Question 1 : Say true or false.If $2y^{2}\, =\, 12\, -\, 5y$, then solution is $\displaystyle \frac{3}{2}\, or\, -4$.<br/>

Question 2 : The least integer $'c'$ which makes the roots of the equation $x^2+3x+2c$ imaginary is

Question 3 : State the following statement is True or False<br/>The product of two numbers $y$ and $(y - 3)$ is $42$, then the equation formed can be represented as $y\, (y\, -\, 3)\, =\, 42$<br/>

Question 4 : If the roots of the equation $ax^2+bx+c=0$ are all real equal then which one of the following is true?

Question 6 : Roots of the equation $\sqrt {\dfrac {x}{1-x}}+\sqrt {\dfrac {1-x}{x}}=2\dfrac {1}{6}$ are

Question 9 : If c is small in comparision with l then ${\left( {\frac{l}{{l + c}}} \right)^{\frac{1}{2}}} + {\left( {\frac{l}{{l - c}}} \right)^{\frac{1}{2}}} = $

Question 10 : If $3$ is one of the roots $x^2-mx+15=0$. Choose the correct options -<br/>

Question 12 : State the following statement is True or False<br/>The sum of a natural number $x$ and its reciprocal is $\displaystyle \frac{37}{6}$, then the equation is&#160;$x\, +\, \displaystyle \frac{1}{x}\, =\, \displaystyle \frac{37}{6}$.<br/>

Question 13 : 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&#160;$10\, (x^{2}\, +\, 5)\, +\, x\, =\, 61$.<br/>

Question 15 : If $y=\cfrac { 2 }{ 3 } $ is a root of the quadratic equation $3{ y }^{ 2 }-ky+8=0$, then the value of $k$ is ..................

Question 16 : The mentioned equation is in&#160;which form?$z\, -\, \cfrac{7}{z}\, =\, 4z\, +\, 5$

Question 17 : Find $ p \in R $ for $x^2 - px + p + 3 = 0 $ has<br/>

Question 18 : Check whether $2x^2 - 3x + 5 = 0$ has real roots or no.<br/>

Question 19 : The nature of the roots of a quadratic equation is determined by the:<br>

Question 20 : 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 22 : If $C &gt; 0$ and the equation $3 a x ^ { 2 } + 4 b x + c = 0$ has no real root, then

Question 24 : Is the following equation quadratic?$(x\, +\, 3) (x\, -\, 4)\, =\, 0$

Question 26 : 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 29 : <p>If the value of '$b^2-4ac$' is less than zero, the quadratic equation $ax^2+bx+c=0$ will have</p><br/>

Question 30 : Is the following equation a quadratic equation?$(x + 2)^3 = x^3 - 4$

Question 31 : A quadratic equation in $x$ is $ax^2 + bx + c = 0$, where $a, b, c$ are real numbers and the other condition is<br/>

Question 32 : Which of the following equations has two distinct real roots ?<br>

Question 34 : For the expression $ax^2 + 7x + 2$ to be quadratic, the necessary condition is<br>

Question 36 : The following equation is a qudratic equation.&#160;$16x^2 \, - \, 3 \, = \, (2x \, + \, 5)(5x \, - \, 3)$

Question 37 : <p>Which of the following statements is TRUE/CORRECT about Quadratic Equations? A quadratic equation is _____</p>

Question 38 : If&#160;$\displaystyle \frac{5x+6}{\left ( 2+x \right )\left ( 1-x \right )}=\frac{a}{2+x}+\frac{b}{1-x}$, then the values of a and b respectively are

Question 39 : Choose the best possible answer<br/>$\displaystyle&#160;32{ x }^{ 2 }-6=\left( 4x+10 \right) \left( 10x-6 \right)&#160;$ is quadratic equation&#160;<br/>

Question 40 : 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 43 : If $x^{2} - 4x + 2 = 0$, then the value of $4x^{2} + 2x + \dfrac {4}{x} + \dfrac {16}{x^{2}}$ is

Question 44 : The factors of the equation, $k(x + 1)(2x + 1) = 0$, find the value of $k$.<br/>

Question 45 : Solve for $x : 15 x^2 - 7x - 36 = 0$<br>

Question 46 : A quadratic equation $ax^2 + bx+c=0$ has two distinct real roots, if<br>

Question 48 : Set of value of $x$, if $\sqrt{(x+8)}+\sqrt{(2x+2)} = 1$, is _____.

