If graph of $y = ax^2 -bx + c$ is following, then sign of $a$, $b$, $c$ are
$a < 0, b < 0, c < 0$
$a < 0, b > 0, c < 0$
$a < 0, b < 0, c > 0$
$a > 0, b > 0, c < 0$
If $x$ is real, then the maximum and minimum values of the expression $\frac{{{x^2} - 3x + 4}}{{{x^2} + 3x + 4}}$ will be
If the roots of the equation $8{x^3} - 14{x^2} + 7x - 1 = 0$ are in $G.P.$, then the roots are
The number of distinct real roots of $x^4-4 x^3+12 x^2+x-1=0$ is
The number of solutions of the equation $x ^2+ y ^2= a ^2+ b ^2+ c ^2$. where $x , y , a , b , c$ are all prime numbers, is
If $|{x^2} - x - 6| = x + 2$, then the values of $x$ are