Question 1 :
We need blocks to build a building. In the same way _______ are basic blocks to form all natural numbers .

Question 2 :
................. states the possibility of the prime factorization of any natural number is unique. The numbers can be multiplied in any order.

Question 3 :
Use Euclid's division lemma to find the HCF of the following<br/>16 and 176

Question 4 :
Write whether every positive integer can be of the form $4q + 2$, where $q$ is an integer.<br/>

Question 5 :
State whether the given statement is True or False :<br/>$4-5\sqrt { 2 }&#160;$ is an irrational number.<br/>

Question 6 :
State whether the given statement is true or false:Every point on the graph of a linear equation in two variables does not represent a solution of the linear equation.<br/>

Question 7 :
The number of pairs of reals (x, y) such that $x =x^2+y^2$ and $y =2xy$ is

Question 8 :
The graph of the lines $x + y = 7$ and $x - y = 3$ meet at the point

Question 9 :
For what value of k does the system of equations$\displaystyle 2x+ky=11\:and\:5x-7y=5$ has no solution?

Question 10 :
Solve the following pair of equations:<br/>$\displaystyle \frac{6}{x}+\displaystyle \frac{4}{y}= 20, \displaystyle \frac{9}{x}-\displaystyle \frac{7}{y}= 10.5$

Question 11 :
Solve the following pairs of equations by reducing them to a pair of linear equations.<br/>$\displaystyle \frac{3}{x+1}-\frac{1}{y+1}=2$ and $\dfrac{6}{x+1}-\dfrac{1}{y+1}=5$

Question 12 :
The sides of a triangle are given below. Check whether or not the sides form a right angled triangle.$50cm, 80cm, 100cm$

Question 13 :
$4\, RN^{2}\, =\, PQ^{2}\, +\, 4\, PR^{2}$<br/><b>State whether the above statement is true or false.</b><br/>

Question 16 :
Divide the first expression by the second. Write the quotient and the remainder.<br/>$a^2-b^2 ; a-b$

Question 18 :
The roots of the equation&#160;$\displaystyle x^{2}+Ax+B=0$ are 5 and 4. The roots of&#160;$\displaystyle x^{2}+Cx+D=0$ are 2 and 9. Which of the following is a root of&#160;$\displaystyle x^{2}+Ax+D=0$?

Question 20 :
A(3 , 2) and B(5 , 4) are the end points of a line segment . Find the co-ordinates of the mid-point of the line segment .

Question 21 :
Find the co-ordinates of the mid point of a point that divides AB in the ratio 3 : 2.

Question 23 :
What will be the value of $y$ if the point $\begin{pmatrix} \dfrac { 23 }{ 5 },y \end{pmatrix}$, divides the line segment joining the points $(5,7)$ and $(4,5)$ in the ratio $2:3$ internally?<br/>

Question 24 :
The point which is equi-distant from the points $(0,0),(0,8) and (4,6)$ is&#160;

Question 25 :
Find the value of&#160;$ \displaystyle &#160;\theta , cos\theta &#160;\sqrt{\sec ^{2}\theta -1}&#160; &#160; &#160;= 0$

Question 26 :
The value of $\sqrt { 3 } \sin { x } +\cos { x } $ is max. when $x$ is equal to

Question 27 :
If&#160;$\displaystyle \tan { \theta &#160;} =\frac { 1 }{ 2 }&#160;$ and&#160;$\displaystyle \tan { \phi &#160;} =\frac { 1 }{ 3 }&#160;$, then the value of&#160;$\displaystyle \theta +\phi&#160;$ is:

Question 29 :
The value of &#160; $\displaystyle \sin { \theta &#160;} \cos { \theta &#160;} -\frac { \sin { \theta &#160;} \cos { \left( { 90 }^{ o }-\theta &#160;\right) &#160;} \cos { \theta &#160;} &#160;}{ \sec { \left( { 90 }^{ o }-\theta &#160;\right) &#160;} &#160;} -\frac { \cos { \theta &#160;} \sin { \left( { 90 }^{ o }-\theta &#160;\right) &#160;} \sin { \theta &#160;} &#160;}{ \text{cosec }\left( { 90 }^{ o }-\theta &#160;\right) &#160;}&#160;$ is :

Question 31 :
Out of the digits $1$ to $9$, two are selected at random&#160;and one is found to be $2$, the probability that their&#160;sum is odd is

Question 32 :
One hundred identical coins each with probability p as showing up heads are tossed. If $0 &lt; p &lt; 1$ and the probability of heads showing on 50 coins is equal to that of heads on 51 coins, then the value of p is

Question 33 :
A coin is tossed $400$ times and the data of outcomes is below:<span class="wysiwyg-font-size-medium">&#160;<span class="wysiwyg-font-size-medium"><br/><table class="wysiwyg-table"><tbody><tr><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">Outcomes&#160;</p></td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$H$</p></td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$T$</p></td></tr><tr><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">Frequency</p></td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$280$</p></td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$120$</p></td></tr></tbody></table><p><br/></p><p>Find:</p><p>(i) $P(H)$, i.e., probability of getting head</p><p>(ii) $P (T)$, i.e., probability of getting tail.&#160;</p><p>(iii) The value of $P (H) + P (T)$.</p>

Question 34 :
If $A$ and $B$ are independent events such that $P\left( A \right) =\dfrac { 1 }{ 5 }$, $P\left( A\cup B \right) =\dfrac { 7 }{ 10 }$, then what is $P\left( \bar { B } \right) $ equal to?

Question 35 :
The probability that atleast one of the events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.2, then$P(\bar{A})+P(\bar{B})$ is.

Question 36 :
The distance between the two parallel chords of length 8 cm and 6 cm in a circle of diameter 10 cm if the chords lic on the same side of the centre is

Question 37 :
A rope by which a cow is tethered is in reased from 16m to 23m. How much additional ground does it have to graze now?

Question 38 :
The perimeter of a sector of a circle is 37cm. If its radius is 7cm, then its arc length is

Question 39 :
A square sheet of paper is converted into a cylinder by rolling it along its length. What is the ratio of the base radius to side of the square ?

Question 40 :
A circular wire of radius $7$ cm is cut and bend again into an arc of a circle of radius $12$ cm. The angle subtended by the arc at the centre is<br/>