Question 49 : The number of solutions of the equation,$2\left\{ x \right\} ^{ 2 }+5\left\{ x \right\} -3=0$ is

Question 50 : STATEMENT - 1 : $(x-2)(x+1)$ $=$ $(x-1)(x+3)$ is a quadratic equation.<br/>STATEMENT - 2 : If $p(x)$ is a quadratic polynomial, then $p(x)$ $=$ $0$ is called a quadratic equation.<br/>

Question 52 : The quadratic equation whose roots are the A.M. and H.M. between the roots of the equation,$2x^2- 3x + 5 = 0$is

Question 53 : Assertion: If $a$ and $b$ are integers and the roots of $x^2+ax+b=0$ are rational then they must be integers. Reason: If the coefficient of $x^2$ in a quadratic equation is unity then its roots must be integers.

Question 54 : Minimum possible number of positive root of the quadratic equation${x^2} - (1 + \lambda )x + \lambda - 2 = 0, \in R:$

Question 55 : If roots of the equation $12x^2 + mx + 5 = 0$ are in the ratio $3 : 2$, then $m =$

Question 56 : If $\alpha $ and $\beta$ are roots of $x^{2}$ - $(k&#160;+ 1)$ $x$ + $\dfrac{1}{2}$ $(k^{2}+k+1)$ $=$ 0, then $\alpha ^{2}+\beta ^{2}$ is equal

Question 57 : If $'r'$ and $'s'$ are the roots of the equation $ax^2+bc+c=0$, then the value of $\displaystyle\frac{1}{r^2}+\frac{1}{s^2}$ is equal to

Question 58 : If roots of the equation $x^2-bx+c=0$ be two consecutive integers, then $b^2-4c$ equals :

Question 59 : The probability of choosing randomly a number c from the set $\{1, 2, 3, ..........9\} $ such that the quadratic equation $x^2+ 4x +c=0$ has real roots is:

Question 60 : If the graph of $f\left(x\right)=x^{2}+\left(3-k\right)x+k,\left(where\ k\in\ R\right)$ lies above and below $x-axis$, then $k$ cannot be

Question 61 : If in applying the quardratic formula to a quadratic equation<br>$f(x) = ax^2 + bx + c = 0$, it happens that $c = b^2/4a$, then the graph of $y = f(x)$ will certainly:

Question 62 : If the roots of the quadratic equation $x^2+6x+b=0$ are real and distinct and they differ by atmost $4$ then the least value of $b$ is-

Question 63 : The roots of the equation $ax^2&#160;+ bx + c = 0$ will&#160;be imaginary if

Question 65 : If $(x-a)(x-5)+2=0$ has only integral roots where $ a\in I,$ then value of 'a' can be:<br>

Question 66 : The roots of the equation $(b+c)x^2-(a+b+c)x+a=0$ $(a,b,c\ \epsilon \Q, b+c \neq a)$ are

Question 67 : Assertion (A): The roots of&#160;$(x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0$ &#160;are real<br/>Reason (R): A quadratic equation with non-negative discriminant has real roots .<br/>

Question 68 : lf $pr=2(q+s)$, then among the equations$\mathrm{x}^{2}+ px +\mathrm{q}=0$ and $\mathrm{x}^{2}+ rx +\mathrm{s}=0$<br>

Question 69 : The values of k&#160;for which the roots are real and equal of the following equation<br/>$4x^2$ - 3kx + 1 = 0 are&#160;$k = \pm \dfrac{4}{3}$<br/>

Question 70 : If the coefficient of $x^2$ and the constant term of a quadratic equation have opposite signs, then the quadratic equation has _______ roots.<br/>

