Alerts
Wishlist
Cart
Sign In
Categories
Current Affairs & GK
Current Affairs
Show All Current Affairs & GK
eBooks
General Aptitude
Arithmetic Aptitude
Data Interpretation
Show All General Aptitude
General Knowledge
Basic General Knowledge
General Science
Show All General Knowledge
Medical Science
Anatomy
Biochemical Engineering
Biochemistry
Biotechnology
Microbiology
Show All Medical Science
Technical
Database
Digital Electronics
Electronics
Networking
Show All Technical
Verbal and Reasoning
Logical Reasoning
Verbal Ability
Verbal Reasoning
Show All Verbal and Reasoning
›
What is the coefficient of x^2 in the expansion of (x + 4)^5?
What is the coefficient of x^2 in the expansion of (x + 4)^5?
Expand All
Collapse All
Practice Questions
1 question
Q1
What is the coefficient of x^2 in the expansion of (x + 4)^5?
80
100
120
160
Show Solution
Copy
The coefficient of x^2 is C(5,2) * 4^3 = 10 * 64 = 640.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the coefficient of x^2 in the expansion of (x + 4)^5?
Solution:
The coefficient of x^2 is C(5,2) * 4^3 = 10 * 64 = 640.
Steps: 9
Show Steps
Step 1: Identify the expression we need to expand, which is (x + 4)^5.
Step 2: Understand that we want the coefficient of x^2 in this expansion.
Step 3: Use the Binomial Theorem, which states that (a + b)^n = Σ (C(n, k) * a^(n-k) * b^k) for k = 0 to n.
Step 4: In our case, a = x, b = 4, and n = 5.
Step 5: We need to find the term where x is raised to the power of 2, which means we need k = 3 (because 5 - 2 = 3).
Step 6: Calculate the binomial coefficient C(5, 2), which is the number of ways to choose 2 items from 5. This is equal to 5! / (2! * (5-2)!) = 10.
Step 7: Calculate 4^3, which is 4 * 4 * 4 = 64.
Step 8: Multiply the coefficient C(5, 2) by 4^3: 10 * 64 = 640.
Step 9: Conclude that the coefficient of x^2 in the expansion of (x + 4)^5 is 640.
Related Questions
W
What is the coefficient of x^4 in the expansion of (x + 1)^8? (2020)
Question: What is the coefficient of x^4 in the expansion of (x + 1)^8? (2020)Options: 7056288Correc..
W
What is the 3rd term in the expansion of (x + 3)^7? (2023)
Question: What is the 3rd term in the expansion of (x + 3)^7? (2023)Options: 1894417291024Correct An..
F
Find the value of 5! (5 factorial). (2019)
Question: Find the value of 5! (5 factorial). (2019)Options: 12010015090Correct Answer: 120Solution:..
C
Calculate the term independent of x in the expansion of (2x - 3)^5.
Question: Calculate the term independent of x in the expansion of (2x - 3)^5.Options: -243024381Corr..
W
What is the value of (3 + 5) × (2 - 1)? (2020)
Question: What is the value of (3 + 5) × (2 - 1)? (2020)Options: 816106Correct Answer: 8Solution: (3..
‹
Biology (School & UG)
Chemistry (School & UG)
Civil Engineering
Commerce & Accountancy
Computer Science & IT
Current Affairs & GK
Data Structures & Algorithms
eBooks
Electrical & Electronics Engineering
English (School)
General Aptitude
General Knowledge
General Knowledge & Current Affairs
Languages & Literature
Law & Legal Studies
Major Competitive Exams
Mathematics (School)
Mechanical Engineering
Medical Science
Physics (School & Undergraduate)
Quantitative Aptitude & Reasoning
Social Science (School)
Technical
Verbal and Reasoning
Vocational & Skill Development
›
Soulshift Feedback
×
On a scale of 0–10, how likely are you to recommend
The Soulshift Academy
?
0
1
2
3
4
5
6
7
8
9
10
Not likely
Very likely
✕
↑
