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

Question 11 Mark
$100$ thousands $=$ ________ lakh.
Answer
We know that, $1$ lakh $= 100000$
$= 100 \times 1000$
$= 100$ thousands
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Question 21 Mark
By adding $1$ to the greatest __________ digit number, we get ten lakh.
Answer
We know that, predecessor is one less than the given number.
$1000000 - 1 = 999999$
So, $999999$ is the greatest 6-digit number.
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Question 31 Mark
The $LCM$ of two numbers is greater than the larger of the numbers.
Answer
Since, $LCM$ of two numbers may be equal to or greater than the larger of the numbers.
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Question 41 Mark
Natural numbers are closed under addition.
Answer
Since, the sum of any two natural numbers is always a natural number.
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Question 51 Mark
$5555 = 5 \times 1000 + 5 \times 100 + 5 \times 10 + 5 \times 1$
Answer
Since, $5 \times 1000 + 5 \times 100 + 5 \times 10 + 5 \times 1 = 5000 + 500 + 50 + 5 = 5555$
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Question 61 Mark
Among kilo, milli and centi, the smallest is centi.
Answer
Since, among kilo, milli and centi, the smallest is milli.
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Question 81 Mark
$786 \times 3 + 786 \times 7 =$ ________
Answer
$786 \times 3 + 786 \times 7 = 786 \times (3 + 7) = 786 \times 10 = 7860$
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Question 91 Mark
$400$ is the predecessor of ________.
Answer
We know that, predecessor of any number is $1$ less than the number.
So, predecessor of $400 = 400 - 1 = 399$
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Question 101 Mark
A number, for which the sum of all its factors is equal to twice the number, is called a __________ number.
Answer
By definition, a number, for which the sum of all its factors is equal to twice the number, is called perfect number.
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Question 111 Mark
There is a natural number which when added to a natural number, gives the natural number itself.
Answer
There is no such natural number which when added to a natural number, gives the natural number itself.
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Question 121 Mark
The number $81652318$ will be read as eighty one crore six lakh fifty two thousand three hundred eighteen.
Answer
Since, the number $81652318$ will be read as eight crore sixteen lakh fifty two thousand three hundred eighteen.
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Question 141 Mark
________ is the successor of the largest $3-$digit number.
Answer
We know that,
largest $3-$digit number $= 999$
Successor of $999 = 999 + 1 $
$= 1000$
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Question 151 Mark
Height of a person is $1\ m\ 65\ cm.$ His height in millimetres is _________.
Answer
We know that, $1\ m = 100\ cm$ and $1\ cm = 10\ mm$
$1\ m = 1000\ mm$ and $65\ cm = 65 × 10\ mm = 650\ mm$
So,
$1\ m\  65\ cm = 1000\ mm + 650\ mm$
$= 1650\ mm$
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Question 161 Mark
$9128 \times $ ________ $= 9128$
Answer
$9128 \times 1 = 9128$​​​​​​​
Solution: If any number is multiplied by $1,$ then it gives the same number.
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Question 171 Mark
In Roman numeration, if a symbol is repeated, its value is multiplied as many times as it occurs.
Answer
Since, in Roman numeration, if a symbol is repeated, its value is added as many times as it occurs.
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Question 181 Mark
$2916\ \times $ _______ $= 0$
Answer
$2916 \times 0 = 0$
Solution:
If any number is multiplied by zero, then their product is always zero.
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Question 191 Mark
A number is a ________ of each of its factors.
Answer
A number is a multiple of each of its factors. Solution: By general rule, a number is a multiple of each of its factors.
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Question 201 Mark
$HCF$ of two or more numbers may be one of the numbers.
Answer
If all the numbers are multiples of same number, then the smallest number among them is their $HCF.$
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Question 211 Mark
On the following numbers, which is the greatest and which is the smallest? $38051425, 30040700, 67205602$
Answer
We have, $38051425, 30040700$ and $67205602$
On comparing the given numbers. we get,
The greatest number $= 67205602$
the smallest number $= 30040700$
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Question 221 Mark
Predecessor of a two-digit number is always a two-digit number.
