C030C1030-C130C1130+……C2030C3030=?
C1130
C1060
C1030
C5565
Explanation for the correct option:
Step 1.Write expansion of 1+x30 and x-130:
⇒(1+x)30=C030+C130x+C230x2+.....+C2030x20+...C3030x30 …....(1)
⇒(x−1)30=C030x30−C130x29+....+C1030x20−C1130x19+C1230x18+...C3030x0 ….....(2)
Step2. Multiply equation (1) and (2):
⇒(x2−1)30=(C030+C130x+C230x2+.....)×(C030x30−C130x29+....)
Step 3. Equate the coefficients of x20 on both sides:
⇒C030C1030−C130C1130+C230C1230−...+C2030C3030=Cr30x2r
=C1030 ∵2r=20
Hence, Option ‘C’ is Correct.
The value of 30C030C10 - 30C130C11 + 30C230C12 - .......... + 30C2030C30 is
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