Let $a, b, c, d$ be real numbers such that $|a-b|=2$, $|b-c|=3,|c-d|=4$. Then, the sum of all possible values of $|a-d|$ is
$9$
$18$
$24$
$30$
In the real number system, the equation $\sqrt{x+3-4 \sqrt{x-1}}+\sqrt{x+8-6 \sqrt{x-1}}=1$ has
The number of real solutions of the equation $|{x^2} + 4x + 3| + 2x + 5 = 0 $are
The solutions of the quadratic equation ${(3|x| - 3)^2} = |x| + 7$ which belongs to the domain of definition of the function $y = \sqrt {x(x - 3)} $ are given by
The number of ordered pairs $(x, y)$ of positive integers satisfying $2^x+3^y=5^{x y}$ is
Suppose $m, n$ are positive integers such that $6^m+2^{m+n} \cdot 3^w+2^n=332$. The value of the expression $m^2+m n+n^2$ is