If graph of $y = ax^2 -bx + c$ is following, then sign of $a$, $b$, $c$ are
$a < 0, b < 0, c < 0$
$a < 0, b > 0, c < 0$
$a < 0, b < 0, c > 0$
$a > 0, b > 0, c < 0$
The equation $x^2-4 x+[x]+3=x[x]$, where $[x]$ denotes the greatest integer function, has:
The set of values of $x$ which satisfy $5x + 2 < 3x + 8$ and $\frac{{x + 2}}{{x - 1}} < 4,$ is
Suppose that $x$ and $y$ are positive number with $xy = \frac{1}{9};\,x\left( {y + 1} \right) = \frac{7}{9};\,y\left( {x + 1} \right) = \frac{5}{{18}}$ . The value of $(x + 1) (y + 1)$ equals
Consider the equation $(1+a+b)^2=3\left(1+a^2+b^{2})\right.$ where $a, b$ are real numbers. Then,
The complete solution of the inequation ${x^2} - 4x < 12\,{\rm{ is}}$