If m is a positive integer and ∆ r = | array ccc 2 r-1 & ^ m C_ r & 1 m^ 2 -1 & 2^ m &…
Mathematics · JEE Advanced · NTA Exams — Matrices and Determinants
If m is a positive integer and
∆r =\[\left|\begin{array}{ccc} 2 r-1 & { }^{m} C_{r} & 1 \\ m^{2}-1 & 2^{m} & m+1 \\ \sin ^{2}\left(m^{2}\right) & \sin ^{2}(m) & \sin ^{2}(m+1) \end{array}\right|\] Then the value of \(\sum_{r=0}^{m} \Delta_{r}\) is
∆r =\[\left|\begin{array}{ccc} 2 r-1 & { }^{m} C_{r} & 1 \\ m^{2}-1 & 2^{m} & m+1 \\ \sin ^{2}\left(m^{2}\right) & \sin ^{2}(m) & \sin ^{2}(m+1) \end{array}\right|\] Then the value of \(\sum_{r=0}^{m} \Delta_{r}\) is
- 0
- m2 – 1
- 2m
- 2m sin2 (2m)
Answer
(A) 0
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