If `(sqrt(2n^2+n)-lambdasqrt(2n^2-n))=1/(sqrt(2))` (where `lambda` is real number),then

Let [x] represent the greatest integer less than or equal to x If [sqrt(n^(2)+lambda)]=[sqrt(n^(2)+1)]+2 ,where lambda,n in N, then lambda can assume (a) 2n+4 different values (b)2n+5 different values (c)2n+3 different values (d)2n+6 different values

Let [x] represent the greatest integer less than or equal to x If [ sqrt(n^2+lambda)]=[sqrt(n^2+1)]+2 , where lambda,n in N , then lambda can assume (a) 2n+4 different values (b) 2n+5 different values (c) 2n+3 different values (d) 2n+6 different values

Let [x] represent the greatest integer less than or equal to x If [ sqrt(n^2+lambda)]=[sqrt(n^2+1)]+2 , where lambda,n in N , then lambda can assume (a) 2n+4 different values (b) 2n+5 different values (c) 2n+3 different values (d) 2n+6 different values

Let [x] represent the greatest integer less than or equal to x If [ sqrt(n^2+lambda)]=[sqrt(n^2+1)]+2 , where lambda,n in N , then lambda can assume (a) 2n+4 different values (b) 2n+5 different values (c) 2n+3 different values (d) 2n+6 different values

Let I_(n)=int(x^(n))/(sqrt(x^(2)+2x+5))dx then I_(n)=(x^(m-1))/(n)sqrt(x^(2)+2x+5)-lambda I_(n-1)-mu I_(n-2) where lambda,mu and m' are involving n' then

lim_(n rarr4)(sqrt(2n+1)-3)/(sqrt(n-1)-sqrt(2))

lim_(n->oo) ((sqrt(n^2+n)-1)/n)^(2sqrt(n^2+n)-1)

int_(2)^(4) (3x^(2)+1)/((x^(2)-1)^(3))dx = (lambda)/(n^(2)) where lambda, n in N and gcd(lambda,n) = 1 , then find the value of lambda + n