Question 1 :
If $a(p+q)^{2}+2 b p q+c=0$ and $a(p+r)^{2}+2 b p r+c=0$ <br> $(a \neq 0),$ then,
Question 2 :
Determine the values of $p$ for which the quadratic equation $2x^2 + px + 8 = 0$ has real roots.
Question 4 :
Determine the value of $k$ for which the $x = -a$ is a solution of the equation $\displaystyle x^{2}-2\left ( a+b \right )x+3k=0 $<br/>
Question 7 :
If $x = 3t, y = 1/ 2(t + 1)$, then the value of $t$ for which $x = 2y$ is
Question 8 :
If the roots of the equation ${ x }^{ 2 }-2ax+{ a }^{ 2 }+a-3=0$ are real and less than $3$, then
Question 9 :
Using factorization find roots of quadratic equation:<br>$\displaystyle10{ z }^{ 2 }-20=0$<br>
Question 10 :
The roots of the equation$\displaystyle \left ( x-a \right )\left ( x-b \right )+\left ( x-b \right )\left ( x-c \right )+\left ( x-c \right )\left ( x-a \right )=0$ are
Question 11 :
If $\left ( p+1 \right )^{th}$ term of an A.P.. is twice its $\left ( q+1 \right )^{th}$ term, then $\left ( 3p+1 \right )^{th}$ term<br>
Question 12 :
In an AP, if $d=4$ and $7th$ term is $52$, then $a$ is<br/>
Question 13 : Find the sum of first 32 terms of the arithmetic series if $a_1 = 12$ and $a_{32} = 40$.<p></p>
Question 14 :
The sum up to $9$ terms of the series $\displaystyle \frac{1}{2}+\frac{1}{3}+\frac{1}{6}+ ...$ is<br/>
Question 15 :
If the third term of an $A.P.$is $7$and its $7^{th}$term is $2$more than three times of its $3^{rd}$term, then sum of its first $20$terms is-
Question 16 :
Let $a_1, a_2, a_3,...,a_n$ be in A.P. If $a_3+a_7+a_{11}+a_{15}=72$, then the sum of its first $17$ terms is equal to.
Question 18 :
If the ratio of sum of m terms and n terms of an A.P. be $m^2 : n^2$, then the ratio of its $m^{th}$ and $n^{th}$ terms will be
Question 19 :
The sum of positive terms of the series $ \\ \displaystyle10+9\frac { 4 }{ 7 } +9\frac { 1 }{ 7 } +...$ is :
