Question 2 :
Divide $\displaystyle 4{ x }^{ 2 }{ y }^{ 2 }\left( 6x-24 \right) \div 4xy\left( x-4 \right) $
Question 3 :
If a root of the equations${x^2} + px + 12 = 0$ is 4 ,while the roots of the equation ${x^2} + px + q = 0$ , are the same ,then the value of q will be
Question 4 :
If ${(5{x}^{2}+14x+2)}^{2}-{(4{x}^{2}-5x+7)}^{2}$ is divided by ${x}^{2}+x+1$, then the quotient $q$ and the remainder $r$ are given by:
Question 5 :
The possible values of p for which the equation$\displaystyle { x }^{ 2 }+px+64=0$ and$\displaystyle { x }^{ 2 }-8x+p=0$ will both have real roots is
Question 7 :
On dividing $x^3-3x^2+x+2$ by polynomial $g(x)$, the quotient and remainder were $x -2$ and $4 - 2x$ respectively, then $g(x)$ is<br/>
Question 8 :
If $\alpha$ and $\beta$ are the roots of $x^2 - ax + b^2 = 0$, then $\alpha^2 + \beta^2$ is equal to
Question 11 :
Find the value of x and y using cross multiplication method: <br>$5x + 2y = 32$ and $6x + 6y = 42$
Question 12 :
Solve the equations using elimination method:<br>$x - 6y = 9$ and $2x - y = 7$
Question 13 :
In the following system of equation determine whether the system has a unique solution, no solution or infinitely many solution. In case there is a unique solution, find it.<br>$2x+3y=7$<br>$6x+5y=11$<br>
Question 14 :
Solve the equations using elimination method:<br>$2x - y = 20$ and $4x + 3y = 0$
Question 16 :
a, b, c (a > c) are the three digits, from left to right of a three digit number. If the number with these digits reversed is subtracted from the original number, the resulting number has the digit 4 in its unit's place. The other two digits from left to right are -
Question 18 :
If $bx+ay=a^2+b^2$ and $ax-by=0$, then the value of $(x-y) $ is<br/>
Question 19 :
Given that $3p + 2q = 13$ and $3p - 2q = 5$, find the value of $p + q$
Question 20 :
One pendulum ticks $57$ times in $58$ seconds and another $608$ times in $609$ seconds. If they start simultaneously, find the time after which will they tick together?
Question 21 :
The value of $\sqrt { 1+2\sqrt { 1+2\sqrt { 1+2+.... } } }$ is
Question 22 :
If these numbers form positive odd integer 6q+1, or 6q+3 or 6q+5 for some q then q belongs to:<br/>
Question 25 :
Mark the correct alternative of the following.<br>The HCF of $100$ and $101$ is _________.<br>
Question 26 :
In a question on division the divisor is  $7$  times the quotient and  $3 $ times the remainder. If the remainder is  $28$  then what is the dividend?
Question 28 :
If HCF of $210$ and $55$ is of the form $(210) (5) + 55 y$, then the value of $y$ is :<br/>
Question 29 :
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 31 :
The coordinates of the point which divides the line segment joining the points $(-7, 4)$ and $(-6, -5)$ internally in the ratio $7 : 2$ is:
Question 32 : <p>x-axis divides line segment joining points (2, -3) and (5,6) in the ratio</p>
Question 33 :
The line segment joining the points $(3, -4)$ and $(1, 2) $ is trisected at the points P and Q. If the and co-ordinates of P and Q are $(p, -2)$ and $(\frac{5}{3}, q)$ respectively, find the value of p and q.
Question 34 :
Point $P$ divide a line segment $AB$ in the ratio $5:6$ where $A(0,0)$ and $B(11,0)$. Find the coordinate of the point $P$:
Question 35 :
<i></i>If the coordinates of opposite vertices of a square are $(1,3)$ and $(6,0)$, the length if a side od a square is 
Question 36 :
There are two point $P(1,-4)$ and $Q(4,2)$. Find a point X dividing the line PQ in the ratio $1:2$
Question 37 :
Find the coordinates of the point which divides the line segment joining $(-3,5)$ and $(4,-9)$ in the ratio $1:6$ internally.
Question 38 :
If the line $2x+y=k$ passes through the point which divides the line segment joining the point $(1,1)$ & $(2,4)$ in the ratio $3:2$ then $k$ equal
Question 39 :
Let $A(-6,-5)$ and $B(-6,4)$ be two points such that a point $P$ on the line $AB$ satisfies $AP=\cfrac{2}{9}AB$. Find the point $P$.
Question 40 :
State whether the following statements are true or false . Justify your answer.<br>The points $ (0 , 5) , (0 , -9) $ and $ (3 , 6) $ are collinear .
Question 41 :
A determinant is chosen at random from the set of all departments of order 2 with elements 0 and 1 only. The probability that the determinant chosen is non-zero is :
Question 42 :
In a single cast with two dice, the odds against drawing $7$ is
Question 43 :
There are three events $A$, $B$ and $C$ out of which one and only one can happen. The odds are $7$ to $3$ against $A$ and $6$ to $4$ against $B$. The odds against C are
Question 44 : <p>From a batch of $100$ items of which $20$ are defective, exactly two items are chosen, one at a time, without replacement. Calculate the probability that the first item chosen is defective.</p>
Question 45 :
There are three events $A, B$ and $C$ one of which must and only one can happen ; the odds are $8$ to $3$ against A, the odds are $5$ to $2$ against $B$, find odds against $C$.
Question 46 :
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 47 :
If two letters are taken at random from the word HOME, what is the probability that none of the letters would be vowels?<br/>
Question 48 :
The odds is favour of winning a race for three horses $A, B$ and $C$ respectively $1:2, 1:3$ and $1:4$. Find the probability for winning of any one of them.
Question 49 :
If the odds in favour of winning a race by three horses are $1 : 4, 1 : 5$ and $1 : 6$, find the probability that exactly one of these horses will win.
Question 50 :
In a ODI cricket match, probability of loosing the game is $\dfrac{1}{4}$. What is the probability of winning the game ?
