INTEGRATION BY PARTS

The microelement which is an integral part of electron carrier that transfers electrons electrons from cyt b-f complex to PS I is also a component of

If in a positive integer such that If a number a=p+f whre p is an integer and 0ltflt1 . Here p is called the integral part of a and f its fractional part. Let n in N and (sqrt(3)+1)^(2n)=p+f , where p is the integral part and 0ltflt1 . On the basis of bove informationi answer teh following question: The integral part p of (sqrt(3)+1)^(2n) is (A) an even number for al n epsilon N (B) an odd number for all nepsilon N (C) anodd or even number according as n is odd or even (D) an even or odd nuber according as n is odd or even

If in a positive integer such that If a number a=p+f whre p is an integer and 0ltflt1 . Here p is called the integral part of a and f its fractional part. Let n in N and (sqrt(3)+1)^(2n)=p+f , where p is the integral part and 0ltflt1 . On the basis of bove informationi answer teh following question: f^2+(p-1)f+4^n= (A) p (B) -p (C) 2p (D) -2p

If three successive terms of as G.P. with commonratio rgt1 form the sides of a triangle and [r] denotes the integral part of x the [r]+[-r]= (A) 0 (B) 1 (C) -1 (D) none of these

int_0^2 x^3[1+cos((pix)/2)]dx , where [x] denotes the integral part of x , is equal to (A) 1/2 (B) 1/4 (C) 0 (D) none of these

int_0^1 [x^2-x+1]dx , where [x] denotes the integral part of x , is (A) 1 (B) 0 (C) 2 (D) none of these

If three successive terms of as G.P. with commonratio rgt1 form the sides of a triangle and [r] denotes the integral part of x the [r]+[-r]= (A) 0 (B) 1 (C) -1 (D) none of these

If [x] denotes the integral part of x and k=sin^-1 ((1+t^2)/(2t))gt0 then integral valueof alpha for which the equation (x-[k])(x+alpha)-1=0 has integral roots is (A) 1 (B) 2 (C) 4 (D) none of these

If [x] denotes the integral part of x and m= [|x|/(1+x^2)],n= integral values of 1/(2-sin3x) then (A) m!=n (B) mgtn (C) m+n=0 (D) n^m=0

Consider the binomial expansion of R = (1 + 2x )^(n) = I = f , where I is the integral part of R and f is the fractional part of R , n in N . Also , the sum of coefficient of R is 2187. If ith term is the geratest term for x= 1/3, then i equal