What is the value of the following?
\( \frac{2\sin 68^{\circ}}{\cos 22^{\circ}} - \frac{2\cot 15^{\circ}}{5\tan 75^{\circ}} - \frac{3\tan 20^{\circ} \tan 40^{\circ} \tan 45^{\circ} \tan 50^{\circ} \tan 70^{\circ}}{5} \)
The perpendicular dropped from a vertex of a right-angled triangle upon the hypotenuse divides it into two segments of lengths 9 units and 16 units respectively. What is the length of the perpendicular?
If \( 43^{x} \times 47^{y} = (2021)^{2} \), \( x \neq 0 \), \( y \neq 0 \), then what is the value of the following?
\( \frac{4xy + x + y}{2xy - x - y} \)
Let a, b, c, d be positive integers. If
\( \frac{1}{a + \frac{1}{b + \frac{1}{c + \frac{1}{d}}}} = \frac{17}{60} \)
then what is the product of a, b, c, d?
A car travels from A to B at a speed of 40 km/hr, travels back from B to A at a speed of 30 km/hr and again goes from A to B at a speed of 60 km/hr. What is the average speed of the car?
