Let m, n, p, q be four positive integers. If \int_{0}^{2 \pi} \sin ^m x \cos ^n x \dx=4 \int_{0}^{\pi \/ 2} \sin ^m x \cos ^n x \dx \int_{0}^{2 \pi} \sin ^p x \cos ^n x \dx=0 \int_{0}^{\pi} \sin ^p x \cos ^q x \dx=0, a=m+n+p \text{ and } b=m+n+q, \text{ then }

Correct Answer is : Both a and b are odd numbers

a is even number and b is odd number

a is odd number and b is even number

TG EAMCET 2 May 2025 Shift 2 Paper

Question : 77 of 160

Marks: +1, -0

Let m,n,p,q be four positive integers.
If ‌

2π

∫

sin‌mxcosnx‌dx=4‌

π∕2

∫

sin‌mxcosnx‌dx‌

2π

∫

sin‌pxcosnx‌dx=0
‌

∫

sin‌pxcosqx‌dx=0,a=m+n+p‌ and ‌b=m+n+q,‌ then ‌

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