JEE Mains · Maths · STD 11 - 7. binomial theoram
Let \(\left( a + bx + cx ^2\right)^{10}=\sum \limits_{ i =0}^{20} p _{ i } x ^{ i }, a , b , c \in N\). If \(p _1=20\) and \(p _2=210\), then \(2( a + b + c )\) is equal to
- A \(8\)
- B \(12\)
- C \(15\)
- D \(6\)
Answer & Solution
Correct Answer
(B) \(12\)
Step-by-step Solution
Detailed explanation
\(\left(a+b x+c x^2\right)^{10}=\sum_{i=0}^{20} p_i x^i\) Coefficient of \(x^1=20\) \(20=\frac{10 !}{9 ! 1 !} \times a^9 \times b^1\) \(a^9 . b =2\) \(a=1, b=2\) Coefficient of \(x ^2=210\) \(210=\frac{10 !}{9 ! 1 !} \times a^9 \times c^1+\frac{10 !}{8 ! 2 !} \times a^8 b^2\)…
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