Question 1 :
If $(x + 1)^{2} = 4$ and $(x -1)^{2} = 16$, find the value of $x$.
Question 4 :
Set of value of $x$, if $\sqrt{(x+8)}+\sqrt{(2x+2)} = 1$, is _____.
Question 5 :
If $(a^{2}-1)x^{2}+(a-1)x+a^{2}-4a+3=0$ be an identity in $x$, then the value of $a$.
Question 6 :
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 7 :
Tick the correct answer is the following and justify your choice: If the perimeter and the area of a circle are numerically equal, then the radius of the circle is
Question 8 :
The square of a positive number exceeds three times that number by $180$. Find the number.<br/>
Question 9 : <span>Say true or false.</span><div>A quadratic equation cannot be solved by the method of completing the square.<br/></div>
Question 10 :
If x, y and z are real number such that $x^2 + y^2 + 2z^2 = 4x -2z +2yz -5$ then the possible value of (x-y-z) is
Question 11 :
A two digit number N contains the smaller of the two digits in the unit place. The product of the digit is 40 and the difference between the digit is 3. The sum of the digit in N is_____.
Question 13 :
If $4x=\cfrac { 81 }{ x } $, then the value of $x$ is
Question 14 :
If p & q are distinct reals, then  <span>$2[{({x - p})({x - q}) + ({p - x})({p - q}) + ({q - x})( { q - p}})] = (p - q)^2 + (x - p)^2 + (x - q)^2$ is satisfied for </span>
Question 15 :
The value of k for which the quadratic equation $x^2-2kx+5k=0$ has equal roots,are
Question 17 :
The product of two consecutive integer is $12$. What is the second integer?<br/>
Question 18 :
The value of $P ( x ) = x ^ { 2 } - 7 x + 12$ at $x = 3$ is
Question 19 :
If a given expression is a complete square, then which of the following formulae we use to factorize it?<br/>
Question 20 :
Difference between the squares of $2$ consecutive numbers is $31$. Find the numbers.
Question 21 :
Find the sum of the roots of the equation:<br>$x^2 -6x + 8 = 0$
Question 23 :
The sum of two numbers is 12 and their product is 35. What is the sum of the reciprocals of these <span>numbers?</span>
Question 25 : <span><p>The Completing Square Method converts the quadratic equation $ax^2+bx+c=0$ into which of the following forms?</p><br></span>
Question 26 :
If $\alpha, \beta$ are the roots of $x^{2}+3x-2=0$ then $\dfrac{\alpha+1}{\beta}+\dfrac{\beta+1}{\alpha}$= ?<br/>
Question 28 :
If $56^{2} - 51^{2} = 5p$, then $p$ is equal is<br>
Question 30 :
The number of integral values of $'x'$ for which $x^{2}+19x+92$ is a perfect square, is
Question 31 :
A positive number whose reciprocal equals one less than the number is
Question 32 :
The product of three consecutive positive integers is $8$ times their sum. The sum of their squares is:
Question 33 :
The product of two consecutive integer is $30$. Find the value of first integer.<br/>
Question 34 :
Solution of the quadratic equation ${x^2} - \left( {\tan \dfrac{a}{2} + \cot \dfrac{a}{2}} \right)x + \tan \frac{a}{2} \times\cot \frac{a}{2} = 0$ is:
Question 36 :
For the quadratic equation $ x^{2} - 2x +1= 0$, the value of $x+\dfrac{1}{x}$ is :<br/>
Question 37 :
Ajay and Vijay solved an equation. In solving it, Ajay made a mistake in the constant term only and got the roots as $8$ and $2$, while Vijay made a mistake in the coefficient of $x$ only and obtained the roots as $-9$ and $-1$. The correct roots of the equation are
Question 39 :
$\displaystyle \frac{2}{3}$rd of a number when multiplied by $\displaystyle \frac{3}{4}$th of the same number make 338.<span>The number is</span>
Question 41 :
Which of the following must be added to $x^2-6x+5$ to make it a perfect square ?
Question 42 :
If $x > 0$, and $x^2 - 6x - 7 = 0$, what is the value of $x$?
Question 43 :
Solve the given equation by the method of Completion of Squares: ${x}^{2}+4x+4=0$?
Question 44 : <span>State true or false:</span><div>Two consecutive odd natural numbers such that the sum of their squares is $130$ are $7$ and $10$.<br/></div>
Question 45 : <span>State true or false:</span><div>If $4(x\, -\, 2)^{2}\,-\,  x^{2}\, =\, (x\, +\, 4)^{2}$, then $x=0$ or $x=10$.<br/></div>
Question 47 :
Two lawns have the same area, $121$ sq. m. One is a square and the other is a rectangle. Four times the perimeter of the rectangle is equal to five times that of the square. The length and breadth of the rectangle are
Question 48 :
Two candidates attempt to solve a quadratic equation $\displaystyle x^{2} + px + q = 0$. One starts with a wrong value of $\displaystyle p$ and gets $2$, $6$ as its roots and other starts with wrong value of $\displaystyle q$ and obtains roots $2$, $-9$. The correct roots are<br/>
Question 49 :
One side of rectangle exceeds its other side by 4 cm. If area = 45. Find breadth.
Question 50 :
The units digit of a two-digit number is $2$ more than the tens digit. If the number is subtracted from the sum of the squares of its digits the result is two-thirds of the product of the digits. What is the number?
Question 51 :
lf the expression $ax^{2}+by^{2}+cz^{2}+2ayz+2bzx+2cxy$ can be resolved into rational fractions then<br>
Question 52 :
Length of rectangle exceeds its base by $10$ cm. If area = $39$. Find breadth.
Question 53 :
The difference between two numbers is $5$ and difference in their squares is $65$. The larger number is 
Question 54 :
Find two consecutive odd natural numbers, the sum of whose square is 202.
