If {\m} \in {\Z}^{+}, {\n}=2 {\m} and \int_{0}^{\frac{\pi}{2}} \sin ^{ {\m}} {\x} \cos ^{ {\n}} {\x} d {\x}= {\K}( {\m}) \int_{0}^{\frac{\pi}{2}} \sin ^{ {\m}} {\x} \dx, then \frac{2^{m-1}(m-1) !}{(2 m-1) !} K(m)=

Correct Answer is : 1m+21m+41m+r...13m

\frac{1}{m+2} \frac{1}{m+4} \frac{1}{m+r} . . . \frac{1}{3 m}

\frac{1}{2 m+2} \frac{1}{2 m+4} \cdots \frac{1}{3 m}

\frac{\pi}{2} \frac{1}{m+2} \frac{1}{m+4} \frac{1}{m+r} \cdots \frac{1}{3 m}

\frac{\pi}{2} \frac{1}{2 m+2} \frac{1}{2 m+4} \cdots \frac{1}{3 m}

AP EAPCET 17th May 2023 Shift 2 Solved Paper

Section: Mathematics

Question : 76 of 160

Marks: +1, -0

If m∈Z+,n=2m and

‌

∫

sin‌mxcosnxdx=K(m)‌

‌

∫

sin‌mx‌dx,

then ‌

2m−1(m−1)!

(2m−1)!

K(m)=

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