100
This can also be written as 2 × (1 + 2 + 3 + 4 + … + 49 + 50)
Now,
(1 + 2 + 3 + 4 + … + 49 + 50 )
= 50 × 512
= 1275
Therefore, (2 + 4 + 6 + 8 + 10 + … + 100)
= 2 × 1275 = 2550
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Question 182 Marks
Divide and check the quotient and remainder:
7772 ÷ 58
Answer
$\frac{7772}{58}=134$

Verification: [Dividend = Divisor × Quotient + Remainder ]
7772 = 58 × 134 + 0
7772 = 7772
L.H.S = R.H.S
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Question 192 Marks
Study the following pattern:
$1 =\frac{1\times2}{2}$
$1+2=\frac{2\times3}{2}$
$1+2+3=\frac{3\times4}{2}$
$1+2+3+4=\frac{4\times5}{2}<$
By observing the above pattern, find:
50 + 51 + 52 + _________ + 100
Answer
50 + 51 + 52 + … + 100
This can also be written as
(1 + 2 + 3 + … + 99 + 100) - (1 + 2 + 3 + 4 + … + 47 + 49)
Now,
(1 + 2 + 3 + … + 99 + 100 ) = 100 × 1012
And, (1 + 2 + 3 + 4 + … + 47 + 49 ) = 49 × 502
So, (50 + 51 + 52 + … + 100 ) = 100 × 1012 - 49 × 502
= 5050 - 1225
= 3825
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Question 202 Marks
Divide and check the quotient and remainder:
6906 ÷ 35
Answer
$\frac{6906}{35}$ gives quotient = 197 and remainder = 11
Verification: [Dividend = Divisor × Quotient + Remainder] 6906 = 35 × 197 + 11 6906 = 6895 + 11 6906 = 6906 L.H.S = R.H.S
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Question 212 Marks
Find the values of the following using properties:
15625 × 15625 - 15625 × 5625
Answer
15625 × 15625 - 15625 × 5625
= 15625 × (15625 - 5625)
(Using distributivity of multiplication over subtraction of whole numbers)
= 15625 × 10000
= 156250000
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Question 222 Marks
Find a number which when divided by 35 gives the quotient 20 and remainder 18.
Answer
Dividend = Divisor × Quotient + Remainder
Dividend = 35 × 20 + 18
= 700 + 18
= 718
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Question 232 Marks
Divide and check the quotient and remainder:
16025 ÷ 1000
Answer
$\frac{16025}{1000}$ gives quotient remainder = 25

Verification: [Dividend = Divisor × Quotient + Remainder]
16025 = 1000 × 16 + 25
16025 = 16000 + 25
16025 = 16025
L.H.S = R.H.S
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Question 242 Marks
Study the following pattern:
$1\times1+2\times2=\frac{2\times3\times5}{6}$
$1\times1+2\times2+3\times3=\frac{3\times4\times7}{6}$
$1\times1+2\times2+3\times3+4\times4=\frac{4\times5\times9}{6}$
By observing the above pattern, write next two steps.
Answer
The next two steps are as follows:
1 × 1 + 2 × 2 + 3 × 3 + 4 × 4 + 5 × 5
= 5 × 6 × 116
= 55
1 × 1+ 2 × 2 + 3 × 3 + 4 × 4 + 5 × 5 + 6 × 6
= 6 × 7 × 136
= 91
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Question 252 Marks
  1. 6 × 2 - 5 = 7
  2. 7 × 3 - 12 = 9
  3. 8 × 4 - 21 = 11
  4. 9 × 5 - 32 = 13
  5. _ × _ - __ = __
  6. _ × _ - __ = __
  7. _ × _ - __ = __
Answer
  1. 6 × 2 - 5 = 7
  2. 7 × 3 - 12 = 9
  3. 8 × 4 - 21 = 11
  4. 9 × 5 - 32 = 13
  5. 10 × 6 - 45 = 15
  6. 11 × 7 - 60 = 17
  7. 12 × 8 - 77 = 19
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Question 262 Marks
Without drawing a diagram, find. 10th square number.
Answer
A square number can easily be remembered by the following rule $N ^{\text {th }}$ square number $= n \times n 10$ th square number $=$ $10 \times 10=100$
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Question 272 Marks
The population of a town was 59000. In one year it was increased by 4563 due to new births. However, 9218 persons died or left the town during the year. What was the population at the end of the year?
Answer
Population of the town = 59000
Increase in the population = 4536
Decrease in the population = 9218
New population = 59000 + 4536 - 9218 = 54318
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Question 282 Marks
Rohit deposited Rs. 125000 in his savings bank account. Later he withdrew Rs. 35425 from it. How much money was left in his account?
Answer
Money deposited by Rohit = Rs. 125000
Money withdrawn by Rohit = Rs. 35425
$\therefore$ Money left in the account = Rs. (125000 - 35425) = Rs. 89575
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Question 292 Marks
What are the whole numbers which when multiplied with itself gives the same number?
Answer
There are two numbers which when multiplied with themselves give the same numbers.
  1. 0 × 0 = 0
  2. 1 × 1 = 1
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Question 302 Marks
The digits of 6 and 9 of the number 36490 are interchanged. Find the difference between the original number and the new number.
Answer
Original number = 39460
New number = -36490
Difference = 39460 - 36490 = 2970
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Question 312 Marks
Can a rectangular number also be a square number?
Answer
Yes, a rectangular number can also be a square number.
For example, 16 is a square number also a rectangular number.
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Question 322 Marks
Write the first four products of two numbers with difference 4 starting from in the following order:
Answer
1, 2, 3, 4, 5, 6 ....1 × 5 = 5 (5 - 1 = 4)
2 × 6 = 12 (6 - 2 =4)
3 × 7 = 21 (7 - 3 = 4)
4 × 8 = 32 (8 - 4 = 4)
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Question 332 Marks
The annual fee charged from a student of class VI in a school is Rs. 8880. If there are, in all, 235 students in class VI, find the total collection.
Answer
Fees charged from 1 student = Rs. 8880
Therefore,
Fees charged from 235 students,
= Rs. 8880 × 235
= 2086800
Thus, the total collection from class VI students is Rs. 2086800.
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Question 342 Marks
What is the difference between the largest number of five digits and smallest number of six digits?
Answer
The largest five - digit number is 99999.
The smallest six - digit number is 100000.
Therefore, difference between them = 100000 - 99999 = 1
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Question 352 Marks
Find the following products.
736 × 93
Answer
736 × 93
Since, 93 = (100 - 7)
Therefore, 736 × (100 - 7)
= (736 × 100) - (736 × 7)
(Using distributivity of multiplication over subtraction of whole numbers)
= 73600 - 5152
= 68448
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Question 372 Marks
The population of a town is 96209. If the number of men is 29642 and that of women is 29167, determine the number of children.
Answer
Total population of the town = 96209
Number of men = 29642
Number of women = 29167
Sum of men and women = (29642 + 29167) = 58809
Therefore, Number of children in the town = (Total population) - (Sum of men and women)
= 96209 - 58809 = 37400
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