Answer
Since, predecessor of a two-digit number cannot be always a two digit number, e.g. Let a two-digit number be $10.$ Then, predecessor of $10 = 10 - 1 = 9$
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Question 231 Mark
Whole numbers are closed under ___________ and under ___________.
Answer
Whole numbers are closed under addition and under multiplication.
Solution:
If $a$ and $b$ are any two whole numbers, then $a + b = c ($whole numbers$).$
Also, $a \times b = c ($whole numbers$)$
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Question 241 Mark
If the sum of two distinct whole numbers is odd, then their difference also must be odd.
Answer
It is a general rule.
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Question 251 Mark
$532235 = 5 \times 100000 + 3 \times 10000 + 2 \times 1000 + 2 \times 100 + 3 \times 10 + 5$
Answer
Since, $5 \times 100000 + 3 \times 10000 + 2 \times 1000 + 2 \times 100 + 3 \times 10 + 5 \times 1$
$= 500000 + 30000 + 2000 + 200 + 30 + 5 = 532235$
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Question 261 Mark
The number five crore twenty three lakh seventy eight thousand four hundred one can be written, using commas, in the Indian System of Numeration as ____________.
Answer
The number five crore twenty three lakh seventy eight thousand four hundred one can be written, using commas, in the Indian System of Numeration as $5,23,78,401.$
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Question 271 Mark
If a number has _________ in ones place, then it is divisible by $10.$
Answer
If a number has zero in ones place, then it is divisible by $10. $
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Question 281 Mark
Any non-zero whole number divided by itself, gives the quotient $1.$
Answer
If a is any whole number, then $a + a = 1$
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Question 291 Mark
Addition is commutative for natural numbers.
Answer
If $a$ and $b$ are two natural numbers, then
$a + b = b + a$
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Question 301 Mark
If the sum of the digits in a number is a of $3,$ then the number is _________ divisible by $3.$
Answer
If the sum of the digits in a number is a of $3,$ then the number is multiple divisible by $3.$
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Question 311 Mark
If a whole number is divided by another whole number, which is greater than the first one, the quotient is not equal to zero.
Answer
It is a standard result.
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Question 321 Mark
The largest $4-$digit number formed by the digits $6, 7, 0, 9$ using each digit only once, is $9760.$
Answer
Since, for making the largest number, we arrange the given digits in descending order. Descending order of the given digits is $9, 7, 6$ and $0.$
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Question 331 Mark
Of the given two natural numbers, the one having more digits, is greater.
Answer
  It is a standard rule.
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Question 341 Mark
Length of river ‘Narmada’ is about $1290\ km.$ Its length in metres is __________.
Answer
Length of river ‘Narmada’ is about $1290\ km.$
Its length in metres is $1290000\ m.$
Solution:
We know that, $1\ km = 1000\ m$
$\therefore 1290\ km = 1290 \times 1000 = 1290000\ m$
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Question 361 Mark
There is a whole number which when added to a whole number, gives the number itself.
Answer
Since, if zero is added to any whole number, then the sum is the number itself.
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Question 381 Mark
The product of two whole numbers need not be a whole number.
Answer
Whole numbers are closed under multiplication.
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Question 391 Mark
If a number exactly divides the sum of three numbers, it must exactly divide the numbers separately.
Answer
If a number divides three numbers exactly, it must divide their sum exactly, but vice-versa is not true.
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Question 401 Mark
If a number divides three numbe exactly, it must divide their sum exactly.
Answer
It is a standard result.
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Question 411 Mark
If $0$ is subtracted from a whole number, then the result is the ________ itself.
Answer
If $0$ is subtracted from a whole number, then the result is the number itself.
Solution:
If $a$ is any whole number, then $a - 0 = a$
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Question 421 Mark
The smallest $6-$digit natural number ending with $5$ is __________.
Answer
The smallest $6-$digit natural number ending with $5$ is $100005.$
Solution:
We know that, smallest $6-$digit natural number $= 100000$
​​​​​​​Smallest $6-$digit natural number ending with $5 = 100005$
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Question 431 Mark
The population of Pune was $2538473$ in $2001.$ Rounded off to nearest thousands, the population was __________.
