JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(\alpha, \beta(\alpha \neq \beta)\) be the values of m , for which the equations \(x+y+z=1 ; x+2 y+4 z=\mathrm{m}\) and \(x+4 y+10 z=m^2\) have infinitely many solutions. Then the value of \(\sum_{n=1}^{10}\left(n^\alpha+n^\beta\right)\) is equal to :
- A 3080
- B 560
- C 3410
- D 440
Answer & Solution
Correct Answer
(D) 440
Step-by-step Solution
Detailed explanation
\(\begin{aligned} \Delta & =\left|\begin{array}{llc} 1 & 1 & 1 \\ 1 & 2 & 4 \\ 1 & 4 & 10 \end{array}\right|=1(20-16)-1(10-4)+1(4-2) \\ & =4-6+2=0 \end{aligned}\) For infinite solutions…
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