If `("lim")_(xvec2)(x^n-2^n)/(x-2)=80a m dm in N ,t h e nfin dt h ev a l u eofndot`

If lim_(x to 2) (X^(n) - 2^(n))/(x - 2) = 448 and n in N , find n

IfI_n=int_x^pix^nsinx dx ,t h e n fin d t h e v a l u eof I_5+20 I_3dot

If L=(lim)_(x->oo)(logx^n-[x])/([x]),\ w h e r e\ n in N ,\ t h e n-2L=

find n in N, if lim_(x rarr2)(x^(n)-2^(n))/(x-2)=80

Each question contains statements given in two columns which have to be matched. Statements a,b,c,d in column I have to be matched with statements p,q,r,s in column II. If the correct match are a-p, a-s, b-r, c-p, c-q, and d-s, then the correctly bubbled 4 x 4 matrix should be as follows: fig Column I, Column II If L=""("lim")_(xvec1)((7-x)3-2)/((x+1)),t h e n12 L= , p. -2 If L=""("lim")_(xvecpi/4)(tan^3x-tanx)/(cos(x+pi/4)),t h e n-L/4= , q. 2 If L=""("lim")_(xvec1)((2x-3)(sqrt(x)-1))/(2x^2+x-3),t h e n20 L= , r. 1 If L=""("lim")_(xvecoo)(logx^n-[x])/([x]),w h e r en in N ,([x] denotes greatest integer less than or equal to x),t h e n-2L= , s. -1

lim_(x rarr2)((1+x)^(n)-3^(n))/(x-2)=n*3^(n-1)

(lim)_(x->oo)(logx^n-[x])/([x]),\ n in N ,\ ([x]\ d e not e s\ t h e\ in t ege r\ l e s stanor\ e q u a l\ to\ x)\

If |x^n x^(n+2)x^(2n)1x^a a x^(n+5)x^(a+6)x^(2n+5)|=0,AAx in R ,w h e r en in N , then value of a is n b. n-1 c. n+1 d. none of these