Question 2 :
A rectangular veranda is of dimension $18$m $72$cm $\times 13$ m $20$ cm. Square tiles of the same dimensions are used to cover it. Find the least number of such tiles.
Question 3 :
A number $x$ when divided by $7$  leaves a remainder $1$ and another number $y$ when divided by $7$  leaves the remainder $2$. What will be the remainder if $x+y$ is divided by $7$?
Question 4 :
Without actually performing the long division, state whether the following rational number will have a terminating decimal expansion or non -terminating decimal expansion$\displaystyle \frac{15}{1600}$
Question 6 :
State the following statement is True or False<br>35.251252253...is an irrational number<br>
Question 8 :
Let $x=\dfrac { p }{ q } $ be a rational number, such that the prime factorization of $q$ is of the form $2^n 5^m$, where $n, m$ are non-negative integers. Then $x$ has a decimal expansion which terminates.
Question 9 :
The ........... when multiplied always give a new unique natural number.
Question 10 :
................. states the possibility of the prime factorization of any natural number is unique. The numbers can be multiplied in any order.
Question 11 :
To get the terminating decimal expansion of a rational number $\dfrac{p}{q}$. if $q = 2^m 5^n$ then m and n must belong to .................
Question 12 :
According to Euclid's division algorithm, HCF of any two positive integers a and b with a > b is obtained by applying Euclid's division lemma to a and b to find q and r such that $a = bq + r$, where r must satisfy<br/>
Question 15 :
Assertion: The denominator of $34.12345$ is of the form $2^n \times 5^m$, where $m, n$ are non-negative integers.
Reason: $34.12345$ is a terminating decimal fraction.
Question 16 :
State whether the following statement is true or false.The following number is irrational<br/>$6+\sqrt {2}$
Question 17 :
State whether the given statement is True or False :<br/>$2\sqrt { 3 }-1 $ is an irrational number.
Question 20 :
The number of possible pairs of number, whose product is 5400 and the HCF is 30 is<br>
Question 21 :
H.C.F. of $x^3 -1$ and $x^4 + x^2 + 1$ is
Question 23 :
Euclids division lemma can be used to find the $...........$ of any two positive integers and to show the common properties of numbers.
Question 24 :
If $a=107,b=13$ using Euclid's division algorithm find the values of $q$ and $r$ such that $a=bq+r$
Question 26 :
State whether the following statement is true or not:$\left( 3+\sqrt { 5 }  \right) $ is an irrational number. 
Question 28 :
What is the HCF of $4x^{3} + 3x^{2}y - 9xy^{2} + 2y^{3}$ and $x^{2} + xy - 2y^{2}$?
Question 29 :
The LCM of 54 90 and a third number is 1890 and their HCF is 18 The third number is
Question 34 :
$2\times 2\times 2\times 3\times 3\times 13 = 2^{3} \times 3^{2} \times 13$ is equal to
Question 36 :
State whether the following statement is true or false.The following number is irrational<br/>$7\sqrt {5}$
Question 38 :
If $a=\sqrt{11}+\sqrt{3}, b =\sqrt{12}+\sqrt{2}, c=\sqrt{6}+\sqrt{4}$, then which of the following holds true ?<br/>
Question 40 :
Use Euclid's division algorithm to find the HCF of :$196$ and $38220$
Question 42 :
Use Euclid's division lemma to find the HCF of the following<br/>16 and 176
Question 43 :
The statement dividend $=$ divisor $\times$ quotient $+$ remainder is called 
Question 45 :
Determine the HCF of $a^2 - 25, a^2 -2a -35$ and $a^2+12a+35$
Question 46 :
For finding the greatest common divisor of two given integers. A method based on the division algorithm is used called ............
Question 48 :
Without actually dividing find which of the following are terminating decimals.
Question 49 :
Euclids division lemma, the general equation can be represented as .......
Question 50 :
Euclid's division lemma states that for two positive integers a and b, there exist unique integers q and r such that $a = bq + r$, where r must satisfy<br>
Question 51 :
If HCF of $210$ and $55$ is of the form $(210) (5) + 55 y$, then the value of $y$ is :<br/>
Question 52 :
 The square of any positive odd integer for some integer $ m$ is of the form <br/>
Question 53 :
Use Euclid's division lemma to find the HCF of the following<br/>27727 and 53124
Question 55 :
When the HCF of $468$ and $222$ is written in the form of  $ 468 x + 222y$ then the value of $ x$ and $y$ is 
Question 56 :
The value of $\sqrt { 1+2\sqrt { 1+2\sqrt { 1+2+.... } } }$ is
Question 57 :
State whether the given statement is true/false:$\sqrt{p} + \sqrt{q}$, is irrational, where <i>p,q</i> are primes.
