Mathematics · 2014
JEE Main · 19 April 2014, Shift 1 · Q65
If Δ_r= |r, 2 r-1, 3 r-2; n/2, n-1, a; 1/2 n(n-1), (n-1)^2, 1/2(n-1)(3 n+4)|, then the value of Σ_r =1^n -1 Δ_r:
If
$$\Delta_r=\left|\begin{array}{ccc}
r & 2 r-1 & 3 r-2 \\
\frac{n}{2} & n-1 & a \\
\frac{1}{2} n(n-1) & (n-1)^2 & \frac{1}{2}(n-1)(3 n+4)
\end{array}\right|,
$$
then the value of $\displaystyle \sum_{\mathrm{r}=1}^{\mathrm{n}-1} \Delta_{\mathrm{r}}$ :
Official answer
(4)
is independent of both a and n.
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JEE Main 2014 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.