If `(x^2+x+1)/(1-x)=a_0+a_1x+a_2x^2+ ,t h e nsum_(r=1)^(50)a_r` is equal to `148` b. `146` c. `149` d. none of these

If (x^(2)+x+1)/(1-x) = a_(0) + a_(1)x+a_(2)x^(2)+"…." , the b sum_(r=1)^(50) a_(r) equal to

If b_(n+1)=1/(1-b_n)forngeq1a n db_1=b_3, t h e nsum_(r=1)^(2001)b r^ 2001 is equal to 2001 b. -2001 c. 0 d. none of these

If (1+2x+3x^2)^(10)=a_0+a_1x+a_2x^2++a_(20)x^(20),t h e na_1 equals 10 b. 20 c. 210 d. none of these

sum_(r=0)^(300)a_r x^r=(1+x+x^2+x^3)^(100)dot If a=sum_(r=0)^(300)a_r ,t h e nsum_(r=0)^(300)r a_r is equal to 300 a b. 100 a c. 150 a d. 75 a

Let f(x)=a_0+a_1x+a_2x^2++a_n x^n+ and (f(x))/(1-x)=b_0+b_1x+b_2x^2++b_n x^n+ , then b_n+b_(n-1)=a_n b. b_n-b_(n-1)=a_n c. b_n//b_(n-1)=a_n d. none of these

If f(x)=int_0^1(dt)/(1+|x-t|) ,then f^(prime)(1/2) is equal to (a)0 (b) 1/2 (c) 1 (d) none of these

If (1-x)^(-n)=a_0+a_1x+a_2x^2++a_r x^r+ ,t h e na_0+a_1+a_2++a_r is equal to (a) (n(n+1)(n+2)(n+r))/(r !) (b) ((n+1)(n+2)(n+r))/(r !) (c) (n(n+1)(n+2)(n+r-1))/(r !) (d)none of these

If x_1=2tan^(-1)((1+x)/(1-x)),x_2=sin^(-1)((1-x^2)/(1+x^2)) , where x in (0,1), then x_1+x_2 is equal to 0 (b) 2pi (c) pi (d) none of these

lim_(x -> oo)(x(log(x)^3)/(1+x+x^2) equals 0 (b) -1 (c) 1 (d) none of these