Question 6 :
State whether the following statement is true or false.The following number is irrational<br/>$7\sqrt {5}$
Question 7 :
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 8 :
Euclids division lemma can be used to find the $...........$ of any two positive integers and to show the common properties of numbers.
Question 10 :
Determine the HCF of $a^2 - 25, a^2 -2a -35$ and $a^2+12a+35$
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 :
Assertion: $\displaystyle \frac{13}{3125}$ is a terminating decimal fraction.
Reason: If $q=2^n \cdot 5^m$ where $n, m$ are non-negative integers, then $\displaystyle \frac{p}{q}$ is a terminating decimal fraction.
Question 14 :
For three irrational numbers $p,q$ and $r$ then $p.(q+r)$ can be
Question 15 :
Without actually dividing find which of the following are terminating decimals.
Question 16 :
Use Euclid's division lemma to find the HCF of the following<br/>16 and 176
Question 18 :
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 20 :
Which of the following irrational number lies between $\dfrac{3}{5}$ and $\dfrac{9}{10}$
Question 21 :
The statement dividend $=$ divisor $\times$ quotient $+$ remainder is called 
Question 24 :
The number of possible pairs of number, whose product is 5400 and the HCF is 30 is<br>
Question 25 :
State whether the given statement is True or False :<br/>$2\sqrt { 3 }-1 $ is an irrational number.
Question 26 :
Without actually performing the long division, state whether the following rational number will have a terminating decimal expansion or non -terminating decimal expansion$\displaystyle \frac{7}{210}$
Question 27 :
................. states the possibility of the prime factorization of any natural number is unique. The numbers can be multiplied in any order.
Question 30 :
In a division sum the divisor is $12$  times the quotient and  $5$  times the remainder. If the remainder is  $48$  then what is the dividend?
Question 31 :
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 32 :
Use Euclid's division algorithm to find the HCF of :$196$ and $38220$
Question 33 :
State whether the following statement is true or not:$\left( 3+\sqrt { 5 }  \right) $ is an irrational number. 
Question 34 :
The greatest number that will divided $398, 436$ and $542$ leaving $7,11$ and $14$ remainders, respectively, is
Question 35 :
What is the HCF of $4x^{3} + 3x^{2}y - 9xy^{2} + 2y^{3}$ and $x^{2} + xy - 2y^{2}$?
Question 36 :
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 37 :
$2\times 2\times 2\times 3\times 3\times 13 = 2^{3} \times 3^{2} \times 13$ is equal to
Question 38 :
For finding the greatest common divisor of two given integers. A method based on the division algorithm is used called ............
Question 39 :
H.C.F. of $x^3 -1$ and $x^4 + x^2 + 1$ is
Question 40 :
State whether the following statement is true or false.The following number is irrational<br/>$6+\sqrt {2}$
Question 43 :
............. states that for any two positive integers $a$ and $b$ we can find two whole numbers $q$ and $r$ such that $a = b \times q + r$ where $0 \leq r < b .$
Question 44 :
State whether the following statement is True or False.<br/>3.54672 is an irrational number.
Question 46 :
Using fundamental theorem of Arithmetic find L.C.M. and H.C.F of $816$ and $170$.
Question 47 :
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 48 :
Fundamental theorem of arithmetic is also called as ______ Factorization Theorem.
Question 49 :
Euclids division lemma, the general equation can be represented as .......
Question 50 :
If $a=107,b=13$ using Euclid's division algorithm find the values of $q$ and $r$ such that $a=bq+r$
