JEE ADVANCED 2016 PAPER 1 OFFLINE
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The increasing order of atomic radii of the following group 13 elements is
The total number of distinct x \(\in\) R for which
\(\left| {\matrix{ x & {{x^2}} & {1 + {x^3}} \cr {2x} & {4{x^2}} & {1 + 8{x^3}} \cr {3x} & {9{x^2}} & {1 + 27{x^3}} \cr } } \right| = 10\) is ______________.
Let \(z = {{ - 1 + \sqrt 3 i} \over 2}\), where \(i = \sqrt { - 1}\), and r, s \(\in\) {1, 2, 3}. Let \(P = \left[ {\matrix{ {{{( - z)}^r}} & {{z^{2s}}} \cr {{z^{2s}}} & {{z^r}} \cr } } \right]\) and I be the identity matrix of order 2. Then the total number of ordered pairs (r, s) for which P2 = \(-\)I is ____________.