JEE Exam  >  JEE Questions  >  The number of dissimilar terms in the expansi... Start Learning for Free
The number of dissimilar terms in the expansion of (a+b)n is n + 1, therefore number of dissimilar terms in the expansion of (a+b+c)12 is
  • a)
    91
  • b)
    78
  • c)
    39
  • d)
    13
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The number of dissimilar terms in the expansion of(a+b)nis n + 1, ther...
To find the number of dissimilar terms in the expansion of (a + b)^n, we can use the concept of binomial coefficients. The binomial coefficient, denoted by C(n, r), represents the number of ways to choose r items from a set of n items without regard to their order.

In the expansion of (a + b)^n, the power of a starts from n and decreases by 1 with each term, while the power of b starts from 0 and increases by 1 with each term. The sum of the powers of a and b in each term is always n.

Now, let's consider the expansion of (a + b + c)^12.

**Step 1: Determine the number of terms in the expansion**
The number of terms in the expansion of (a + b + c)^12 can be found using the formula (n + 1), where n is the power of the binomial.

Number of terms = (12 + 1) = 13

**Step 2: Determine the powers of a, b, and c in each term**
In the expansion of (a + b + c)^12, the powers of a, b, and c in each term will be non-negative integers that satisfy the condition a + b + c = 12.

One way to determine the powers is to consider all possible combinations of powers that add up to 12. We can use the concept of binomial coefficients to find these combinations.

For example, the term a^2b^3c^7 can be represented as C(12, 2) * C(10, 3) * C(7, 7), where C(12, 2) represents the number of ways to choose 2 items from a set of 12 items, C(10, 3) represents the number of ways to choose 3 items from a set of 10 items, and C(7, 7) represents the number of ways to choose 7 items from a set of 7 items.

**Step 3: Calculate the number of dissimilar terms**
To determine the number of dissimilar terms, we need to count the number of unique combinations of powers.

In the expansion of (a + b + c)^12, there are 13 terms. Each term corresponds to a unique combination of powers of a, b, and c. Therefore, the number of dissimilar terms is 13.

Hence, the correct answer is option A) 91.
Explore Courses for JEE exam
The number of dissimilar terms in the expansion of(a+b)nis n + 1, therefore number of dissimilar terms in the expansion of(a+b+c)12 isa)91b)78c)39d)13Correct answer is option 'A'. Can you explain this answer?
Question Description
The number of dissimilar terms in the expansion of(a+b)nis n + 1, therefore number of dissimilar terms in the expansion of(a+b+c)12 isa)91b)78c)39d)13Correct answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The number of dissimilar terms in the expansion of(a+b)nis n + 1, therefore number of dissimilar terms in the expansion of(a+b+c)12 isa)91b)78c)39d)13Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of dissimilar terms in the expansion of(a+b)nis n + 1, therefore number of dissimilar terms in the expansion of(a+b+c)12 isa)91b)78c)39d)13Correct answer is option 'A'. Can you explain this answer?.
Solutions for The number of dissimilar terms in the expansion of(a+b)nis n + 1, therefore number of dissimilar terms in the expansion of(a+b+c)12 isa)91b)78c)39d)13Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of The number of dissimilar terms in the expansion of(a+b)nis n + 1, therefore number of dissimilar terms in the expansion of(a+b+c)12 isa)91b)78c)39d)13Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of The number of dissimilar terms in the expansion of(a+b)nis n + 1, therefore number of dissimilar terms in the expansion of(a+b+c)12 isa)91b)78c)39d)13Correct answer is option 'A'. Can you explain this answer?, a detailed solution for The number of dissimilar terms in the expansion of(a+b)nis n + 1, therefore number of dissimilar terms in the expansion of(a+b+c)12 isa)91b)78c)39d)13Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of The number of dissimilar terms in the expansion of(a+b)nis n + 1, therefore number of dissimilar terms in the expansion of(a+b+c)12 isa)91b)78c)39d)13Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice The number of dissimilar terms in the expansion of(a+b)nis n + 1, therefore number of dissimilar terms in the expansion of(a+b+c)12 isa)91b)78c)39d)13Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice JEE tests.
Explore Courses for JEE exam

Top Courses for JEE

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev