Question 1 :
If $p$ is chosen at random in the interval $0 \le p \le 5$,the probability that the equations $x^{2}+px+p/4+1/2=0$ are real is
Question 2 :
Is the following equation quadratic?$(x\, +\, 3) (x\, -\, 4)\, =\, 0$
Question 3 :
If $9y^{2}\, -\, 3y\, -\, 2\, =\, 0$, then $y\, =\, \displaystyle -\frac{2}{3}, \, \displaystyle \frac{1}{3}$.<br/>
Question 4 :
Choose best possible option.<br>$\displaystyle\left( x+\frac { 1 }{ 2 } \right) \left( \frac { 3x }{ 2 } +1 \right) =\frac { 6 }{ 2 } \left( x-1 \right) \left( x-2 \right)$ is quadratic.<br>
Question 5 :
If $x^{2} - 4x + 2 = 0$, then the value of $4x^{2} + 2x + \dfrac {4}{x} + \dfrac {16}{x^{2}}$ is
Question 7 :
If $x - 4$ is one of the factor of $x^{2} - kx + 2k$, where $k$ is a constant, then the value of $k$ is
Question 10 :
Check whether the following is a quadratic equation.$(x - 3) (2x + 1) = x (x + 5)$<br/>
Question 12 :
The roots of the equation $\sqrt{3y + 1} = \sqrt{y - 1}$  are?<br/>
Question 13 :
Check whether the given equation is a quadratic equation or not.<br/>$3{ x }^{ 2 }-4x+2=2{ x }^{ 2 }-2x+4$
Question 14 :
If roots of $(a - 2b + c)x^2 + (b - 2c +a)x + (c - 2a +b) = 0$ are equal, then :
Question 16 :
State the following statement is True or False<br/>The digit at ten's place of a two digit number exceeds the square of digit at units place ($x$) by 5 and the number formed is $61$, then the equation is $10\, (x^{2}\, +\, 5)\, +\, x\, =\, 61$.<br/>
Question 19 :
If $\displaystyle \frac{5x+6}{\left ( 2+x \right )\left ( 1-x \right )}=\frac{a}{2+x}+\frac{b}{1-x}$, then the values of a and b respectively are
Question 20 :
Find $ p \in R $ for $x^2 - px + p + 3 = 0 $ has<br/>
Question 21 :
Is the following equation a quadratic equation?$\displaystyle \frac{3x}{4} - \frac{5x^2}{8} = \frac{7}{8}$
Question 23 :
If $\alpha \epsilon \left( -1,1 \right) $ then roots of the quadratic equation $\left( a-1 \right) { x }^{ 2 }+ax+\sqrt { 1-{ a }^{ 2 } } =0$ are
Question 25 :
The difference of two natural numbers is $4$ and the difference of their reciprocals is $\dfrac{1}{3}$. Find the numbers.
Question 26 :
In a rectangle the breadth is one unit less than the length and the area is $12$ sq.units. Find the length of the rectangle.
Question 27 :
Is the following equation quadratic?$n^{3}\, -\, n\, +\, 4\, =\, n^{3}$
Question 28 :
The discriminant of $x^2 - 3x + k = 0$ is 1 then the value of $k = .............$
Question 29 :
Which of the following is a quadratic polynomial in one variable?<br>
Question 30 :
The length of a rectangular verandah is $3\:m$ more than its breadth. The numerical value of its area is equal to the numerical value of its perimeter. Taking $x$ as the breadth of the verandah, write an equation in $x$ that represents the above statement.
Question 31 :
Before Robert Norman worked on 'Dip and Field Concept', his predecessor thought that the tendency of the magnetic needle to swing towards the poles was due to a point attractive. However, Norman showed with the help of experiment that nothing like point attractive exists. Instead, he argued that magnetic power lies is lodestone. Which one of the following is the problem on which Norman and others worked?
Question 33 :
The roots of the following quadratic equations are real and distinct.<br/>$(x - 2a) (x - 2b) = 4ab$
Question 34 :
If the roots of the equation $ax^2+bx+c=0$ are all real equal then which one of the following is true?
Question 35 :
Is the following equation a quadratic equation?$\displaystyle 3x + \frac{1}{x} - 8 = 0$
Question 36 :
State the nature of the given quadratic equation $(x + 4)^2 + 8x = 0$
Question 37 :
The discrimination of the equation $x^2 + 2x\sqrt3 + 3 = 0$ is zero. Hence, its roots are:
Question 38 :
For what value of k will$\displaystyle x^{2}-\left ( 3k-1 \right )x+2k^{2}+2k=11$ have equal roots?
Question 39 :
Let $f(x)=x^{2}-3x+4 $ , the value(s) of $x$ which satisfies $f(1)+f(x) = f(1)f(x)$ are:
Question 41 :
For what values of $k$ will the quadratic equation : $\displaystyle { 2x }^{ 2 }-kx+1=0$ have real and equal roots?
Question 42 :
The values of $a$ for which the equation $3x^2 + 2(a^2 -3a + 2) = 0$ will have roots of opposite sign lie in the interval
Question 43 :
A trader bought an article for Rs. $x$ and sold it for Rs. $52$, thereby making a profit of $(x-10)$ per cent on his outlay. Calculate the cost price.
