જો $m, l, r, s, n$ એવા પૂર્ણાંકો હોય કે જેથી $9 > m > l > s > n > r > 2$ અને $\int_{-2 \pi}^{2 \pi} \sin ^m x \cos ^n x \, dx = 4 \int_0^\pi \sin ^m x \cos ^n x \, dx$, $\int_{-\pi}^\pi \sin ^r x \cos ^s x \, dx = 4 \int_0^{\pi / 2} \sin ^r x \cos ^s x \, dx$ અને $\int_{-\pi / 2}^{\pi / 2} \sin ^l x \cos ^m x \, dx = 0$ હોય, તો નીચેનામાંથી કયું સાચું છે?

  • A
    $(s-2)(l-2) = mr$
  • B
    $(s-2)(l+2) = rm + 5$
  • C
    $(s-2)(s+2) = ln - 3$
  • D
    $(l-2)(l+2) = ms - 5$

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