Find the sum of all powers of 2 between 500 and 50000.

Find \(x\) if \({\log _e}x = 7\), correct to 4 significant figures.

Find the constant term in the expansion of \({\left( {x + \dfrac{2}{{{x^2}}}} \right)^{15}}\).

State the domain and range of \(y = \sqrt {1 – x} + 2\).

The solutions of \(- 2{x^2} – 8x + 3 = 0\) are \( A \pm \sqrt {\dfrac{B}{C}} \). Find \(A\), \(B\) and \(C\).

The function  \(y = f\left( x \right)\)  is transformed to the function  \(g\left( x \right) = 3 + 2f\left( {0.5x + 1} \right)\).   Find the corresponding point of the point  \(\left( { – 1, – 2} \right)\)  on  \(f\left( x \right)\).

Find   \(x\)  and    \(y\),   correcting to one decimal place.

Find \(A \), if the radius of a circle of the centre angle \(24^\circ \) and the arc length 12 cm is \(\dfrac{A}{\pi }\) cm.

Solve  \(\sin 4x = \sin 2x\)  for  \(0^\circ \le x \le 360^\circ \).   Write answers in ascending order.

A biased coin has a 60% of probability of getting a Tail. This coin is tossed five times. Find the probability of obtaining at least two Tails.