9- indicies

Prove that X = 4ⁿ⁺¹.9ⁿ⁺² + 6²ⁿ⁺¹.9 - 2²ⁿ.9ⁿ⁺¹ is divisible by 369. Given that n ε N.

7-indicies

Find the value of x for which a= 2¹⁰⁰ + (2⁵⁰)² + (2²⁵)⁴ + (2⁵)²⁰ and b = 2⁹⁹ + (2³³)³ + (2¹¹)⁹ + (2³)³³ +2⁹⁹.x are equal (a = b).

numbers

Find the natural number for which 2010ⁿ –n²⁰¹⁰ = 2009

number and divisibility

Prove that 2⁰ + 2¹ + 2² + 2³ + …. 2⁹⁸ is divisible by 7

Numbers

If x and y are digits such that 23xy + xy23 + xyxy = 11413, then find the value of x + y.

Ratio and proportion

Show that:

If,

                 ax+cy+bz=0 ---- (1)
                 cx+by+az=0 ---- (2)
                 bx+ay+cz=0 ---- (3)

Then, a³+b³+c³ = 3abc
 

Mean

The average of 13 observations is 23. The average of the first 7 observation is 27 and the average of the last 7 observation is 24. What is the value of the seventh observation?

percentage

The inflation in the economy is @ 9% per annum. A company decides to revise the salary of all its employees by 5%. By how much should the consumption by individuals come down so as to beat the inflation?

percentage

A farmer stores 10000 kg of potatoes in an underground cellar. At the prevailing buying rates in the whole sale market he is unable to make any profit. He is advised that the market price of potatoes will climb @ 3% per month, whereas the loss in weight of potatoes due to evaporation of water was @1% per month.

After how many months should he sell his stock of potatoes so as to make a profit of 10%.

 

 Check the answer: