Find the fission fragment X produced in the fission , reaction `""_(0)^(1)n+""_(92)^(235)Urarr""_(41)^(99)Nb+X+4""_(0)^(1)n`

Find the energy released during the most probable fission of ""^(235)U.""_(9)^(235)U +""_(0)^(1)n rarr""_(56)^(141)Ba +""_(36)^(92)Kr +3""_(0)^(1)n Average binding energy per nucleon of ""^(235)U, ""^(141)Ba and ""^(92)Kr are 7.61 MeV, 8.32 MeV and 8.80 MeV respectively.

int_(0)^(1)x(1-x)^(n)dx=

Assertion (A) Fragments produced in the fission of ""_(92)U^(235) are radioactive. Reason (R) The fragments in the fission of ""^(235)U have a proton to neutron ratio of 2.5.

The value of the integral I=int_(0)^(1)x(1-x)^(n) is

Lt_(x to 0)((a_(1)^(x)+a_(2)^(x)+...+a_(n)^(x))/(n))^(1//x)=

Find Lt_(xto0)((2+x)^(n)-2^(n))/x

Show that the coefficient of x^(k) (0 le k le n) in the expansion of 1+(1+x)+(1+x)^(2)+…+(1+x)^(n) is ""^(n+1)C_(K+1) .

Prove that : If n is a positive integer and x is any nonzero real number, then prove that C_(0)+C_(1)(x)/(2)+C_(2).(x^(2))/(3)+C_(3).(x^(3))/(4)+….+C_(n).(x^(n))/(n+1)=((1+x)^(n+1)-1)/((n+1)x)