IPMAT IndoreAlgebra > Hard-343026-38✅ Correct Option: 1Related questions:IPMAT Indore 2019If (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 isIPMAT Indore 2021The sum up to 101010 terms of the series 1⋅3+5⋅7+9⋅11+...1 \cdot 3 + 5 \cdot 7 + 9 \cdot 11 + ...1⋅3+5⋅7+9⋅11+... isIPMAT Indore 2024The 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 is