Question 2 :
Choose the correct answer which satisfies the linear equation: $2a + 5b = 13$ and $a + 6b = 10$

Question 3 :
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 4 :
What is the equation of straight line passing through the point (4, 3) and making equal intercepts on the coordinate axes ?

Question 5 :
A choir is singing at a festival. On the first night $12$ choir members were absent so the choir stood in $5$ equal rows. On the second night only $1$ member was absent so the choir stood in $6$ equal rows. The same member of people stood in each row each night. How many members are in the choir?

Question 6 :
If $\alpha , \beta $ are the roots of the equation $ax^{2}+bx+c=0$, find the value of $\alpha ^{2}+\beta ^{2}$.

Question 7 :
Divide:$\left ( 15y^{4}- 16y^{3} + 9y^{2} - \cfrac{1}{3}y - \cfrac{50}{9} \right )$ by $(3y-2)$Answer: $5y^{3} + 2y^{2} - \cfrac{13}{3}y + \cfrac{25}{9}$

Question 8 :
If the roots of ${ x }^{ 2 }-2mx+{ m }^{ 2 }-1=0$ lie between $-2$ and $4$, then

Question 9 :
The degree of the remainder is always less than the degree of the divisor.

Question 10 :
$\alpha $ and $\beta $ are zeroes of polynomial $x^{2}-2x+1,$ then product of zeroes of a polynomial having zeroes $\dfrac{1}{\alpha }$ &#160;and &#160; &#160;$\dfrac{1}{\beta }$ is

Question 11 :
The LCM of 54 90 and a third number is 1890 and their HCF is 18 The third number is

Question 12 :
State True or False:$4\, - \,5\sqrt 2 $ is irrational if $\sqrt 2 $ is irrational.

Question 14 :
Let $x=\dfrac { p }{ q }&#160;$ 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 15 :
Use Euclid's division lemma to find the HCF of the following<br/>16 and 176

Question 16 :
The sides of a triangle are given below.&#160;Check whether or not the sides form a right-angled triangle.$13cm, 12cm, 5cm$

Question 17 :
In $\triangle ABC$, $\angle C={90}^{o}$. If $BC=a, AC=b$ and $AB=c$, find $b$ when $c=13 \ cm$ and $a=5 \ cm$.

Question 18 :
In $\triangle ABC$, $\angle C={90}^{o}$. If $BC=a, AC=b$ and $AB=c$, find&#160;$a$ when $c=25 \ cm$ and $b=7 \ cm$.

Question 19 :
The sides of a triangle are given below. Check whether or not the sides form a right angled triangle.$50cm, 80cm, 100cm$

Question 20 :
$4\, RN^{2}\, =\, PQ^{2}\, +\, 4\, PR^{2}$<br/><b>State whether the above statement is true or false.</b><br/>

Question 21 :
The distance between the points (sin x, cos x) and (cos x -sin x) is

Question 22 :
If $P \left( \dfrac{a}{3}, 4\right)$ is the mid-point of the line segment joining the points $Q ( 6, 5) $ &#160;and $R( 2, 3)$, then the value of $a$ is <br/>

Question 24 :
If A(x,0), B(-4,6), and C(14, -2) form an isosceles triangle with AB=AC, then x=

Question 25 :
Harmonic conjugate of the point $C(5, 1)$ with respect to the point $A(2, 10)$ and $B(6, -2)$ is?

Question 26 :
Simplest form of $\displaystyle \dfrac{1}{\sqrt{2 + \sqrt{2 + \sqrt{2 + 2 cos 4x}}}}$ is

Question 27 :
The expression$ \displaystyle \left (\tan \Theta +sec\Theta \right )^{2} $ is equal to

Question 28 :
The value of $[\dfrac{\tan 30^{o}.\sin 60^{o}.\csc 30^{o}}{\sec 0^{o}.\cot 60^{o}.\cos 30^{o}}]^{4}$ is equal to

Question 29 :
Select and wire the correct answer from the given alternatives.&#160;<br/>$\cos \left(\dfrac {3\pi}{2}+\theta \right)=$ ____

Question 30 :
If $A+B+C=\dfrac { 3\pi }{ 2 } $, then $cos2A+cos2B+cos2C$ is equal to

Question 31 :
In a circle with radius $5.7\ cm$, the perimeter of a sector is $27.2\ cm$. Find the area of this sector.

Question 32 :
The angle of sector with area equal to one fifth of total area of whole circle&#160;

Question 33 :
Area of a circle with diameter 'm' radius 'n' and circumference 'p' is

Question 34 :
Which of the following is not a sector of a circle?<br/>

Question 35 :
If the radius of a circle is $\dfrac{7}{\sqrt{\pi}}$, what is the area of the circle (in $cm^2$)?

Question 36 :
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 37 :
The probability of an event happening and&#160;the probability of the same event not happening (or the&#160;complement) must be a <br/>

Question 38 :
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 39 :
The probability of guessing the correct answer to a certain test is $\displaystyle\frac{x}{2}$. If the probability of not guessing the correct answer to this questions is $\displaystyle\frac{2}{3}$, then $x$ is equal to ______________.

Question 40 :
A bag contains 5 blue and 4 black balls. Three balls are drawn at random. What is the probability that 2 are blueand 1 is black?