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Question

The number of values of r satisfying the equation 39C3r−1 − 39Cr2 = 39Cr2−1 − 39C3r is:

A
1
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B
2
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C
3
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D
4
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Solution

The correct option is C 2
39C3r139Cr2=39Cr2139C3r
As nCr+nCr+1=n+1Cr+1
So, 39C3r139Cr=39Cr2139C3r2
40C3r=40Cr2
here either 3rr2 or 403r=r2
So, for 3r=r2 r2+3r40=0
r=3,0 r=5,8
As r can't be 8 and 0 because 39C3r1 is not define.
Hence, the answer is two values of r=3,5.

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