Question 1 :
find whether ${ \left( \sin { \theta  } +co\sec { \theta  }  \right)  }^{ 2 }+{ \left( \cos { \theta  } +\sec { \theta  }  \right)  }^{ 2 }=7+\tan ^{ 2 }{ \theta  } +\cos ^{ 2 }{ \theta  } $ is true or false.
Question 2 :
The value of$\tan {203^ \circ } + \tan {22^ \circ } + \tan {203^ \circ }\tan {22^ \circ }$ is
Question 3 :
In a $\Delta ABC$, if $\cos A \cos B \cos C=\displaystyle\dfrac {\sqrt 3-1}{8}$ and $\sin A. \sin B. \sin C=\displaystyle \dfrac {3+\sqrt 3}{8}$, then- On the basis of above information, answer the following questions:The angles of $\Delta ABC$ are:<br/>
Question 4 :
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 5 :
State whether the given statement is True or False :<br/>$2\sqrt { 3 }-1 $ is an irrational number.
Question 6 :
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 7 :
The number of possible pairs of number, whose product is 5400 and the HCF is 30 is<br>
Question 8 :
............. 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 9 :
For three irrational numbers $p,q$ and $r$ then $p.(q+r)$ can be
Question 10 :
State the following statement is True or False<br>35.251252253...is an irrational number<br>
Question 12 :
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 14 :
State whether the following statement is true or false.The following number is irrational<br/>$6+\sqrt {2}$
Question 16 :
................. states the possibility of the prime factorization of any natural number is unique. The numbers can be multiplied in any order.
Question 17 :
Without actually dividing find which of the following are terminating decimals.
Question 18 :
H.C.F. of $x^3 -1$ and $x^4 + x^2 + 1$ is
Question 19 :
Euclids division lemma can be used to find the $...........$ of any two positive integers and to show the common properties of numbers.
Question 20 :
State whether the following statement is true or not:$\left( 3+\sqrt { 5 }  \right) $ is an irrational number. 
Question 21 :
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 23 :
 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 24 :
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 25 :
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