1.

The number of ordered 5-tuple `(u, v, w, x, y)` where `(u, v, w, x, y in [1, 11])` which satisfy the inequality `2^(sin^2u+3cos^2v).3^(sin^2w+cos^2x).5^(cos^2y)>=720` isA. 216B. 246C. 432D. 432

Answer» Correct Answer - C
Given `2^(sin^(2)u+3cos^(2)v).3^(sin^(2)w + cos^(2)x).5^(cos^(2)y)ge 2^(4).3^(2).5^(1)`
The equality holds when `sin^(2)u=sin^(2)w=cos^(2)v=cos^(2)x`
`=cos^(2)y=1`
`therefore u,w in {(pi)/(2),(3pi)/(2),(5pi)/(2),(7pi)/(2)}` and `x, y, v in {pi, 2pi, 3pi}`
Number of ordered 5-tuples `=4^(2)xx3^(3)=432`


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