Question 1 :
The roots of the equation $(c^2- ab)x^2 - 2(a^2 -bc)x + (b^2 - ac) =0$ are equal then
Question 2 :
The quadratic equation $ax^2+bx+c=0$ will have real and distinct roots if :
Question 4 :
For what value of 'm', the equation $(3m + 1)x^{2} + 2 (m + 1)x + m = 0$ have equal root?
Question 5 :
State the nature of the given quadratic equation <span>$(x + 4)^2 + 8x = 0$</span>
Question 6 :
State the nature of roots of the given quadratic equation <span>$(x \sqrt{2} )^2 + 2(x + 1) = 0$</span>
Question 7 :
State the nature of the given quadratic equation <span>$2x^2 +6x + \cfrac{9}{2} = 0$</span>
Question 8 :
If the roots of ${a}^{2}{x}^{2}+2bx+{c}^{2}=0$ are imaginary then the roots of $b({x}^{2}+1)+2acx=0$ are
Question 9 :
The ratio of the roots of the equation $a{ x }^{ 2 }+bx+c=0$ is same as the ratio of the roots of the equation $p{ x }^{ 2 }+qx+r=0$. If ${ D }_{ 1 }$ and ${ D }_{ 2 }$ are the discriminants of $a{ x }^{ 2 }+bx+c=0$ and $p{ x }^{ 2 }+qx+r=0$ respectively, then ${ D }_{ 1 }:{ D }_{ 2 }$ is equal to
Question 10 :
Given that '$x$' is real then the solution set of the equation $\sqrt { x-1 } +\sqrt { x+1 } =1$.
Question 11 :
The roots of the equation $x^ {2}+ax-4=0$ are, where $a\in R$
Question 12 :
The integral values of $ m $ for which the roots of the equation $ m x^{2}+(2 m-1) x+(m-2)=0 $ are rational are given by the expression [where $ n$ is integer ]
Question 13 :
If the roots of the equation $ax^{2} + bx + c = 0$ are real and distinct. Then
Question 14 :
If the equation $4x^{2} + x(p + 1) + 1 = 0$ has exactly two equal roots, then one of the values of $p$ is<br/>
Question 15 :
If the roots of the quadratic equation $5x^{2} - 2kx + 20 = 0$ are real and equal then the value of $k$ is ________.
Question 16 :
If $\displaystyle ax^{2}+bx+1= 0, a \in R, b\in R,$ does not have distinct real roots, then the maximum value of $b^2$ is
Question 17 :
The value of $p$ for which the equation $x^2+4=(P+2)x $ has equal roots?
Question 18 :
The number of values of $k$ for which $\displaystyle \left \{x^{2}-(k-2)x+k^{2}\right\}+ \left \{x^{2}+kx+(2k-1)\right \}$ is a perfect square is/are
Question 19 :
Suppose $a, b, c$ are real numbers, and each of the equations $x^2+2ax+b^2=0$ and $x^2+2bx+c^2=0$ has two distinct real roots. then the equation $x^2+2cx+a^2=0$ has
Question 20 :
What is the smallest integral value of $k$, such that $2x(kx -4)-x^2+ 6 =0$ has no real roots?
Question 21 :
The value of $p > 0$, for which both the equations $x^2 + px + 64 = 0$ & $x^2 - 8x + p = 0$ have equal roots is 
Question 22 :
Values of $k$ for which the quadratic equation $2x^2+ kx + k = 0$ has equal roots.<br>
Question 24 :
............... is true for discriminate of quadratic equation $x^2 + x + 1 = 0$.
Question 25 :
The root of $x^{2}+kx+k=0$ are real and equal , find $k$.
Question 26 :
For what value of k, does the equation $[kx^{2} + (2k + 6) x + 16 = 0]$ have equal roots?
Question 27 :
 If $x^{2}+px+25=0$, has  equal roots, then the value of $p~ (p>0) $ is
Question 28 : <span>Find the value of discriminant for the following equation.</span><div>$2x^{2}\, +\, x\, +\, 1\, =\, 0$</div>
Question 29 :
The value (s) of $k$ for which the quadratic equation $\displaystyle kx^{2}-kx+1=0$ has equal roots 
Question 30 :
Find $m$, so that roots of the equation $(4 + m ) x^2 + (m + 1) x + 1 = 0$ may be equal.
