IPMAT Indore 2021Algebra > Medium9:59:59:55:95:95:93:53:53:55:35:35:3✅ Correct Option: 1Related questions:Let a1,a2,a3a_{1}, a_{2}, a_{3}a1,a2,a3 be three distinct real numbers in geometric progression. If the equations a1x2+2a2x+a3=0a_{1} x ^ 2 + 2a_{2}x + a_{3} = 0a1x2+2a2x+a3=0 and b1x2+2b2x+b3=0b_{1} x ^ 2 + 2b_{2}x + b_{3} = 0b1x2+2b2x+b3=0 have a common root, then which of the following is necessarily true?The 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 isIf (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 is