Simplify the following

  $${\sqrt { 10+{\sqrt { 25+ {\sqrt { 108 +\sqrt { 154+ \sqrt { 225} \ } \ } \ }} \ } } \ }\over \sqrt { 16+ 19.25×4^2} $$

If the highest common factor (HCF) of x and y is 15, then the HCF of 36x² – 81y² and 81x² – 9y² is divisible by __________

Find the value of given expression.

3 – (– 6) {– 2 – 9 – 3} ÷ 7{1 + (– 2) (– 1)}

Find the number of diagonals of a regular polygon, sum of whose interior angles is 2700⁰.

If △ABC is right angled at B, AB = 12 cm and ∠CAB = 60°, determine the length of BC.

A dishonest dealer marks up his goods by 50% and then gives a discount of 20% on the marked price. Apart from this, he uses a faulty balance which reads 1kg for 900 gm. What is his net profit percentage (rounded off to the nearest integer)?

Reshma covers 45 km at a speed of 15 km/h by bicycle, 80 km at a speed of 40 km/h by car, and another 6 km at a speed of 2 km/h on foot. Find her average speed for the whole journey (correct to 2 decimal places).

A, B and C invested capital in the ratio of 3 : 4 : 8. At the end of the business term, they received the profit in the ratio of 2 : 3 : 5. What is the ratio of their invested time?