In ( 2 x + 3 y ) 12 = T 1 + ⋯ + T 13 , put x = 1/3 , y = 1/2 . Statement I: ∑ r = 1 12 sgn ( T r − T r + 1 ) = − 4 . Statement II: T 1 T 11 > T 12 > T 13 .

The consecutive term ratio is ( 13 − r ) ⋅ 9/ ( 4 r ) , giving maxima T 9 = T 10 . The sign sum is − 8 + 0 + 3 = − 5 , not -4.

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Mathematics - Binomial Theorem Question with Solution | TestHub

MathematicsBinomial TheoremSpecific TermsMedium2 minQB

MathematicsMediumsingle choice

In $(2 x + 3 y)^{12} = T_{1} + \dots + T_{13}$ , put $x = 1/3, y = 1/2$ . Statement I: $\sum_{r = 1}^{12} sgn (T_{r} - T_{r + 1}) = - 4$ . Statement II: $T_{1} < \dots < T_{8} < T_{9} = T_{10} > T_{11} > T_{12} > T_{13}$ .

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The consecutive term ratio is $(13 - r) \cdot 9/ (4 r)$ , giving maxima $T_{9} = T_{10}$ . The sign sum is $- 8 + 0 + 3 = - 5$ , not -4.

Stream:JEESubject:MathematicsTopic:Binomial TheoremSubtopic:Specific Terms

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