Question 31 :
If $(3)^{x + y} = 81$ and $(81)^{x - y} = 3$, then the values of $x$ and $y$ are<br>
Question 32 :
Solve by using substitution method. $3x +4y =10$ & $2x - 2y =2$
Question 33 :
$5$ pencils and $7$ pens together costs Rs. $50$ whereas $7$ pencils and $5$ pens together costs Rs. $46$. Thus the cost of one pencil and one pen respectively is:<br/>
Question 34 : <span>Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method:</span><div>Five years ago Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?<br/></div>
Question 35 :
Two bus tickets from city A to B and three tickets from city A to C cost Rs. 77 but three tickets from city A to B and two tickets from city A to C cost Rs. 73. What are the fares for cities B and C from A ?
Question 36 :
Find the value of x and y using substitution method:<br><span>$5x - 6y = 2$ and $6x - 5y = 9$</span>
Question 39 :
Classes A and B have $35$ students each. If seven girls shift from class $A$ to class $B$, then the number of girls in the classes would interchange. If four girls shift from class $B$ to class $A$, then the number of girls in class $A$ would be twice the original number of girls in class $B$. What is the number of boys in Class $A$ and in Class $B$?
Question 40 :
In covering a distance of $30$ km, Abhay takes $2$ hours more than Sameer. If Abhay doubles his speed, then he would take $1$ hour less than Sameer. What is Abhay's speed? (in km/hr)
Question 41 :
Using substitution method find the value of x and y:<br><span>$x - 9y = 18$ and $-x + 3y = -15$<br></span>
Question 42 : <div><span>Form the pair of linear equations for the following problem and find their solution by substitution method.</span></div><div>The difference between the two numbers is $26$ and one number is three times the other.<br/></div>
Question 43 :
If the sum of $2$ real numbers is $20$ and their difference is $6$, find the value of their product.
Question 44 :
Use the method of substitution to solve the equations<br>$x+2y=-4$ and $4x+5y=2$<br>
Question 45 :
<span>Based on equations reducible to linear equations</span><br/><span>Solve for x and y </span>$\dfrac {1}{3x}-\dfrac {1}{7y}=\dfrac {2}{3}; \dfrac {1}{2x}-\dfrac {1}{3y}=\dfrac {1}{6}$<br/>
Question 46 :
Solve for $x$ and $y$ in the following question:<br/>$\displaystyle \frac{2}{x + 2y} + \frac{1}{2x - y} + \frac{5}{9} = 0$, $\displaystyle \frac{9}{x + 2y} + \frac{6}{2x - y} + 4 = 0$
Question 47 :
Three chairs and two tables cost Rs1,850. Five chairs and three tables cost Rs 2,850. Then the total cost of one chair and one table is<br>
Question 48 :
Solve: $4x+\displaystyle \frac{6}{y}= 15$ and $6x-\displaystyle \frac{8}{y}= 14$. <span>Hence find the value of $k$, if $y= kx-2$.</span>
Question 49 :
A number is $\dfrac{2}5{}$ times another number. If their sum is $70$, Find the numbers.
Question 50 : <div>A fraction becomes $\dfrac  {1}{3}$ when $1$ is subtracted from the numerator and it becomes $\dfrac  {1}{4}$ when $8$ is added to its denominator. Find the fraction.<br/></div>
Question 51 : Solve the following pair of equations by reducing them to a pair of linear equations<span>:</span><div><br/><div><span>$\dfrac {1}{(3x+y)}+\dfrac {1}{(3x-y)}=\dfrac {3}{4},\  \dfrac {1}{2(3x+y)}-\dfrac {1}{2(3x-y)}=\dfrac {-1}{8}$</span></div></div>
Question 52 :
Using substitution method find the value of x and y:<br><span>$4x + 9y = 5$ and $-5x + 3y = 8$</span>
Question 54 :
Solve the equations using the method of substitution method :<br>$3x+4y=-43$ and $-2x+3y=11$<br>
Question 55 :
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 56 :
Two articles $A$ and $B$ are sold for Rs. $1,167$ making $5\%$ profit on $A$ and $7\%$ profit on B. If the two articles are sold for Rs. $1,165$, a profit of $7\%$ is made on $A$ and a profit of $5\%$ is made on $B$. Find the cost price of each article.
Question 58 :
Solve equations using substitution method: $x-y = 3$ and $x + y = 0$<span><br/></span>
Question 60 :
Using substitution method find the value of $x$ and $y:$<br/><span>$x + 4y = -4$ and $2x-  3y = 2$</span>
