IPMAT Indore 2025Algebra > Medium-48-242448✅ Correct Option: 2Related questions:If (1+x−2x2)6=A0+∑r=112Arxr(1 + x - 2x^2)^6 = A_0 + \sum_{r=1}^{12} A_r x^r(1+x−2x2)6=A0+∑r=112Arxr, then the value of A2+A4+A6+⋯+A12A_2 + A_4 + A_6 + \cdots + A_{12}A2+A4+A6+⋯+A12 isThe terms of a geometric progression are real and positive. If the ppp-th term of the progression is qqq and the qqq-th term is ppp, then the logarithm of the first term isIt is given that the sequence {xnx_nxn} satisfies x1=0,xn+1=xn+1+2√(1+xn)x_1 = 0, x_{n+1} = x_n + 1 + 2√(1+x_n)x1=0,xn+1=xn+1+2√(1+xn) for n=1,2,...n = 1,2,...n=1,2,... Then x31x_{31}x31 is _______