If the equation $\frac{{{x^2} + 5}}{2} = x - 2\cos \left( {ax + b} \right)$ has atleast one solution, then $(b + a)$ can be equal to
$0$
$\pi $
$2\pi $
$4\pi $
The number of real solutions of the equation $x\left(x^2+3|x|+5|x-1|+6|x-2|\right)=0$ is
The roots of the equation ${x^4} - 2{x^3} + x = 380$ are
If $x$ is real and satisfies $x + 2 > \sqrt {x + 4} ,$ then
Let $\mathrm{S}=\left\{x \in R:(\sqrt{3}+\sqrt{2})^x+(\sqrt{3}-\sqrt{2})^x=10\right\}$. Then the number of elements in $\mathrm{S}$ is :
If $x$ be real, then the maximum value of $5 + 4x - 4{x^2}$ will be equal to