Question 71 : If both a and b belong to the set $\displaystyle \left\{ 1,2,3,4 \right\}$ then the number of equations of the form $ ax^{2}+bx+1=0$ having real roots is :<br>

Question 72 : If one root of the quadratic equation $ax^2+bx+c=0$ is the reciprocal of the other, then<br/>

Question 73 : If $\alpha$, $\beta$&#160; are the roots of $3x^{2} - 4x + 1 = 0$ the equation whose roots are $\dfrac{\alpha}{\beta}, \dfrac{\beta}{\alpha}$ is?<br/>

Question 74 : If the roots of the equation $px^2+2qx+r=0$ and $qx^2-2\sqrt{pr}x+q=0$ be real, then <br/>

Question 75 : If $b_1b_2=2(c_1+c_2)$, then at least one of the equations $x^2+b_1x+c_1=0$ and $x^2+b_2x+c_2=0$ has

Question 76 : If&#160;${x_1},{x_2}$ are the roots of&#160;${x^2} - 3x + a = 0,a \in R$ and&#160;${x_1} &lt; 1 &lt; {x_2}$ then $a$ belongs to:&#160;<br/>

Question 77 : For what values of $k$ will the quadratic equation :&#160;$\displaystyle { 2x }^{ 2 }-kx+1=0$ have real and equal roots?

Question 78 : If $x=1+i$ is a root of the equation $x^3-ix+1-i=0$, then the other real root is

Question 79 : The given equation has real roots. State true or false:&#160;$8x^2 + 2x -3 = 0$<br/>

Question 80 : Which of the following equations has no solution for $a$ ?

Question 81 : If $a,b,c$ are positive real numbers, then the number of real roots of the equation$ ax^{2}+b\left |x \right |+c=0 $is

Question 82 : Equation of the tangent at (4 , 4) on $x^2$ = 4y is

Question 83 : I. lf one root of the equation $5x^{2}+13x+k=0$ is the reciprocal of the other, then $k=5$<br>II. lf the roots of the equation $a(b-c)x^{2}+b(c-a)x+c(a-b)=0$ are equal, then $a, b,c$ are in H.P.<br>Which of the above statement is true?<br>

Question 85 : Determine the value of $k$ for which the $x = -a$ is a solution of the equation&#160;$\displaystyle x^{2}-2\left ( a+b \right )x+3k=0 $<br/>

Question 86 : Say true or false:The following equation has real roots$\cfrac{1}{2x-3}-\cfrac{1}{x-5}=1, &#160; x \neq \{\cfrac{3}{2},5\}$<br/>

Question 87 : Construct a quadratic in x such that A.M. of its roots is A and G.M. is G.

Question 88 : If the roots of the equation&#160;$\displaystyle \left ( a^{2}+b^{2} \right )x^{2}-2b\left ( a+c \right )x+\left ( b^{2}+c^{2} \right )=0 $ are equal then

Question 90 : Find the value of K so that sum of the roots of the equations $3x^2 + (2x - 11) x K - 5 = 0$ is equal to the product of the roots.

Question 91 : Which of the following equation has two equal real toots ?

Question 92 : Assertion: If roots of the equation $ x^{2}-b x+c=0 $ are two consecutive integers, then $ b^{2}-4 c=1 $ Reason: If $ a, b, c $ are odd integer, then the roots of the equation $4 abc<br>x^{2}+\left(b^{2}-4 a c\right) x-b=0 $ are real and distinct.

Question 93 : Consider quadratic equation $ax^2+(2-a)x-2=0$, where $a \in R$.If exactly one root is negative, then the range of $a^2+2a+5$ is

Question 94 : The quadratic $x^2+ax+b+1=0$ has roots which are positive integers, then $(a^2+b^2)$ can be equal to

Question 95 : The set of values of '$p$' for which the expression $x^2-2px+3p+4$ is negative for at least one real $x$ is-

Question 96 : Find the values of $k$ for the following&#160;quadratic equation, so that they have two real and&#160;equal roots:$4x^2 - 2(k + 1)x + (k + 4) = 0$

Question 97 : If $x_1$ and $x_2$ are the roots of $3x^2 - 2x - 6 = 0$, then $x_1^2 + x_2^2$ is equal to

Question 98 : Determine the values of $p$ for which the&#160;quadratic equation $2x^2 + px + 8 = 0$ has&#160;real roots.

