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 Option 1: 5050 Option 2: 2575 Option 3: 3030 Option 4: 1250

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 f(x)=x^3-x^2+100x+2002 ,t h e n f(1000)>f(1001) f(1/(2000))>f(1/(2001)) f(x-1)>f(x-2) f(2x-3)>f(2x)

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 "____" .

If f(x+1)+f(x-1)=2f(x)a n df(0),=0, then f(n),n in N , is nf(1) (b) {f(1)}^n (c) 0 (d) none of these

Prove that: sum_(k=1)^(100)sin(k x)cos(101-k)x=50"sin"(101 x)

If f(x)=(1+x)^n, then the value of f(0)+f^(prime)(0)+(f^('')(0))/(2!)+(f^(''')(0))/(3!)+......(f^n(0))/(n !)dot

The coefficient of x^(50) in (x+^(101)C_(0))(x+^(101)C_(1)).....(x+^(101)C_(50)) is

If f(x)=x^n ,f(1)+(f^1(1))/1+(f^2(1))/(2!)+(f^n(1))/(n !),w h e r ef^r(x) denotes the rth order derivative of f(x) with respect to x , is

If alpha, beta are the roots of the equation x^(2)-3 x-15=0 , and f(n)=alpha^(n)+beta^(n) , then (f(8)-3 f(7)+f(6))/(2 f(6)) is equal to