Question 1 :
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 2 :
Is the following equation a quadratic equation?$(x + 2)^3 = x^3 - 4$
Question 3 :
Which one of the following condition will satisfy the zero product roots of the equation $(x - a)(x - b)$?<br>
Question 4 :
Let x and y be two 2- digit number such that y is obtain by reversing the digits of x.suppose they also satisfy $x^2-y^2=m^2$ for some positive integer m. The value of $x+y+m$ is.
Question 6 :
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 $x\, +\, \displaystyle \frac{1}{x}\, =\, \displaystyle \frac{37}{6}$.<br/>
Question 7 :
The nature of the roots of a quadratic equation is determined by the:<br>
Question 9 :
Which point satisfies the linear quadratic system y=x+3 and y=5-x$\displaystyle ^{2}$?
Question 10 :
The quadratic polynomial whose sum of zeroes is $3$ and product of zeroes is $- 2$ is:<br/>
Question 11 :
If the roots of the quadratic equation $x^2 - 4x - \log_3 a = 0$ are real, then the least value of $a$ is
Question 12 :
If the equation $x^2- m (2x - 8) - 15 = 0$ has equalroots, then $m =$
Question 13 :
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 14 :
The quadratic equations $x^{2}-6x+a=0$ and $x^{2}-cx+6=0$ have one root in common. The other roots of the first and second equations are integers in the ratio $4: 3$. Then the common root is<br><br>
Question 15 :
In the following, determine whether the given quadratic equation have real roots and if so, find the roots :<br/>$\sqrt{3}x^2 \, + \, 10x \, - \, 8\sqrt{3} \, = \, 0$
Question 16 :
If $p, q$ are odd integers, then the roots of the equation $2px^{2} + (2p + q) x + q = 0$ are
Question 17 :
If a, b, c $\epsilon\ Q\ $, then the roots of the equation $(b + c - 2a) x^{2} + (c+a-2b) x+ (a+b-2c) = 0$ are<br/>
Question 18 :
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 19 :
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 20 :
The factors of the equation, $(x + k)\left (x + \dfrac{1}{2}\right) = 0$, find the value of $k$.<br/>
Question 22 :
$\alpha ,\beta $ are roots of the equation $2{x^2} - 5x - 6 = 0$ then
Question 23 :
If $a < b < c < d$, then for any real non-zero $\lambda$, the quadratic equation $(x-a)(x-c)+\lambda (x-b)(x-d)=0$ has<br>
Question 24 :
If a,b,c >0 and $a=2b+3c$, then the roots of the equation $ax^2+bx+c=0$ are real if
Question 25 :
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 26 :
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 27 :
If $22^3 +23^3+24^3+.........+88^3 $is divided by 110 then the remainder will be
Question 28 :
If both the roots of the equation ${ x }^{ 2 }-32x+c=0$ are prime numbers then the possible values of $c$ are
Question 29 :
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 30 :
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 31 :
If $m_1$ and $m_2$ are the roots of the equation $x^2+\left(\sqrt{3}+2\right)x+\left(\sqrt{3}-1\right)=0$, then the area of the triangle formed by the lines $y=m_1x,y=m_2x$ and $y=2$ is :
Question 32 :
Divide 15 into 2 parts such that the product of 2 numbers is 56.
Question 33 :
Given expression is $x^{2} - 3xb + 5 = 0$. If $x = 1$ is a solution, what is $b$?
Question 34 :
If the roots of the equation ${ x }^{ 2 }-2ax+{ a }^{ 2 }+a-3=0$ are real and less than $3$, then
Question 35 :
The roots of the equation $\displaystyle x^{2}-px+q=0$ are consecutive integers. Find the discriminate of the equation.
Question 36 :
If the roots of the equation ${ 12x }^{ 2 }+mx+5=0$ are in the ratio $5:4$ then $m=$
Question 37 :
The number of integral values of $a$ for which the quadratic expression $(x-a)(x-10)+1$ can be factored as a product $(x+\alpha)(x+\beta)$ of two factors $\alpha, \beta, \in I$, is
Question 38 :
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 39 :
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 41 :
If the quadratic equation $ax^2 + bx + 6 = 0$does not have distinct real roots, thenthe least value of $2a + b$ is
Question 42 :
The number of values of $\displaystyle k$for which$\displaystyle \left ( x^{2} - \left ( k - 2 \right )x + k^{2} \right ) \left ( x^{2} + kx + \left ( 2k - 1 \right ) \right )$is a perfect square
Question 43 :
Let $r,s,t$ be roots of the equation $8x^3+1001x+2008=0$. The value of $(r+s)^3+(s+t) ^3+(t+r) ^3$is
Question 44 :
 If  the sum of the roots of the quadratic  equation $ax^2+bx+c=0$  is equal to the sum of the square of their reciprocals, then  $\dfrac{a}{c},\dfrac{b}{a}$ and $\dfrac{c}{b}$ are in<br/>
Question 45 :
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 46 :
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 47 :
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 48 :
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 49 :
If both the roots of the equation$\displaystyle x^{2}-6ax+2-2a+9a^{2}=0$ exceed $3$, then
Question 50 :
The value of $'a'$ for which the equations $x^{2}-3x+a=0$ and $x^{2}+ax-3=0$ have a common root is
