A person borrows Rs 4000 from a bank at 7 ½% per annum compound interest, compounded annually. At the end of every year, he pays Rs 1500 as part of the repayment of loan & interest. How much does he still owe to the bank after 3 such installments?

A is as efficient as B and C together. Working together A and B can complete a work in 36 days and C alone can complete it in 60 days. A and C work together for 10 days, then B alone will complete the remaining work in :

If \(sin {πx\over 2}=x^2-2x+2\), then the value of x is 

If \(3(cot^2\theta-cos^2\theta)=cos^2\theta\), \(0^0<\theta<90^0\), then the value of \((tan^2\theta+cosec^2\theta+sin^2\theta)\) is :