Question 99 : The nature of roots of the equation<br>$\left( a+b+c \right) { x }^{ 2 }-2\left( a+b \right) x+\left( a+b-c \right) =0\left( a,b,c\epsilon Q \right) $

Question 100 : The value of $a$ for which one root of the quadratic equation $(a^2-5a+3) x^2+(3a-1)x+2=0 $ is twice as large as the other, is :<br/>

Question 101 : The roots of $(x-a)(x-c)+k(x-b)(x-d)=0$ are real and distinct for all real $k$ if<br>

Question 102 : Let $m, n$ be positive integers and the quadratic equation $\displaystyle 4x^2 + mx + n = 0$ has two distinct real roots $p$ and $q$ $(p \leq q)$. Also, the quadratic equations $\displaystyle x^2 - px + 2q = 0$ and $\displaystyle x^2 - qx + 2p = 0$ have a common root say $\displaystyle \alpha$.<br/>Number of possible ordered pairs $(m, n)$ is equal to

Question 103 : If one of the roots of the quadratic equation $a{ x }^{ 2 }-bx+a=0$ is $6$, then the value of $\cfrac { b }{ a } $ is equal to

Question 105 : Let $f: R\rightarrow R $ be the function $f(x) = (x - a_{1}) (x - a_{2}) + (x - a_{2}) (x - a_{3})+ (x - x_{3})(x-x_{1})$ with $a_{1}, a _{2}, a_{3}\in R $ Then $f(x)=\geq 0 $if and only if<br>

Question 106 : Using factorization find roots of quadratic equation:<br>$\displaystyle10{ z }^{ 2 }-20=0$<br>

Question 107 : 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 108 : &#160;If &#160;the sum of the roots of the quadratic &#160;equation $ax^2+bx+c=0$ &#160;is equal to the sum of the square of their reciprocals, then &#160;$\dfrac{a}{c},\dfrac{b}{a}$ and $\dfrac{c}{b}$ are in<br/>

Question 109 : If the roots of the quadratic equation $x^2+6x+b=0$ are real and distinct and they differ by at most $4$, then the range of values of $b$ is:

Question 111 : If the roots of equation $x^2-2ax+a^2+a-3=0$ are less than $3$, then

Question 113 : Divide 15 into 2 parts such that the product of 2 numbers is 56.

Question 114 : Find the term independent of x in the expansion of $\left(2x^2-\dfrac{3}{x^3}\right)^{25}$.

Question 115 : 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/>

Question 116 : If each pair of the following three equations $ { x }^{ 2 }+ax+b=0$, ${ x }^{ 2 }+cx+d=0$, ${ x }^{ 2 }+ex+f=0$ has exactly one root in common, then <br/>

Question 117 : 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 118 : $\alpha ,\beta $ are roots of the equation $2{x^2} - 5x - 6 = 0$ then

Question 119 : If both the roots of the equation$\displaystyle x^{2}-6ax+2-2a+9a^{2}=0$ exceed $3$, then

Question 120 : All the values of '$a$' for which the quadratic expression $ax^2+(a-2)x-2$ is negative for exactly two integral values of $x$ may lie in

Question 121 : If the quadratic equation $ax^2 + bx + 6 = 0$does not have distinct real roots, thenthe least value of $2a + b$ is

Question 123 : If $|2x + 3|\le 9$ and $2x + 3 &lt; 0$, then

Question 124 : If $22^3 +23^3+24^3+.........+88^3 $is divided by 110 then the remainder will be

Question 125 : If a,b,c &gt;0 and $a=2b+3c$, then the roots of the equation $ax^2+bx+c=0$ are real if

Question 126 : For what value of $k$ is $x^2 + kx + 9=(x+3)^2$?

