Binomial Theorem and Bayes Theorem 10 1. Find the binomial expansion of the expression 2. Which member of the binomial expansion of the algebraic expression 2x- contains x* ? 3. Find two intermediate members of the binomial expansion of the expression (x+y)³. 4. Find intermediate members of the binomial expansion of the expression (x+y)+ 5. Find: a) The fifth member of the binomial expansion of expression (x - y) b) The ninth member of the binomial expansion of expression 6. Find the intermediate member of the binomial expansion of the expression (√x-1). X 2√x 12 7. Which member of the binomial expansion of the algebraic expression √²+√x contains x²? 8. For what value of x the fifth member of the binomial expansion of the algebraic 10 1 expression equals to the number 105 ?

Binomial Theorem and Bayes Theorem 10 1. Find the binomial expansion of the expression 2. Which member of the binomial expansion of the algebraic expression 2x- contains x* ? 3. Find two intermediate members of the binomial expansion of the expression (x+y)³. 4. Find intermediate members of the binomial expansion of the expression (x+y)+ 5. Find: a) The fifth member of the binomial expansion of expression (x - y) b) The ninth member of the binomial expansion of expression 6. Find the intermediate member of the binomial expansion of the expression (√x-1). X 2√x 12 7. Which member of the binomial expansion of the algebraic expression √²+√x contains x²? 8. For what value of x the fifth member of the binomial expansion of the algebraic 10 1 expression equals to the number 105 ?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Answer no. 2,3 and 4 show sollution if there is

Exercises
Binomial Theorem and Bayes Theorem
10
^{(x-1)²⁰.
1. Find the binomial expansion of the expression x-
2. Which member of the binomial expansion of the algebraic expression 2x-
contains x* ?
3. Find two intermediate members of the binomial expansion of the expression
(x+y)³.
4. Find intermediate members of the binomial expansion of the expression (x+y)+
5. Find:
a) The fifth member of the binomial expansion of expression (x−y)
1
b) The ninth member of the binomial expansion of expression x²
6. Find the intermediate member of the binomial expansion of the expression
(√x-1).
X
7. Which member of the binomial expansion of the algebraic expression
12
14
X
12
(√²+√x¹² contains x²?
8. For what value of x the fifth member of the binomial expansion of the algebraic
10
1 1
expression
equals to the number 105 ?
2√x 2
9. Find out which member of the binomial expansion of the algebraic expression
8
1
(x²-
equals to the number 70.
10. Find out which member of the binomial expansion of the algebraic expression
is the product of the coeficient and of the unknown √x.
11. A particular study showed that 12% of men will likely develop colon cancer. A
man with colon cancer has a 95% chance of a positive test result from a medical
screening exam. A man without colon cancer has a 6% chance of getting a false
positive test result. What is the probability that a man has cancer given that he
has a positive test result?
12. In a particular pain clinic, 10% of patients are prescribed narcotic pain killers.
Overall, 5% of the clinic's patients are addicted to narcotics (including pain killers
and illegal substances). Out of all the people prescribed pain pills, 8% are
addicts. If a patient is an addict, what is the probability that they will be
prescribed pain pills?

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