List of top General Aptitude Questions on Algebra asked in GATE CE

If a positive real \(x\) satisfies the following equation
\[ \log_2 x + \log_{\sqrt{2}} x = 48, \]
then the value of \(x\) is

At how many points will the curves \(y = x^2\) and \(y = -x^2 - 2x - 1\) intersect in the real \((x, y)\) plane?