Let `a in (0,1]` satisfies the equation `a^(2008)-2a+1=0` and `S=1+a+a^2+.....+a^2007` Then sum of all possible values of S is a. `2010` b. `2009` c. `2008` d. `2`

Let a,b,c,d be real numbers such that |a-b|=2, |b-c|=3, |c-d|=4 Then the sum of all possible values of |a-d|=

If the system of equations x-k y-z=0, k x-y-z=0,x+y-z=0 has a nonzero solution, then the possible value of k are a. -1,2 b. 1,2 c. 0,1 d. -1,1

The real value of a for which the value of m satisfying the equation (a^2-1)m^2-(2a-3)m+a=0 given the slope of a line parallel to the y-axis is(a) 3/2 (b) 0 (c) 1 (d) +-1

The sum of real roots of the equation |x-2|^2+|x-2|-2=0 is (A) 4 (B) 1 (C) 2 (D) -2

A is a 2xx2 matrix such that A[[1],[-1]]=[[-1],[ 2]] and A^2[[1],[-1]]=[[1],[ 0]]dot The sum of the elements of A is a. -1 b. 0 c. 2 d. 5

Let r ,s ,a n dt be the roots of equation 8x^3+1001 x+2008=0. Then find the value of (r+s)^3 +(s+t)^3+(t+r)^3 .

Sum of roots of the equation x^4-2x^2sin^2(pix/2)+1=0 is 0 (b) 2 (c) 1 (d) 3

Given that a,c are the roots of the equation px^2-3x+2=0 and b,d are the roots of the equation qx^2-4x+2=0 , find the values of p and q such that 1/a,1/b,1/c and 1/d are in A.P.

Consider two functions y=f(x) and y=g(x) defined as f(x)= {[a x^2 +b, 0lexle1],[ bx + 2b, 1ltxle3],[(a-1)x + 2c - 3 , 3ltxle4]} And g(x)={[c x + d , 0le x le 2],[a x+3-c ,2ltxlt3],[x^2+b+1,3lexle4]} Let f be differentiable at x=1a n dg(x) be continuous at x=3. If the roots of the quadratic equation x^2+(a+b+c)alphax+49(k+kalpha)=0 are real distinct for all values of alpha then possible value of k will be a) k in (-1,0) b). k in (oo,0) c). k in (1,5) d). k in (-1,1)

If the equation 2^(2x)+a*2^(x+1)+a+1=0 has roots of opposite sign, then the exhaustive set of real values of a is (a)(−∞,0) (b)(−1,−2/3) (c)(−∞,−2/3) (d)(−1,∞)