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

Question 2 :
Is the following equation a quadratic equation?$\displaystyle \frac{3x}{4} - \frac{5x^2}{8} = \frac{7}{8}$

Question 5 :
When $a = \dfrac {4}{3}$, the value of $27a^{3} - 108a^{2} + 144a - 317$ is

Question 6 :
The factors of the equation, $k(x + 1)(2x + 1) = 0$, find the value of $k$.<br/>

Question 9 :
The difference between the product of the roots and the sum of the roots of the quadratic equation $6x^{2} - 12x + 19 = 0$ is

Question 10 :
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 11 :
The mentioned equation is in&#160;which form?<br/>$m^{3}\, +\, m\, +\, 2\, =\, 4m$

Question 12 :
If $C &gt; 0$ and the equation $3 a x ^ { 2 } + 4 b x + c = 0$ has no real root, then

Question 13 :
Difference between the squares of $2$ consecutive numbers is $31$. Find the numbers.

Question 14 :
Which point satisfies the linear quadratic system y=x+3 and y=5-x$\displaystyle ^{2}$?

Question 15 :
The sum of roots of the equation$a{x^2} + bx + c = 0$ is equal to the sum of squares of their reciprocals.The$b{c^2},c{a^2}$ and $a{b^2}$ are in

Question 17 :
If $9y^{2}\, -\, 3y\, -\, 2\, =\, 0$, then&#160;$y\, =\, \displaystyle -\frac{2}{3}, \, \displaystyle \frac{1}{3}$.<br/>

Question 18 :
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 20 :
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 21 :
If one root of $x^{2}+ax+8=0$ is $4$ and the equation $x^{2}+ax+b=0$ has equal roots, then $b=$

Question 22 :
If roots of the equation $x^2-bx+c=0$ be two consecutive integers, then $b^2-4c$ equals :

Question 23 :
The condition for the equations $ax^{2} + bx + c = 0$ and $a'x^{2} + b'x + c' = 0$ to have reciprocal roots is $\dfrac{a}{c'}=\dfrac{b}{b'}=\dfrac{c}{a'}$<br/>

Question 25 :
Minimum possible number of positive root of the quadratic equation${x^2} - (1 + \lambda )x + \lambda - 2 = 0, \in R:$

Question 27 :
For what value of k will$\displaystyle x^{2}-\left ( 3k-1 \right )x+2k^{2}+2k=11$ have equal roots?

Question 28 :
The roots of the following quadratic equation are not real<br/>$2x^2- 3x + 5$ = 0

Question 29 :
Find the value of $k$ for the following&#160;quadratic equation, so that they have two real and&#160;equal roots:$x^2 - 2(k + 1)x + k^2 = 0$

Question 30 :
Find the discriminant of the equation and the nature of roots. Also find the roots.$2x^2 + 5 \sqrt 3x + 6 =0$

Question 31 :
The least value of $a$ for &#160;which roots of the equation $x^2-2x-\log_4 a=0$ are real is

Question 32 :
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 33 :
Assertion: If $a + b + c = 0$ and $a, b, c$ are rational, then the roots of the equation $(b + c - a)x^2 + (c + a - b)x + (a + b - c) = 0$ are rational . Reason: Discriminant of $(b + c - a)x^2 + (c + a - b)x + (a + b - c) = 0$ is a perfect square .

Question 34 :
If the roots of the equation $ax^2+ bx + c = 0$ arereciprocal to each other, then

Question 35 :
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