Question 2 :
Find the value of $(2+w + w^2)^3-( 1- 3 w +w^2)^3-(1-3w +w^2)^3$
Question 4 :
The argument of the complex number $\sin \dfrac{{6\pi }}{5} + i\left( {1 + \cos \dfrac{{6\pi }}{5}} \right)$ is
Question 6 :
If $ \displaystyle\ z=\frac{\sqrt{3}+i}{\sqrt{3}-i}$ then the fundamental amplitude of z is
Question 8 :
If $\omega $ is an imaginary cube root of unity, then the value of $(1 + \omega) (1 + \omega^2) (1 + \omega^3) (1 + \omega^4)(1 + \omega^5) .... (1 + \omega^{3n})$ is
Question 9 :
Given $z = (1 + i \sqrt 3)^{100}$, then $\displaystyle \frac{Re(z)}{Im(z)}$ equals
Question 10 :
What is the distance between the lines 3x + 4y = 9 and 6x + 8y = 18 ?
Question 11 :
Find the distance from the point (2, 3) to the line 3x + 4y + 9 = 0
Question 12 :
If $p$ is the length of the perpendicular from the origin on the line $\displaystyle \frac{x}{a}+\frac{y}{b}=1$ and $a^{2}$, $p^{2}$, $b^{2}$ are in A.P. then $ab$ is equal to<br>
Question 13 :
A$(-3, 4)$, B$(5, 4)$, C and D form a rectangle. If $x -4y + 7 = 0$ is a diameter of the circumcircle of the rectangle ABCD then area of rectangle ABCD is
Question 14 :
The equation of the line passing through $(-3,5)$ and perpendicular to the line through the points $(1,0)$ and $(-4,1)$<br>
Question 16 :
Equation of the line equidistant from the lines $2{x}+{y}+4=0,3{x}+6{y}-5=0$ is <br/>
Question 17 :
If discriminant of a quadratic equation is $D=0,$ then ___________is not possible for its roots $\alpha$ and $\beta$.
Question 18 :
Discriminant of a quadratic equation $\displaystyle p{ x }^{ 2 }+qx+r=0$ is given by.
Question 19 :
The sum of the squares of two consecutive positive integers is $545$. Find the integers.
Question 20 :
If $ \alpha, \beta $ are the roots of $ ax^{2}+bx+c=0 $, then $ \alpha\beta^{2}+\alpha^{2}\beta+\alpha\beta= $
Question 21 :
The sum of a number and its reciprocal is $2\cfrac{x}{12}$ then the value of $x$ is
Question 22 :
$x^2+3ax+2a^2=0$ <br/>If the above equation has roots $\alpha ,\beta $ and it is given that $\alpha^2 +\beta ^2=5$, then the product of roots is<br/>
Question 23 :
If $a\neq b,$ if the equations ${ x }^{ 2 }+ax+b=0$ and ${ x }^{ 2 }+bx+a=0$ have a common root, the value of $(a+b) $ is