Answer
The population of Pune was $2538473$ in $2001.$ Rounded off to nearest thousands, the population was $2538000.$
Solution:
Rounded off $2538473$ to nearest thousands $= 2538000$
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Question 441 Mark
A number with three or more digits is divisible by $6,$ if the number formed by its last two digits (i.e. ones and tens) is divisible by $6.$
Answer
According to the divisibility test for $6,$ if a number is divisible by $2$ and $3$ both, then it is divisible by $6.$
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Question 451 Mark
A number with $4$ or more digits is divisible by $8,$ if the number formed by the last three digits is divisible by $8.$
Answer
According to the divisibility test for $8, 4$ or more digit number is divisible by $8,$ if the number formed by the last three digits is divisible by $8.$
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Question 461 Mark
$19 \times 12 + 19 = 19 \times (12 +$ _______$)$
Answer
$19 \times 12 + 19 = 19 \times (12 + 1)$
Solution:
If $a, b$ and $c$ are three whole numbers, then,
$a \times b + a \times c = a(b + c) [$by distributive property$]$
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Question 471 Mark
The $LCM$ of two or more given numbers is the lowest of their common ___________.
Answer
The $LCM$ of two or more given numbers is the lowest of their common multiples.
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Question 481 Mark
$a.\ 1$ metre $= .......$ millimetres.
$b.\ 1$ centimetre $= ........ $ millimetres.
$c.\ 1$ kilometre $= ....... $ millimetres.
Answer
$a.$ We know that,
$10\ mm = 1\ cm$ and $100\ cm = 1\ m$
$1\ m = 1000\ mm$
$b.\ 1\ cm = 10\ mm$
$c.\ $ We know that,
$10\ mm = 1\ cm$
$100\ cm = m$ and $1000\ m = 1\ km$
$1\ km = 1000 \times 100 \times 10$
$= 1000000\ mm$
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Question 491 Mark
$39746 = 3 \times 10000 + 9 \times 1000 + 7 \times 100 + 4 \times 10 + 6$
Answer
Since, $3 \times 10000 + 9 \times 1000 + 7 \times 100 + 4 \times 10 + 6 \times 1$
$= 30000 + 9000 + 700 + 40 + 6 = 39746$
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Question 501 Mark
Estimated sum of $7826$ and $12469$ rounded off to hundreds is $20000.$
Answer
Since, rounded off $7826$ to nearest hundreds $= 7800$ And rounded off $12469$ to nearest hundreds $= 12500$
So, estimated sum $= 7800 + 12500 = 20300$
Here, $20300$ is nearest to $20000.$
So, the given statement is true.
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Question 521 Mark
The $LCM$ of two coprime numbers is equal to product of the numbers.
Answer
 Consider a pair of coprime numbers $3$ and $4.$
$HCF$ of $3$ and $4 = 1$
$LCM \times HCF =$ Product of the two numbers Now,
$LCM \times HCF = 3 \times 4 $
$\Rightarrow LCM \times 1 = 3 \times 4 $
$\Rightarrow LCM = 12$
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Question 531 Mark
Natural numbers are closed under subtraction.
Answer
Since, the difference of any two natural numbers is not always a natural number.
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Question 541 Mark
Successor of a one-digit number is always a one-digit number.
Answer
Since, successor of a one-digit number may be a two-digit number. e.g.
Let one-digit number be $9.$
Then, successor of $9 = 9 + 1 = 10,$
which is a two-digit number.
 
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Question 551 Mark
Every whole number is the successor of another whole number.
Answer
Since, $0$ (whole number) is not the successor of any whole number.
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Question 561 Mark
$2395\ \times $ _________ $= 6195 \times 2395.$
Answer
$2395 \times 6195 = 6195 \times 2395.$
Solution: If $a$ and $b$ are two whole numbers,
then $a \times b = b \times a [$by commutative property$]$
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Question 571 Mark
If the $HCF$ of two numbers is one of the numbers, then their $LCM$ is the other number.
