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Pascal's triangle row 6 (corresponding to $(a+b)^6$) is
A$1, 5, 10, 10, 5, 1$
B$1, 6, 15, 20, 15, 6, 1$
C$1, 6, 12, 20, 12, 6, 1$
D$1, 6, 15, 15, 6, 1$
Answer & Solution
Correct answer: B. $1, 6, 15, 20, 15, 6, 1$
1. Pascal's triangle: each entry is the sum of the two entries directly above it.
2. Row 0: $1$. Row 1: $1, 1$. Row 2: $1, 2, 1$. Row 3: $1, 3, 3, 1$. Row 4: $1, 4, 6, 4, 1$. Row 5: $1, 5, 10, 10, 5, 1$. Row 6: $1, 6, 15, 20, 15, 6, 1$.
3. Confirm via $\binom{6}{r}$ for $r = 0, \ldots, 6$: $1, 6, 15, 20, 15, 6, 1$.
4. Option A is row 5. Option C has $\binom{6}{2} = 12$ (wrong — should be 15). Option D is missing the middle term.
_Source: NCERT Class 11 Mathematics, Ch 7, §7.2 (Pascal's Triangle), p. 2–3._
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