Simplified form of $$ [(^5\sqrt{x^{-3\over 5}}\ )^{-5\over3}]^{-5}$$

A and B enter into a partnership with capital in the ratio 5: 6. After 4 months, A withdraws $$1\over 5$$of his capital, while B increases his capital by $$33{1\over 3}\%$$. What is the share (in ₹ lakhs) of B in the annual profit of ₹6.3 lakhs?

A sum of money at simple interest amounts to ₹ 1,012 in $$2{1\over2}\%$$ years and to ₹ 1,067.20 in 4 years. The rate of interest per annum is:

what is the value of the expression
 cos 2A cos2B+sin²(A-B)-sin²(A+B)?

A man buys a scooter on making a cash down payment of Rs. 16224 and promises to pay two more yearly installments of equivalent amount in next two years. If the rate of interest is 4% per annum, compounded. yearly, the cash value of the 50 scooter, is:

What should come in place of the question mark '?' in the following number series?

46, ?, 284, 345, 378, 391

In a circle with centre O, BC is a chord. Points D and A are on the circle, on the opposite side of BC, such that ∠DBC = 28° and BD = DC. What is the measure of ∠BOC?

Directions : Study the following pie chart carefully and answer the questions. The pie chart represents the percentage of people involved in various occupations.
Total number of people = 20000

How many more people are involved in service than in trade?