Question 1 :
Mark the correct alternative of the following.<br>The HCF of $$100$$ and $$101$$ is _________.<br>
Question 5 :
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 6 :
State whether the following statement is true or not:$$7-\sqrt { 2 } $$ is irrational.
Question 7 :
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 9 :
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 10 :
Write whether every positive integer can be of the form $$4q + 2$$, where $$q$$ is an integer.<br/>
Question 11 :
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 12 :
State whether the given statement is true/false:$$\sqrt{p} + \sqrt{q}$$, is irrational, where <i>p,q</i> are primes.
Question 13 :
In a division sum, the divisor is $$10$$ times the quotient and five times the remainder. What is the dividend, if the remainder is $$46?$$
Question 14 :
Use Euclid's division lemma to find the HCF of the following<br/>8068 and 12464
Question 15 :
The greatest number which divides $$134$$ and $$167$$ leaving $$2$$ as remainder in each case is
Question 18 :
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 19 :
If the H.C.F. of $$A$$ and $$B$$ is $$24$$ and that of $$C$$ and $$D$$ is $$56,$$ then the H.C.F. of $$A, B, C$$ and $$D$$ is
Question 20 :
In a question on division if four times the divisor is added to the dividend then how will the new remainder change in comparison with the original remainder?
Question 21 :
The divisor when the quotient, dividend and the remainder are respectively $$547, 171282$$ and $$71$$ is equal to 
Question 22 :
If HCF of numbers $$408$$ and $$1032$$ can be expressed in the form of $$1032x -408 \times 5$$, then find the value of $$x$$.
Question 23 :
The value of $$\sqrt { 1+2\sqrt { 1+2\sqrt { 1+2+.... } } }$$ is
Question 24 :
State whether the given statement is True or False :<br/>$$2-3\sqrt { 5 }$$ is an irrational number.
Question 26 :
$$HCF$$ of two or more number may be one of the numbers.
Question 27 :
Assuming  that x,y,z  are positive real numbers,simplify the following :<br/>$$ (\sqrt{x})^{-2/3}\sqrt{y^{4}}\div \sqrt{xy^{-1/2}} $$<br/>
Question 29 :
State true or false of the following.<br>The predecessor of a two digit number cannot be a single digit number.<br>
Question 31 :
State whether the given statement is True or False :<br/>$$5-2\sqrt { 3 } $$ is an irrational number.
Question 33 :
If HCF of $$210$$ and $$55$$ is of the form $$(210) (5) + 55 y$$, then the value of $$y$$ is :<br/>
Question 34 :
In algebra $$a \times b$$ means $$ab$$, but in arithmetic $$3 \times 5$$ is
Question 36 :
Sum of digits of the smallest number by which $$1440$$ should be multiplied so that it becomes a perfect cube is
Question 37 :
State true or false of the following.<br>If a and b are natural numbers and $$a < b$$, than there is a natural number c such that $$a < c < b$$.<br>
Question 38 :
Without actually performing the long division, state whether the following rational number will have terminating decimal expansion or a non-terminating repeating decimal expansion. Also, find the numbers of places of decimals after which the decimal expansion terminates.<br/>$$\dfrac { 13 }{ 3125 } $$
Question 39 :
The simplified form of the expression $$\sqrt { \sqrt [ 3 ]{ 729{ x }^{ 12 } }  } -\dfrac { { x }^{ -2 }-{ x }^{ -3 } }{ { x }^{ -4 }-{ x }^{ -5 } } $$ is
Question 40 :
Find the dividend which when a number is divided by $$45$$ and the quotient was $$21$$ and remainder is $$14.$$
Question 41 :
Use Euclid's division lemma to find the HCF of the following 65 and 495.
Question 42 :
State whether the given statement is True or False :<br/>$$4-5\sqrt { 2 } $$ is an irrational number.<br/>
Question 43 :
If a = 0.1039, then the value of $$\sqrt{4a^2-4a+1}+3a$$ is :<br>
Question 44 :
If $$x=6+2\sqrt {6}$$, then what is the value of $$\sqrt { x-1 } +\cfrac { 1 }{ \sqrt { x-1 } } $$?
Question 45 :
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 47 :
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 48 :
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 49 :
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 50 :
$$n$$  is a whole number which when divided by  $$4$$  gives  $$3 $$ as remainder. What will be the remainder when  $$2n$$  is divided by $$4$$ ?<br/>
