In the real number system, the equation $\sqrt{x+3-4 \sqrt{x-1}}+\sqrt{x+8-6 \sqrt{x-1}}=1$ has
no solution
exactly two distinct solutions
exactly four distinct solutions
infinitely many solutions
If $a, b, c, d$ and $p$ are distinct real numbers such that $(a^2 + b^2 + c^2)\,p^2 -2p\, (ab + bc + cd) + (b^2 + c^2 + d^2) \le 0$, then
The maximum value $M$ of $3^x+5^x-9^x+15^x-25^x$, as $x$ varies over reals, satisfies
The number of real solutions of the equation $\mathrm{x}|\mathrm{x}+5|+2|\mathrm{x}+7|-2=0$ is .....................
Let $P(x) = x^3 - ax^2 + bx + c$ where $a, b, c \in R$ has integral roots such that $P(6) = 3$, then $' a '$ cannot be equal to