Question 58 :
Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion.<br/>$\dfrac {29}{343}$<br/>
Question 59 :
If the square of an odd positive integer can be of the form $6q + 1 $ or  $6q + 3$ for some $ q$ then q belongs to:<br/>
Question 60 :
Use Euclid's division lemma to find the HCF of $40$ and $248$.
Question 63 :
State whether the given statement is True or False :If $p,  q $ are prime positive integers, then $\sqrt { p } +\sqrt { q } $ is an irrational number.<br/>
Question 64 :
State whether the given statement is True or False :<br/>$5-2\sqrt { 3 } $ is an irrational number.
Question 65 :
There are five odd numbers $1, 3, 5, 7, 9$. What is the HCF of these odd numbers?
Question 66 :
A number when divided by  $156$  gives  $29$  as remainder. If the same number is divided by  $13$ , what will be the remainder?<br/><br/>
Question 68 :
In a division operation the divisor is $5$ times the quotient and twice the remainder. If the remainder is $15,$ then what is the dividend?
Question 69 :
The divisor when the quotient, dividend and the remainder are respectively $547, 171282$ and $71$ is equal to 
Question 70 :
Use Euclid's division lemma to find the HCF of the following<br/>8068 and 12464
Question 72 :
If $a$ is an irrational number then which of the following describe the additive inverse of $a$.
Question 73 :
Three ropes are $7\ m, 12\ m\ 95\ cm$ and $3\ m\ 85\ cm$ long. What is the greatest possible length that can be used to measure these ropes?
Question 75 :
 One and only one out of  $n, n + 4, n + 8, n + 12\  and \ n + 16 $ is ......(where n is any positive integer)<br/>
Question 76 :
State whether the following statement is true or not:$7-\sqrt { 2 } $ is irrational.
Question 77 :
Say true or false:A positive integer is of the form $3q + 1,$ $q$  being a natural number, then you write its square in any form other than  $3m + 1$, i.e.,$ 3m $ or $3m + 2$  for some integer $m$.<br/>
Question 78 :
In a question on division the divisor is  $7$  times the quotient and  $3 $ times the remainder. If the remainder is  $28$  then what is the dividend?
Question 79 :
The number of times $79$ must be subtracted from $50,000,$ so that the remainder is $43759$ is 
Question 81 :
The H.C.F. of two expressions is x and their L.C.M is $ \displaystyle x^{3}-9x  $  IF one of the expression is $ \displaystyle x^{2}+3x  $  then,the other expression is 
Question 82 :
If any positive' even integer is of the form 4q or 4q + 2, then q belongs to:<br/>
Question 83 :
The given pair of number $ 231, 396$ are __________ .<br/>
Question 84 :
Use Euclid's division lemma to find the HCF of the following 65 and 495.
Question 85 :
State whether the following statements are true or false . If a statement is false , justify your answer.<br>HCF of an even number and odd number is always $ 1$.
Question 86 :
In algebra $a \times b$ means $ab$, but in arithmetic $3 \times 5$ is
Question 88 :
Using the theory that any positive odd integers are of the form $4 q + 1$ or $4 q + 3$ where $q$ is a positive integer. If quotient is $4$, dividend is $19$ what will be the remainder?
Question 90 :
If a = 0.1039, then the value of $\sqrt{4a^2-4a+1}+3a$ is :<br>
Question 92 :
$HCF$ of two or more number may be one of the numbers.
Question 94 :
Find the HCF of $92690,7378$ and $7161$ by Euclid's division algorithm.
Question 96 :
The H.C.F of $ 144 $ and $ 198 $ is
Question 97 :
Find HCF of $70$ and $245$ using Fundamental Theorem of Arithmetic. 
Question 98 :
State whether True or False :<br/>All the following numbers are irrationals.<br/>(i) $\dfrac { 2 }{ \sqrt { 7 }  } $ (ii) $\dfrac { 3 }{ 2\sqrt { 5 }  }$ (iii) $4+\sqrt { 2 } $ (iv) $5\sqrt { 2 } $
Question 99 :
The H. C. F. of $252$, $324$ and $594$ is ____________.
Question 100 :
Find the dividend which when a number is divided by $45$ and the quotient was $21$ and remainder is $14.$
Question 101 :
When a natural number x is divided by 5, the remainder is 2. When a natural number y is divided by 5, the remainder is 4. The remainder is z when x+y is divided by 5. The value of $\dfrac { 2z-5 }{ 3 } $ is