Question 127 : The condition that the roots of the equation&#160;$\displaystyle ax^{2}+bx+c=0$ be such that one root is $n$ times the other is&#160;

Question 128 : The value of $a$ for which one root of the quadratic equation $&#160;(a^{2}-5a+3)x^{2}+(3a-1)x+2=0 $&#160;is twice&#160;as large as the other is&#160;

Question 129 : If one root of the equation $a{ x }^{ 2 } + bx + c = 0$ be the square of the other, then the value of${ b }^{ 3 } + { a }^{ 2 }c + a{ c }^{ 2 } $ is<br>

Question 130 : Assertion: If the roots of the equations $x^2-bx+c=0$ and $x^2-cx+b=0$ differ by the same quantity, then $b+c$ is equal to $-4$ Reason: If $\alpha,\beta$ are the roots of the equation $Ax^2+Bx+C=0,$ then $\displaystyle&#160;\alpha -\beta =\frac { \sqrt { { B }^{ 2 }-4AC } &#160;}{ A } $

Question 132 : Hypotenuse length is$\displaystyle3\sqrt { 10 }$. Base length istripled and perpendicular doubles, new length of hypotenuse will be$\displaystyle 9\sqrt { 5 }$. Find the length of base.

Question 133 : The quadratic equation $p(x) =0$ with real coefficients has purely imaginary roots. Then the equation $p(p(x)) =0$ has

Question 135 : If $\alpha$, $\beta$ are the roots of the equation $a{ x }^{ 2 }+bx+x=0$, then the roots of the equation $\left( a+b+c \right) { x }^{ 2 }-\left( b+2c \right) x+c=0$ are

Question 136 : If one of the roots of $x^2-bx+c=0,\:(b,c)\:\epsilon\:Q$ is $\sqrt{7-4\sqrt 3}$ then:

Question 137 : The difference between two positive integers is $13$ and their product is $140$. Find the two integers.<br/>

Question 138 : If $a, b$ and $c$ are in arithmetic progression, then the roots of the equation $ax^{2} - 2bx + c = 0$ are&#160;

Question 139 : Divide 20 into 2 parts such that the product of 2 numbers is 36.

Question 140 : The value of $a$ for which the equation $a ^ { 2 } + 2 a + \csc ^ { 2 } \pi ( a + x ) = 0$ has a solution, is/are

Question 141 : 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&#160;

Question 142 : If $\alpha \,\&amp; \beta $ are&#160; roots if the equation ${x^2} + 5x - 5 = 0$, then evaluate $\dfrac{1}{{{{(\alpha&#160; + 1)}^3}}} + \dfrac{1}{{{{(\beta&#160; + 1)}^3}}}$

Question 143 : If the roots of the equation ${ x }^{ 2 }-2ax+{ a }^{ 2 }+a-3=0$ are real and less than $3$, then

Question 144 : If $b_1b_2=2(c_1+c_2)$, then at least one of the equations $x^2+b_1x+c_1=0$ and $x^2+b_2x+c_2=0$ has<br>

Question 145 : The rectangular fence is enclosed with an area $16$cm$^{2}$. The width of the field is $6$ cm longer than the length of the fields. What are the dimensions of the field?<br/>

Question 147 : Let $f(x)\, =\, x^2\, +\, ax\, +\, b,$ where a, b $\epsilon$&#160;R. If $f(x) = 0$ has all its&#160;roots imaginary, then the roots of $f(x) + f' (x) + f&#34; (x) = 0$ are

Question 149 : Find the values of $K$ so that the quadratic equations $x^2+2(K-1)x+K+5=0$ has atleast one positive root.

Question 150 : If&#160;$\displaystyle r_{1}\:$ and $ r_{2}$ are the roots of&#160;$\displaystyle x^{2}+bx+c=0$ and&#160;$\displaystyle S_{0}=r_{1}^{0}+r_{2}^{0}$,&#160;$\displaystyle S_{1}=r_{1}+r_{2}$ and&#160;$\displaystyle S_{2}=r_{1}^{2}+r_{2}^{2}$, then the value of&#160;$\displaystyle S_{2}+bS_{1}+cS_{0}$ is