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Binomial theorem

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Q. In the expansion of (2x - 3)^3, what is the coefficient of x?
  • A. -9
  • B. -18
  • C. -27
  • D. -6
Q. In the expansion of (2x - 3)^5, what is the coefficient of x^1?
  • A. -15
  • B. -30
  • C. 30
  • D. 15
Q. In the expansion of (2x - 3)^5, what is the coefficient of x^2?
  • A. -90
  • B. -120
  • C. -150
  • D. -180
Q. In the expansion of (2x - 3)^5, what is the coefficient of x^3?
  • A. -540
  • B. -720
  • C. -960
  • D. -1080
Q. In the expansion of (2x - 3)^5, what is the coefficient of x^4?
  • A. -90
  • B. -120
  • C. -150
  • D. -180
Q. In the expansion of (x + 1/x)^6, what is the coefficient of x^0?
  • A. 6
  • B. 15
  • C. 20
  • D. 30
Q. In the expansion of (x + 1/x)^8, what is the coefficient of x^4?
  • A. 70
  • B. 56
  • C. 28
  • D. 84
Q. In the expansion of (x + 2)^5, what is the coefficient of x^3?
  • A. 40
  • B. 60
  • C. 80
  • D. 100
Q. In the expansion of (x + 2)^6, what is the term containing x^4?
  • A. 240
  • B. 360
  • C. 720
  • D. 480
Q. In the expansion of (x + 2)^7, what is the term containing x^5?
  • A. 672
  • B. 6720
  • C. 67200
  • D. 672000
Q. In the expansion of (x + 5)^6, what is the coefficient of x^3?
  • A. 150
  • B. 200
  • C. 250
  • D. 300
Q. In the expansion of (x - 2)^6, what is the coefficient of x^4?
  • A. 15
  • B. 60
  • C. 90
  • D. 120
Q. In the expansion of (x - 2)^8, what is the coefficient of x^5?
  • A. -2240
  • B. -1280
  • C. -1120
  • D. -960
Q. What is the coefficient of x^0 in the expansion of (3x - 4)^5?
  • A. -1024
  • B. 243
  • C. -243
  • D. 1024
Q. What is the coefficient of x^0 in the expansion of (x + 5)^3?
  • A. 125
  • B. 100
  • C. 75
  • D. 50
Q. What is the coefficient of x^0 in the expansion of (x + 5)^5?
  • A. 3125
  • B. 625
  • C. 125
  • D. 25
Q. What is the coefficient of x^2 in the expansion of (3x - 4)^4?
  • A. 144
  • B. 216
  • C. 432
  • D. 576
Q. What is the coefficient of x^2 in the expansion of (x - 4)^6?
  • A. 240
  • B. 360
  • C. 480
  • D. 720
Q. What is the coefficient of x^3 in the expansion of (2x + 3)^5?
  • A. 90
  • B. 100
  • C. 120
  • D. 150
Q. What is the coefficient of x^4 in the expansion of (2x + 3)^6?
  • A. 540
  • B. 720
  • C. 810
  • D. 960
Q. What is the coefficient of x^4 in the expansion of (2x - 3)^5?
  • A. 240
  • B. 300
  • C. 360
  • D. 420
Q. What is the coefficient of x^4 in the expansion of (x + 1)^6?
  • A. 15
  • B. 20
  • C. 30
  • D. 35
Q. What is the coefficient of x^5 in the expansion of (x + 1/2)^10?
  • A. 252
  • B. 210
  • C. 120
  • D. 300
Q. What is the coefficient of x^5 in the expansion of (x + 2)^7?
  • A. 21
  • B. 42
  • C. 35
  • D. 28
Q. What is the coefficient of x^5 in the expansion of (x + 2)^8?
  • A. 672
  • B. 1280
  • C. 960
  • D. 720
Q. What is the coefficient of x^5 in the expansion of (x + 3)^8?
  • A. 1680
  • B. 1440
  • C. 1260
  • D. 1080
Q. What is the coefficient of x^6 in the expansion of (x + 5)^8?
  • A. 6720
  • B. 5600
  • C. 4480
  • D. 3360
Q. What is the middle term in the expansion of (x + 2)^8?
  • A. 128
  • B. 112
  • C. 256
  • D. 64
Q. What is the sum of the coefficients in the expansion of (2 + 3x)^4?
  • A. 81
  • B. 64
  • C. 100
  • D. 125
Q. What is the sum of the coefficients in the expansion of (x + 1)^5?
  • A. 5
  • B. 6
  • C. 31
  • D. 32
Showing 31 to 60 of 69 (3 Pages)

Binomial theorem MCQ & Objective Questions

The Binomial theorem is a fundamental concept in algebra that plays a crucial role in various examinations. Understanding this theorem not only enhances your mathematical skills but also boosts your confidence in solving complex problems. Practicing MCQs and objective questions related to the Binomial theorem is essential for effective exam preparation, as it helps you identify important questions and reinforces your grasp of the topic.

What You Will Practise Here

  • Understanding the Binomial theorem and its applications
  • Deriving the Binomial expansion formula
  • Identifying coefficients using Pascal's Triangle
  • Solving problems involving positive and negative integer exponents
  • Exploring the concept of binomial coefficients
  • Applying the theorem in real-life scenarios
  • Working through previous years' exam questions

Exam Relevance

The Binomial theorem is a significant topic in various educational boards, including CBSE and State Boards, as well as competitive exams like NEET and JEE. Questions on this topic often appear in multiple-choice formats, testing students' understanding of the theorem's principles and applications. Common question patterns include finding specific coefficients, expanding binomials, and solving related word problems, making it vital for students to master this area for better performance in exams.

Common Mistakes Students Make

  • Confusing the Binomial theorem with other algebraic identities
  • Misapplying the formula when dealing with negative exponents
  • Overlooking the importance of binomial coefficients
  • Failing to simplify expressions correctly after expansion

FAQs

Question: What is the Binomial theorem?
Answer: The Binomial theorem provides a formula for the expansion of powers of a binomial, expressed as (a + b)^n.

Question: How can I find the coefficients in the expansion?
Answer: Coefficients can be found using the formula C(n, k) = n! / (k!(n-k)!), where C(n, k) represents the binomial coefficient.

Now is the time to strengthen your understanding of the Binomial theorem! Dive into our practice MCQs and test your knowledge to excel in your exams.

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