Answer
Since, $HCF \times LCM =$ First number $\times$ Second number
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Question 581 Mark
The number of factors of a prime number is ___________.
Answer
Every prime number has only two factors, $1$ and the number itself.
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Question 591 Mark
$a.\ 10$ million $= .......$ crore $10.$
$b.\ $ lakh $= ........$ million.
Answer
$a.$ We know that,
$1$ crore $= 100$ lakh and $1$ million $= 10$ lakh
$1$ crore $= 10$ million
$b.$ We know that,
$1$ million $= 10$ lakh
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Question 601 Mark
Successor of a $3-$digit number is always a $3-$digit number.
Answer
Since, successor of a $3-$digit number cannot be always a $3-$digit number, e.g. Successor of $999 = 999 + 1 = 1000$
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Question 611 Mark
$1$ is the identity for multiplication of whole numbers.
Answer
If a is any whole number, then $a \times 1 = a$
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Question 631 Mark
Any two consecutive numbers are coprime.
Answer
By definition, coprime numbers are those numbers, whose $HCF$ is $1.$
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Question 641 Mark
$1$ is identity for addition of whole numbers.
Answer
Since, $1$ is the identity for multiplication of whole numbers.
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Question 651 Mark
$1001 \times 2002 = 1001 \times (1001 +$ ________$).$
Answer
$1001 \times 2002 = 1001 \times (1001 + 1001).$
Solution:
Let $x$ be the missing number, then $1001 \times 2002 = 1001(1001 + x) $
$\Rightarrow 2002 = (1001 + x) $
$\Rightarrow 2002 - 1001 = x$
$\therefore x = 1001$
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Question 661 Mark
A number is divisible by __________ if it has any of the digits $0, 2, 4, 6$ or $8,$ in its ones place.
Answer
According to the divisibility test for $2,$
if the last digit of a number is either $0$ or $2$ or $4$ or $6$ or $8,$
then the number is divisible by $2.$
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Question 671 Mark
By reversing the order of digits of the greatest number made by five different non-zero digits, the new number is the __________ number of five digits.
Answer
 For making smallest number from given digits, we arrange them in ascending order and for greatest number, we arrange them in descending order.
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Question 681 Mark
A whole number divided by another whole number greater than $1,$ never gives the quotient equal to the former.
Answer
It is a standard result.
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Question 691 Mark
Natural numbers are closed under __________ and under ____________.
Answer
Natural numbers are closed under addition and under multipication.
Solution:
If $a$ and $b$ are any two natural numbers,
then $a + b = c ($natural numbers$)$
Also, $a \times b = c ($natural numbers$)$
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Question 701 Mark
If the sum of the digits of a number is divisible by $3,$ then the number itself is divisible by $9.$
Answer
According to the divisibility test of $9,$ a number is divisible by $9,$ if the sum of the digits of a number is divisible by $9.$
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Question 711 Mark
The smallest whole number is _______.
Answer
We know that, whole numbers start from $0.$
Therefore, the smallest whole number is $0.$
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Question 721 Mark
The highest common factor of two or more numbers is greater than their lowest common multiple.
Answer
 Since, $HCF$ of two or more numbers is less than their lowest common multiple.
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Question 731 Mark
Predecessor of $100000$ is __________.
Answer
For getting predecessor of the given number,
we subtract $1$ from the given number.
So, predecessor of $100000 = 100000 - 1 = 99999$
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Question 741 Mark
$125 + (68 + 17) = (125 + $______ $) + 17$
Answer
$125 + (68 + 17) = (125 + 68) + 17$
Solution: If $a, b$ andc are three whole numbers,
then $a + (b + c) = (a + b) + c [$by associative property$]$
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Question 751 Mark
Sum of two distinct whole numbers is always less than their product.
Answer
Let us understand this through example.
$1 + 2 = 3$ and $1 \times 2 = 2$
Here, sum $(3)\ > $ product $(2)$ We can say that sum of two whole numbers is not always less than their product.
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Question 761 Mark
A number is divisible by $5,$ if it has _________ in its ones place.
Answer
According to divisibility test for $5,$
if a number has $0$ or $5$ in its ones place,
then it is divisible by $5.$
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Question 771 Mark
$a.\ 1$ gram $= ......$ milligrams.
