2 Marks Questions - MATHS STD 6 Questions - Vidyadip

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2 Marks Questions

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

Question 12 Marks

How many $8-$digit numbers are there in all$?$

Answer

There are $10$ digits i.e., $0, 1, 2, 3, 4, 5, 6, 7, 8, 9.$
We cannot use $‘0’$ at the place having the highest place value in $8$ digit numbers.
So, we can use only $9$ digits at the place having the highest place value in $8$ digit numbers.
Also, we can use $10$ digits at the remaining places in $8$ digit numbers So, total numbers of $8-$digit
numbers $= 9 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 = 90000000$

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Question 22 Marks

Simplify each of the following: $109 \times 107$

Answer

$109 \times 107 = (100 + 9) \times 107$
$= 100 \times 107 + 9 \times 107$
$= 100 \times (100 + 7) + 9 \times (100 + 7)$
$= 10000 + 700 + 900 + 63$
$= 11663$

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Question 32 Marks

Simplify each of the following: $12 \times 105$

Answer

$12 \times 105 = (10 + 2) \times 105$
$= 10 \times 105 + 2 \times 105$
$= 10 \times (100 + 5) + 2 \times (100 + 5)$
$= 1000 + 50 + 200 + 10$
$= 1260$

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Question 42 Marks

Write: The smallest

Answer

Four smallest digits are $0, 1,2$ and $3.$
In order to generate the smallest $6-$digit number using digits $0, 1, 2$ and $3,$
we write the smallest non-zero digit at the place having the highest place value and the largest digit at the place having least place value.
Thus, we put $1$ in the left-most place and $3$ in the right-most place.
Digit $2$ is put at ten's place and at all other places we write zero.
Hence, the required number $= 100023.$

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Question 52 Marks

A famous cricket player has so far scored $6978$ runs in test matches. He wishes to complete $10,000$ runs. How many more runs does he need$?$

Answer

Runs scored by cricket player in test matches $= 6,978$
Therefore, Remaining runs required to complete $10,000$ runs $= 10,000 - 6,978 = 3,022$
Thus, the player needs to score $3,022$ more runs to complete $10,000$ runs.

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Question 62 Marks

Simplify each of the following:
$17 \times 109$

Answer

$17 \times 109 = (10 + 7) \times 109$
$= 10 \times 109 + 7 \times 109$
$= 10 \times (100 + 9) + 7 \times (100 + 9)$
$= 1000 + 90 + 700 + 63$
$= 1853$

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Question 72 Marks

How many different $3-$digit numbers can be formed by using the digits $0,2,5$ without repeating any digit in the number$?$

Answer

The three-digit numbers formed using the digits $0, 2$ and $5 ($without repeating any digit in the number$)$ are $250, 205, 502$ and $520.$ Therefore, four such numbers can be formed.

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Question 82 Marks

Which digits have the same face value and place value in $92078634?$

Answer

The place value of a digit depends on the place where it occurs, while the face value is the value of the digit itself.
In a number, the digits that have same face value and place value are the ones digit and all the zeroes of the number.
Therefore, in $9,20,78,634,4$ (the ones digit) and $0$ (the lakhs digit) have the same face value and place value.

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Question 92 Marks

Simplify each of the following:
$16 \times 108$

Answer

$16 \times 108 = (10 + 6) \times 108$
$= 10 \times 108 + 6 \times 108$
$= 10 \times (100 + 8) + 6 \times (100 + 8)$
$= 1000 + 80 + 600 + 48$
$= 1728$

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Question 102 Marks

Write all natural numbers between $500$ and $600$ which do not change if the digits are written in the reverse order.

