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 (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 a_(n+1)=1/(1-a_n) for n>=1 and a_3=a_1 . then find the value of (a_2001)^2001 .

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

The value of sum_(r=1)^(n+1)(sum_(k=1)^n "^k C_(r-1)) ( where r ,k ,n in N) is equal to a. 2^(n+1)-2 b. 2^(n+1)-1 c. 2^(n+1) d. none of these

The value of sum_(r=1)^n(-1)^(r+1)("^n C r)/(r+1) is equal to a. -1/(n+1) b. 1/n c. 1/(n+1) d. n/(n+1)

If y=(1+t a n A)(1-t a n B), where A-B=pi/4, then (y+1)^(y+1) is equal to 9 (b) 4 (c) 27 (d) 81

If f(1)=3,f^(prime)(1)=2,f''(1)=4,t h e n f^(-1)(3)= a. 1 b. -1/2 c. -2 d. none of these

If sum_(r=0)^nr/(^n C_r)=sum_(r=0)^n(n^2-3n+3)/(2.^n C_r) , then a. n=1 b. n=2 c. n=3 d. none of these

If Aa n dB are symmetric matrices of the same order and X=A B+B Aa n dY=A B-B A ,t h e n(X Y)^T is equal to X Y b. Y X c. -Y X d. none of these

if Aa n dB are squares matrices such that A^(2006)=Oa n dA B=A+B ,t h e n"det"(B) equals 0 b. 1 c. -1 d. none of these