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 number of real solutions of the equation $|{x^2} + 4x + 3| + 2x + 5 = 0 $are
If $x$ is real, the function $\frac{{(x - a)(x - b)}}{{(x - c)}}$ will assume all real values, provided
What is the sum of all natural numbers $n$ such that the product of the digits of $n$ (in base $10$ ) is equal to $n^2-10 n-36 ?$
If the inequality $kx^2 -2x + k \geq 0$ holds good for atleast one real $'x'$ , then the complete set of values of $'k'$ is
If $x,\;y,\;z$ are real and distinct, then $u = {x^2} + 4{y^2} + 9{z^2} - 6yz - 3zx - zxy$ is always