$b.\ 1$ litre $= ......$ millilitres.
$c.\ 1$ kilogram $= .......$ milligrams.
Answer
$a.\ 1\ g = 1000\ mg$
$b.\ 1\ L = 1000\ mL$
$c.$ We know that,
$1000\ mg = 1\ g$ and $1000\ g = 1\ kg$
$1\ kg = (1000 \times 1000)\ mg$
$= 1000000\ mg$
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Question 781 Mark
The number $LIV$ is greater than $LVI.$
Answer
Since, $LIV = 50 + 4 = 54$
$LVI = 50 + 5 + 1 = 56$
$\therefore LVI > LIV$
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Question 791 Mark
Two numbers having only $1$ as a common factors, are called __________ numbers.
Answer
Two numbers having only $1$ as a common factors, are called coprime numbers.
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Question 801 Mark
In Roman numeration, the symbol $X$ can be subtracted from __________ $M$ and $C$ only.
Answer
By general rule, in Roman numeration, the symbol $X$ can be subtracted from $L, M$ and $C$ only.
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Question 811 Mark
$2$ is the only ________ number, which is even.
Answer
$2$ is the only prime number, which is even.
Solution:
Those numbers which are divisible by $1$ and the number itself, are known as prime numbers.
$2$ is the only prime number which is even.
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Question 831 Mark
All numbers which are divisible by $4,$ may not be divisible by $8.$
Answer
Since, $4$ is divisible by $4,$ but it is not divisible by $8.$
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Question 841 Mark
$24 \times 35 = 24 \times 18 + 24\ \times $_______
Answer
Let a be the missing number, then
$24 \times 35 = 24 \times 18 + 24 \times a $
$\Rightarrow 24 \times 35 - 24 \times 18 = 24 \times a $
$\Rightarrow 24(35 - 18) = 24 \times a $
$\Rightarrow 24 \times 17 = 24 \times a$
$\therefore a = 17$
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Question 851 Mark
Natural numbers are not closed under multiplication.
Answer
Since, the sum of any two natural numbers is always a natural number.
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Question 871 Mark
$82546 = 8 \times 1000 + 2 \times 1000 + 5 \times 100 + 4 \times 10 + 6$
Answer
Since, $8 \times 1000 + 2 \times 1000 + 5 \times 100 + 4 \times 10 + 6 \times 1$
$= 8000 + 2000 + 500 + 40 + 6 = 10546 \neq 82546$
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Question 881 Mark
The $HCF$ of two or more given numbers is the highest of their common ____________.
Answer
The $HCF$ of two or more given numbers is the highest of their common factors.
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Question 891 Mark
Multiplication is distributive over ___________ for whole numbers.
Answer
Multiplication is distributive over addition for whole numbers.
Solution:
If $a, b$ and $c$ are three whole numbers,
then $a(b + c) = (a \times b) + (a \times c)$
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Question 901 Mark
Every whole number has its predecessor.
Answer
Since, every whole number does not have a predecessor, e.g. $0$ does not have a predecessor.
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Question 911 Mark
$32 \times (27 \times 19) = (32 \times $ ______$) \times 19$
Answer
$32 \times (27 \times 19) = (32 \times 27) \times 19$
Solution: If $a, b$ and $c$ are any three natural numbers,
then $a \times (b \times c) = (a \times b) \times c [$by multiplicative property$]$
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Question 921 Mark
The largest six-digit telephone number that can be formed by using digits $5, 3, 4, 7, 0$ and $8$ only once, is $875403.$
Answer
Since, for making largest six-digit number,
we arrange the given digits in descending order,
we get i.e. $8, 7, 5, 4, 3$ and $0.$
Largest six-digit number $= 875430$
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Question 931 Mark
The number $85764$ rounded off to nearest hundreds is written as $85700.$
Answer
Since, rounded off $85764$ to nearest hundreds $= 85800$
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Question 941 Mark
Successor of $106159$ is _________.
Answer
For getting successor of the given number,
we add $1$ to the given number.
