AP EAMCET · Maths · Permutation Combination
Choose the correct option regarding the following statements
1. \(C_0+C_2+C_4+\ldots+C_n=2^{n-1}\), if \(n\) is even
2. \(C_1+C_3+C_5+\ldots+C_{n-1}=2^{n-1}\), if \(n\) is even
- A 1 is true, 2 is false
- B 1 is false, 2 is true
- C Both 1 and 2 are false
- D Both 1 and 2 are true
Answer & Solution
Correct Answer
(D) Both 1 and 2 are true
Step-by-step Solution
Detailed explanation
Since, \((1+x)^n=C_0+C_1 x+C_2 x^2+C_3 x^3+\ldots \ldots+C_n x^n\) On putting \(x=1\) and \(x=-1\) respectively, we get \(\begin{aligned} 2^n & =C_0+C_1+C_2+C_3+\ldots \ldots+C_n \\ 0 & =C_0-C_1+C_2-C_3+\ldots \ldots+(-1)^n C_n \end{aligned}\) and…
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