The correct option is E 65
limx→0(109sin9xsin10x)(87sin7xsin8x)(65sin5xsin6x)(43sin3xsin4x)(sinxsin2x)
=limx→0⎛⎜
⎜
⎜⎝sin9x9x⋅1sin10x10x⎞⎟
⎟
⎟⎠⎛⎜
⎜
⎜⎝sin7x7x⋅1sin8x8x⎞⎟
⎟
⎟⎠⎛⎜
⎜
⎜⎝sin5x5x⋅1sin6x6x⎞⎟
⎟
⎟⎠⎛⎜
⎜
⎜⎝sin3x3x⋅1sin4x4x⎞⎟
⎟
⎟⎠⎛⎜
⎜
⎜⎝sinxx1sin2x2x⋅12⎞⎟
⎟
⎟⎠
=12 [∵limf(x)→0sinf(x)f(x)=1]