So, successor of $106159 = 106159 + 1 = 106160$
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Question 951 Mark
The numbers $4578, 4587, 5478$ and $5487$ are in descending order.
Answer
Since, in descending order, we arrange the given numbers from largest to smallest,
$5487 > 5478 > 4587 > 4578$
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Question 961 Mark
The numbers having more than two factors are called __________ numbers.
Answer
The numbers having more than two factors are called composite numbers.
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Question 971 Mark
$10001 \times 0 = $_________.
Answer
If any number is multiplied by zero, then their product is always zero.
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Question 981 Mark
The smallest $4-$digit number is the successor of the largest $3-$digit number.
Answer
Since, the largest $3-$digit number $= 999$
Successor of $999 = 999 + 1 = 1000 [$smallest $4-$digit number$]$
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Question 1001 Mark
Number of primes between $1$ to $100$ is __________.
Answer
Prime numbers between $1$ to $100$ are $2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89$ and $97.$
Number of prime numbers between $1$ to $100 = 25$
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Question 1011 Mark
If a number exactly divides the sum of three numbers, it must exactly divide the numbers separately.
Answer
If a number divides three numbers exactly, it must divide their sum exactly, but vice-versa is not true.
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Question 1021 Mark
Every number is a multiple of itself.
Answer
There are infinite number of multiples of any given number.
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Question 1031 Mark
$24 \times 35 = 24 \times 18 + 24 \times $_______
Answer
Let a be the missing number,
then $24 \times 35 = 24 \times 18 + 24 \times a $
$\Rightarrow 24 \times 35 - 24 \times 18 = 24 \times a $
$\Rightarrow 24(35 - 18) = 24 \times a $
$\Rightarrow 24 \times 17 = 24 \times a$
$\therefore a = 17$
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Question 1041 Mark
If the difference between the sum of digits at odd places (from the right) and sum of digits at even places (from the right) of a number is either $0$ or divisible by , then the number is divisible by _______.
Answer
According to the divisibility test for $11,$ if the difference between the sum of digits at odd places and sum of digits at even places of a number is either $0$ or divisible by $11,$ then number is divisible by $11.$
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Question 1051 Mark
$LCM$ of two or more numbers may be one of the numbers.
Answer
If all the numbers are multiples of same number, then the greatest number among them is their $LCM.$
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Question 1061 Mark
$24 \times 25 = 24\ \times $_____$ /4 = 600$
Answer
Let a be the missing number, then $\times\ 24$
$24 \times 25$
$=24\times\big(\frac{\text{a}}{4}\big)$
$=\big(\frac{24}{24}\big)\times25\times4$
$\Rightarrow\text{a}=100$
$24\times25=24\times\Big(\frac{100}{4}\Big)=600$
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Question 1071 Mark
$LCM$ of two numbers is $28$ and their $HCF$ is $8.$
Answer
Since, $LCM (28)$ is not divisible by $HCF (8).$
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Question 1081 Mark
The number of multiples of a given number is finite.
Answer
There are infinite number of multiples of any given number.
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Question 1091 Mark
Between any two natural numbers, there is one natural number.
Answer
Between any two natural numbers $a$ and $b,$ there are $(b - a - 1)$ natural numbers, where $b > a.$
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Question 1101 Mark
Division of a whole number by ____________ is not defined.
Answer
Division of a whole number by $0$ (zero) is not defined.
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Question 1111 Mark
Writing of numbers from the greatest to the smallest is called an arrangement in __________ order.
Answer
Writing of numbers from the greatest to the smallest is called an arrangement in Descending order.
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Question 1121 Mark
The $HCF$ of two numbers is smaller than the smaller of the numbers.
Answer
Since, $HCF$ of two numbers is either equal to or greater than the smaller of the numbers.
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Question 1131 Mark
The distance between Srinagar and Leh is $422\ km.$ The same distance in metres is ___________.
Answer
The distance between Srinagar and Leh is $422\ km.$
The same distance in metres is $422000\ m.$
Solution: We know that,
$1\ km = 1000\ m $
$422\ km = 422 \times 1000 = 422000\ m$
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