The population of a country increases by 2% every year. If it increases `k` times in a century, then prove that `[k]=7,w h e r e[dot]` represents the greatest integer function.

Evaluate: int_(-100)^(100)[tan^(-1)x]dx ,w h e r e[x] represents greatest integer function.

Evaluate: int_(0)^(oo)[2e^(-x)]dx, where [x] represents greatest integer function.

If momentum is increased by 20% then K.E. increases by

When the momentum of a body increases by 100%, its K.E. increases by :

If N is the number of different paths of lentght-12 which leads from A to B in the grid which do not pass through M, then the value of [N//10]w h e r e[dot] represents the greatest integer function is __________. Fig

If f(x)=x((e^(|x|+[x])-2)/(|x|+[x])) then (where [.] represent the greatest integer function)

Draw the graph of f(x) = [log_(e)x], e^(-2) lt x lt 10 , where [*] represents the greatest integer function.

When the momentum of a body increases by 10%, its K.E. increases by