“The Key Responsibility Of Leadership Is To Think About The Future. No One Else Can Do It For You.”


Question 26. Insert two numbers between 3 and 81 so that the resulting sequence is G.P.

Question 27. Find the value of n so that \( \frac{a^{n+1}+b^{n+1}}{a^n+b^n}\) may be the geometric mean between a and b.

Question 28. The sum of two numbers is 6 times their geometric mean, show that numbers are in the ratio \( (3+2\sqrt{2}):(3-2\sqrt{2})\).

Question 29. If A and G be A.M. and G.M., respectively between two positive numbers, prove that the numbers are \(A pm \sqrt{(A+G)(A-G)}\).

Question 30. The number of bacteria in a certain culture doubles every hour. If there were 30 bacteria present in the culture originally, how many bacteria will be present at the end of 2nd hour, 4th hour and nth hour?

Question 31. What will Rs 500 amounts to in 10 years after its deposit in a bank which pays annual interest rate of 10% compounded annually?

Question 32. If A.M. and G.M. of roots of a quadratic equation are 8 and 5, respectively, then obtain the quadratic equation.