Answer

To write the natural numbers between $500$ and $600$ which do not change if the digits are written in the reverse order we must have the same digit at the hundred's place and unit's place. Hence, the required numbers are $505, 515, 525, 535, 545. 555, 565, 575, 585, 595.$

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Question 112 Marks

Simplify each of the following: $9 \times 105$

Answer

$9 \times 105 = 9 \times (100 + 5)$
$= 9 \times 100 + 9 \times 5$
$= 900 + 45 = 945$

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Question 122 Marks

Simplify each of the following:
$6 \times 112$

Answer

$6 \times 112 = 6 \times (100 + 12)$
$= 6 \times 100 + 6 \times 12$
$= 600 + 6 \times (10 + 2)$
$= 600 + 6 \times 10 + 6 \times 2$
$= 600 + 60 + 12$
$= 672$

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Question 132 Marks

Simplify each of the following:
$101 \times 105$

Answer

$101 \times 105 = (100 + 1) \times 105$
$= 100 \times 105 + 1 \times 105$
$= 100 \times (100 + 5) + 105$
$= 10000 + 500 +105$
$= 10605$

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Question 142 Marks

Determine the difference of the place values of $7’s$ in $257839705.$

Answer

Place value of first $7 = 7 \times 10 = 700$
Place value of second $7 = 7 \times 10,000 = 70,00,000$
Required difference $= 70,00,000 - 700 = 69,99,300$

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Question 152 Marks

Simplify each of the following: $102 \times 103$

Answer

$102 \times 103 = (100 + 2) \times 103$
$= 100 \times 103 + 2 \times 103$
$= 100 \times (100 + 3) + 2 \times (100 + 3)$
$= 10000 + 300 + 200 + 6$
$= 10506$

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Question 162 Marks

Write: The largest.

Answer

To write the greatest $6-$digit number having four different digits, we will have to use four largest digits.
Clearly $9, 8, 7$ and $6$ are four largest digits.
In order to write the largest $6-$digit number using digits $6, 7, 8$ and $9,$
we put the largest digit $9$ at the place having the highest place value.
The smallest digit $8$ is put at the hundred's place,
the smallest digit $6$ is put at the right most place i.e. at unit's place and the digit $7$ is put at the ten's place.
All other places are filled by $9.$
Hence, the required number $= 999876.$

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Question 172 Marks

Determine the difference between the place value and the face value of $5$ in $78654321.$

Answer

The number $= 7,86,54,321$
The place value of $5 = 5$ ten thousands $= 50,000$
The face value of $5 = 5$
Therefore, the difference $= 50,000 - 5 = 49,995$

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Question 182 Marks

A machine, on an average, manufactures $2825$ screws a day. How many screws did it produce in the month of January $2006?$

Answer

As given in the question, Number of screws produced by a machine in a day $= 2,825$
Therefore, Number of screws produced by the same machine in the month of January $2006 = 2,825 × 31 = 87,575$
Thus, machine-produced $87,575$ screws in the month of January $2006.$

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Question 192 Marks

Determine the product of the place values of two fives in $450758.$

Answer

Place value of first $5 = 5 \times 10 = 50$
Place value of second $5 = 5 \times 10,000 = 50,000$
Required product $= 50 \times 50,000 = 25,00,000$

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Question 202 Marks

How many four-digit numbers are there in all?

Answer

There are $10$ digits i.e., $0, 1, 2, 3, 4, 5, 6, 7, 8, 9.$
We cannot use $‘0’$ at thousand’s place.
So, we can use only $9$ digits at thousand’s place.
Also, we can use $10$ digits at hundred’s, $10$ digits at ten’s and $10$ digits at unit’s place.
So, total numbers of four-digit numbers $= 9 \times 10 \times 10 \times 10 = 9000$

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Question 212 Marks

A book exhibition was held for four days in a school. The number of tickets sold at the counter on the first, second, third and final days were respectively $1094, 1812, 2050$ and $2751.$ Find the total number of tickets sold on all the four days.

Answer

Total number of tickets sold on all four days is the sum of the tickets sold on the first, second, third and final days.
Therefore, total number of tickets sold on all four days is given by $ :\ = 1094 + 1812 + 2050 + 2751 = 7707$

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