Question 1 :
What is the HCF of $4x^{3} + 3x^{2}y - 9xy^{2} + 2y^{3}$ and $x^{2} + xy - 2y^{2}$?
Question 2 :
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 3 :
State whether the following statement is True or False.<br/>3.54672 is an irrational number.
Question 4 :
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 5 :
The number of possible pairs of number, whose product is 5400 and the HCF is 30 is<br>
Question 6 :
If $a=107,b=13$ using Euclid's division algorithm find the values of $q$ and $r$ such that $a=bq+r$
Question 8 :
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 9 :
Use Euclid's division lemma to find the HCF of the following<br/>16 and 176
Question 10 :
H.C.F. of $x^3 -1$ and $x^4 + x^2 + 1$ is
Question 11 :
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 16 :
State whether the following statement is true or false.The following number is irrational<br/>$6+\sqrt {2}$
Question 17 :
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 18 :
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 21 :
For three irrational numbers $p,q$ and $r$ then $p.(q+r)$ can be
Question 25 :
Euclids division lemma, the general equation can be represented as .......
Question 27 :
................. states the possibility of the prime factorization of any natural number is unique. The numbers can be multiplied in any order.
Question 28 :
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 29 :
The LCM of 54 90 and a third number is 1890 and their HCF is 18 The third number is
Question 31 :
The statement dividend $=$ divisor $\times$ quotient $+$ remainder is called 
Question 32 :
State whether the given statement is True or False :<br/>$2\sqrt { 3 }-1 $ is an irrational number.
Question 34 :
Without actually dividing find which of the following are terminating decimals.
Question 35 :
Use Euclid's division algorithm to find the HCF of :$196$ and $38220$
Question 38 :
Determine the HCF of $a^2 - 25, a^2 -2a -35$ and $a^2+12a+35$
Question 39 :
Which of the following irrational number lies between $\dfrac{3}{5}$ and $\dfrac{9}{10}$
Question 40 :
Using fundamental theorem of Arithmetic find L.C.M. and H.C.F of $816$ and $170$.
Question 42 :
Euclids division lemma can be used to find the $...........$ of any two positive integers and to show the common properties of numbers.
Question 44 :
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 45 :
We need blocks to build a building. In the same way _______ are basic blocks to form all natural numbers .
Question 46 :
............. 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 47 :
State the following statement is True or False<br>35.251252253...is an irrational number<br>
Question 48 :
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 50 :
State True or False:$4\, - \,5\sqrt 2 $ is irrational if $\sqrt 2 $ is irrational.