Duration: 0:00

15 views

0

Which of the following statement(s) is(are) correct?
\( \mathrm{P} \)
(A) The coefficient of \( x^{2} \) in the expansion of \( \sum_{r=0}^{100}{ }^{100} C_{r}(x-4)^{100-r} \quad(5)^{r} \) is equal to 4950 .
W
(B) If the sixth term in the expansion of \( \left(x^{\frac{-8}{3}}+x^{2} \log _{10} x\right)^{8} \) is 5600 , then \( x \) is equal to 100 .
(C) Let \( A_{n}={ }^{n} C_{0}{ }^{n} C_{1}+{ }^{n} C_{1}{ }^{n} C_{2}+\ldots \ldots \ldots . .+{ }^{n} C_{n-1}{ }^{n} C_{n} \) and \( \frac{A_{n+1}}{A_{n}}=\frac{15}{4} \), then the sum of possible values of \( n \) is equal to 6 .
(D) If \( \mathrm{A}_{\mathrm{k}}=\frac{{ }^{n} C_{\mathrm{k}}}{{ }^{n} C_{k}+{ }^{n} C_{k+1}} \) and \( \sqrt[3]{\sum_{\mathrm{k}=0}^{\mathrm{n}-1} \mathrm{~A}_{\mathrm{k}}}=4 \), then \( \mathrm{n} \) is equal to 128 .
📲 PW App Link - https://bit.ly/YTAI_PWAP
🌐 PW Website - https://www.pw.live/