Question 1 : <span>Is the following equation quadratic?</span><div>$\displaystyle -\frac{5}{3}\, x^{2}\, =\, 2x\, +\, 9$</div>
Question 3 :
The number of solutions of the equation,$2\left\{ x \right\} ^{ 2 }+5\left\{ x \right\} -3=0$ is
Question 4 :
The expression $21x^2 + ax + 21$ is to be factored into two linear prime binomial factors with integer coefficients. This can be done if a is:
Question 5 :
The quadratic polynomial whose sum of zeroes is $3$ and product of zeroes is $- 2$ is:<br/>
Question 6 : <div><span>State the following statement is True or False</span><br/></div>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 8 : <span>Is the following equation a quadratic equation?</span><div>$16x^2 - 3 = (2x + 5) (5x - 3)$</div>
Question 9 :
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 10 :
Choose best possible option.<br><span>$\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.</span><br>
Question 11 :
<span>Check whether the given equation is a quadratic equation or not.</span><br/>$\quad { x }^{ 2 }+\cfrac { 1 }{ { x }^{ 2 } } =2\quad $<br/>
Question 13 : <span>Is the following equation quadratic?</span><div>$(x\, +\, 3) (x\, -\, 4)\, =\, 0$</div>
Question 14 : <span>The mentioned equation is in which form?</span><div>$z\, -\, \cfrac{7}{z}\, =\, 4z\, +\, 5$</div>
Question 15 : <span>Is the following equation a quadratic equation?</span><div>$(x + 2)^3 = x^3 - 4$</div>
Question 16 : <div><span>State the following statement is True or False</span><br/></div>The digit at ten's place of a two digit number exceeds the square of digit at units place ($x$) by 5 and the number formed is $61$, then the equation is $10\, (x^{2}\, +\, 5)\, +\, x\, =\, 61$.<br/>
Question 17 :
The condition for $px^{2} + qx + r = 0$ to be a pure quadratic equation is
Question 18 :
<span>Check whether the given equation is a quadratic equation or not.</span><br/>$3{ x }^{ 2 }-4x+2=2{ x }^{ 2 }-2x+4$
Question 19 : <div><span>Check whether the following is a quadratic equation.</span></div><div><span>$(x - 3) (2x + 1) = x (x + 5)$</span><br/></div>
Question 20 :
Find the roots of the following quadratic equation by using the quadratic formula <br>$4{x^2} + 3x + 5 = 0$<br>
Question 21 :
For which values of 'a' and 'b' does the following pair of linear equations have infinite number of solutions -<br>$2x+3y=7, (a-b)x+(a+b)y=3a+b-2$
Question 22 :
If $ \alpha $ and $ \beta $ are the roots of $ x^{2}+p x+q=0 $ and $ \alpha^{4}, \beta^{4} $ are the roots of $ x^{2}-r x+s=0, $ then the equation $ x^{2}-4 q x+2 q^{2}-r =0 $ has always
Question 23 :
If one root of the equation $x^2-4x+k=0$ is $6$, then the value of k will be
Question 24 :
m, n are zeroes of $\displaystyle ax^{2}+7x+c $ Find the value of a and c if the sum of zeroes is -7 and sum of squares of zeroes is 25
Question 25 :
If $ y = x + \dfrac {1}{x} , x \ne 0, $ then the equation $ ( x^2 - 3x + 1 )(x^2 - 5x + 1 ) = 6x $ reduces to :
Question 26 :
The product of two consecutive natural numbers is $12$. The equation form of this statement is
Question 27 :
The number of roots of the equation $ \sqrt{x-2}\left(x^{2}-4 x+3\right)=0 $ is
Question 28 :
A root of the equation $( x - 1 ) ( x - 2 ) = \dfrac { 30 } { 49 }$ is
Question 29 :
If $x^2 + y^2 = 7xy$, then which of the following are true?
Question 30 :
The number of real roots of the equation ${ x }^{ 4 }+\sqrt { { x }^{ 4 }+20 } =22$ is
Question 31 :
For what value of $k$ is $x^2 + kx + 9=(x+3)^2$?
Question 32 :
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 34 :
The difference between two positive integers is $13$ and their product is $140$. Find the two integers.<br/>
Question 35 :
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/>
