NET JRF PART - A : Questions and Solutions : NET DEC-2012

NET JRF PART - A : Questions and Solutions:

NET DEC-2012

1.) Which is the least among the following ?

0.33^0.33 , 0.44^0.44 , π^-1/π , e^-1/e

a.) 0.33^0.33

b.) 0.44^0.44 

c.) π^-1/π 

d.) e^-1/e

Ans. : (d) e^-1/e .

Solution:

0.33^0.33 = 0.69360082359 .

0.44^0.44 = 0.69681770628 .

π^-1/π = 3.14159265359^{-0.31830988618} = 0.69462799225 .

e^-1/e = 2.71828182846^{-0.36787944117} = 0.69220062755 .