If $\frac{x}{a}=\frac{1}{a}-\frac{1}{x}$, then the value of $x-x^2$ is :

The sum of the roots of the equation, $x+1-2{\log }_2\left(3+2^x\right)+2{\log }_4\left(10-2^{-x}\right)=0,$ is :

For how many different values of $a$ does the following system have at least two distinct solutions?

$ax+y=0$

$x+\left(a+10\right) y=0$

The factors of equation $x^2+7x+12=0$  are-

(A) -3 and -4 

(B) 3 and -4 

(C) -3 and 4 

(D) 3 and 4 

FInd the factors of $(x^2 - x - 132):$

1. $(x - 11) (x -12)$
2. $(x + 12) (x -11)$
3. $(x + 11) (x + 12)$
4. $(x - 12) (x + 11)$