If `f(x)=prod_(n=1)^(100)(x-n)^(n(101-n))`; then `(f(101))/(f'(101))=`

If f(x)=(x-1)^(100)(x-2)^(2(99))(x-3)^(3(98))…(x-100)^(100), then the value of (f'(101))/(f(101)) is

If f(n)=prod_(r=1)^(n)cos r,n in N , then

If f(n)=prod_(i=2)^(n-1)log_i(i+1) , the value of sum_(k=1)^100f(2^k) equals

The sum of the series (.^(101)C_(1))/(.^(101)C_(0)) + (2..^(101)C_(2))/(.^(101)C_(1)) + (3..^(101)C_(3))/(.^(101)C_(2)) + "….." + (101..^(101)C_(101))/(.^(101)C_(100)) is "____" .

If {F(x)}^(101)=int_0^x(F(t))^(100)(dt)/(1+sint), then find F(x)

if f(n,theta)=prod_(r=1)^(n) (1-tan^(2)(theta)/(2^(r))) then the value of lim_(thetato0) [lim_(ntoinfty) f(n,theta)] , (where [x] represent the greatest integer function) is

If int(dx)/(x^2(x^n+1)^((n-1)/n))=-(f(x))^(1/n)+C then f(x) is (A) 1+x^n (B) 1+x^-n (C) x^n+x^-n (D) x^n-x^-n

If (+x)^n=sum_(r=0)^n a_r x^r&b_r=1+(a_r)/(a_(r-1))&prod_(r=1)^n b_r=((101)^(100))/(100!), then equals to: 99 (b) 100 (c) 101 (d) None of these

if f (x) = lim _(x to oo) (prod_(i=l)^(n ) cos ((x )/(2 ^(l)))) then f '(x) is equal to:

The total number of different terms in the product (.^(101)C_(0) - .^(101)C_(1)x+.^(101)C_(2)x^(2)-"….."-.^(101)C_(101)x^(101))(1+x+x^(2)+"…."+x^(100))^(101) is "____" .