Question 44 :
If the roots of the equation  $ \dfrac { { 1 } }{ x+p } +\dfrac { 1 }{ x+q } =\dfrac { 1 }{ r } $ are equal in magnitude but opposite in sign, then which of the following are true?<br/>
Question 45 :
The ______ product rule says that when the product of two terms is zero, then either of the terms is equal to zero.<br>
Question 46 :
$x^2-(m-3)x+m=0\:\:(m \in R)$ be a quadratic equation. Find the value of $m$ for which both the roots are greater than $2$
Question 47 :
$kx^2-2\sqrt 5x +4 = 0$For what value of $k$ will the quadratic equation have real and equal roots ?
Question 49 :
If k be the ratio of the roots of the equation$ \displaystyle x^{2}-px+q=0 $ , the value of$ \displaystyle \frac{k}{1+k^{2}} $ is
Question 50 :
If one root of the quadratic equation $ax^2+bx+c=0$ is the reciprocal of the other, then<br/>
Question 51 :
If $x=5+2\sqrt{6}$, then the value of ${ \left( \sqrt { x } -\cfrac { 1 }{ \sqrt { x } } \right) }^{ 2 }$ is _____
Question 52 :
Consider quadratic equation $ax^2+(2-a)x-2=0$, where $a \in R$.Let $\alpha ,\beta $ be roots of quadratic equation. If there are at least four negative integers between $\alpha$ and $\beta$, then the complete set of values of $a$ is
Question 53 :
If $x=1+i$ is a root of the equation $x^3-ix+1-i=0$, then the other real root is
Question 54 :
If $p, q$ are odd integers, then the roots of the equation $2px^{2} + (2p + q) x + q = 0$ are
Question 55 :
If $\alpha $ and $\beta$ are roots of $x^{2}$ - $(k + 1)$ $x$ + $\dfrac{1}{2}$ $(k^{2}+k+1)$ $=$ 0, then $\alpha ^{2}+\beta ^{2}$ is equal
Question 56 : <p>State the following statement is True or False</p><p>If the roots of the equation $x^2\,+\,px\,+\,q\,=\,0$ differ by $1$, then $p^2\,=\,1\,+\,4q$</p>
Question 57 :
If one of the roots of $\displaystyle x^{2}+f(a)x+a=0$ is equal to third power of the other for all real $a$, then 
Question 58 :
If <b>p</b> and <b>q</b> are positive then the roots of the equation $x^2-px-q=0$ are-
Question 59 :
The equation $\displaystyle 9y^{2}(m+3)+6(m-3)y+(m+3)=0 $, where $m$ is real has real roots then 
Question 60 :
Assertion: If $\displaystyle a+b+c=0$ and $a, b, c $ are rational, then roots of the equation $\displaystyle \left (b+c-a \right )x^{2}+\left (c+a-b \right )x+\left ( a+b-c \right )=0 $ are rational.
Reason: For quadratic equation given in Assertion, Discriminant is perfect square.
Question 61 :
If a,b,c >0 and $a=2b+3c$, then the roots of the equation $ax^2+bx+c=0$ are real if
Question 62 :
The real number $k$ for which the equation $2x^ {3}+3x+k=0$ has two distinct real roots in $[0,1]$
Question 63 :
If the equation $\displaystyle\frac{x^{2}-bx}{ax-c}=\frac{m-1}{m+1}$has roots equal in magnitude but opposite in sign, then $m=$<br>
Question 64 :
A tradesman finds that by selling a bicycle for Rs. 75, which he had bought for Rs. $x$, he gained $x$%. Find the value of $x$.
Question 65 :
The coefficient of $x$ in the equation $x^2+px+q=0$ was wrongly written as $17$ in place of$13$ and the roots thus found was $-2$ and $-15$.<br>Then the roots of the correct equation are
Question 66 :
The total cost price of certain number of books is $450$. By selling the books at $50$ each, a profit equal to the cost price of $2$ books is made. Find the approximate number of books.<br/>
Question 67 :
If $\alpha$ and $ \beta$ are the roots of the equation $ { x^{ 2 } }-ax+b=0$ and $ { v }_{ n }={ \alpha  }^{ n }+{ \beta  }^{ n }$, then<br/>
Question 68 :
If the roots of the equation ${ x }^{ 2 }-2ax+{ a }^{ 2 }+a-3=0$ are real and less than $3$, then
Question 69 :
Equation $x^2 - x + q = 0$ has imaginary roots if 
Question 70 :
Let $a,b,c$ be real and $ { ax }^{ 2 }+bx+c=0$ has two real roots, $\alpha$ and $\beta$ where $\alpha <-1$ and $\beta > 1$, then $ 1+\dfrac { c }{ a } +\left| \dfrac { b }{ a } \right| < 0$ is
Question 71 :
$\alpha ,\beta $ are roots of the equation $2{x^2} - 5x - 6 = 0$ then
Question 72 :
If $x^2-10ax-11b=0$ has roots $c$ and $d$, then, $x^2-10x-11d=0$ has roots $a$ and $b$, then $a+b+c+d=$
Question 74 :
If $\alpha \,\& \beta $ are  roots if the equation ${x^2} + 5x - 5 = 0$, then evaluate $\dfrac{1}{{{{(\alpha  + 1)}^3}}} + \dfrac{1}{{{{(\beta  + 1)}^3}}}$
Question 75 :
A company wants to know when the sale of their product reaches a profit level of Rs. $1000$. The revenue equation is R $=$ $200x-0.5x^{2}$, and the cost to produce x product is determined with $C = - 6000 - 40x$. How many products have to be produced and sold to net a profit of Rs. $1000$?<br/>
