Top Strategies to Excel in JEE Main Binomial Theorem Mock Tests
Binomial Theorem and Its Simple Applications is a pivotal chapter in JEE Mathematics, covering binomial expansions, coefficients, term finding, and their practical uses. Strengthening your grasp on these concepts can significantly enhance your problem-solving speed for polynomial expressions and combinatorial questions. Take this exclusive mock test now to practice exam-level MCQs and solidify your preparation for JEE Main 2025!
Mock Test Instructions for the Binomial Theorem And Its Simple Applications (Mock Test-3):
- 20 questions from Binomial Theorem And Its Simple Applications
- Time limit: 20 minutes
- Single correct answer per question
- Correct answers appear in bold green after submission
How Can JEE Mock Tests Help You Master Binomial Theorem And Its Simple Applications?
- Strengthen your grasp of binomial expansions, term formulas, and coefficients through regular mock test practice.
- Identify your weak areas in advanced binomial questions by tracking your performance in timed mock tests.
- Improve speed in solving series and polynomial problems by simulating the actual exam environment.
- Build confidence by tackling application-based and PYQ-style problems on Binomial Theorem.
- Analyze feedback on your attempts for focused revision of key JEE Mathematics concepts.
Boost JEE 2025 Maths Scores with Expert-Designed Binomial Theorem Mock Tests
- Expose yourself to a variety of MCQs covering different facets of the Binomial Theorem.
- Refine your term identification and coefficient calculation techniques through practice sets.
- Master tricky applications, such as finding the greatest term or middle term, with targeted practice.
- Track time spent per question to improve accuracy and speed for the Binomial Theorem section.
- Utilize instant feedback to recognize and overcome common conceptual pitfalls in the chapter.
Subject-Wise Excellence: JEE Main Mock Test Links
| S.No. | Subject-Specific JEE Main Online Mock Tests |
|---|---|
| 1 | Online FREE Mock Test for JEE Main Chemistry |
| 2 | Online FREE Mock Test for JEE Main Maths |
| 3 | Online FREE Mock Test for JEE Main Physics |
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FAQs on Binomial Theorem Mock Test for JEE Main 2025-26: Practice & Solutions
1. What is the Binomial Theorem?
The Binomial Theorem is a mathematical formula that provides the expansion of powers of a binomial expression, such as (a + b)n. It states that for any positive integer n, the expansion is given by Σ [nCr × an–r × br], where nCr is the binomial coefficient.
2. State the general expansion of (a + b)n according to the Binomial Theorem.
The general expansion of (a + b)n using the Binomial Theorem is: (a + b)n = nC0 an + nC1 an-1b + nC2 an-2b2 + ... + nCn bn, where nCr denotes the binomial coefficient.
3. What is a binomial coefficient?
The binomial coefficient, expressed as nCr or (n/r), represents the total number of ways to choose r items from n distinct objects. It is calculated using the formula nCr = n! / [r!(n–r)!].
4. How can you find the middle term in the binomial expansion of (a + b)n?
The middle term in the expansion of (a + b)n depends on whether n is even or odd:
• If n is even, the expansion has n+1 terms, and the single middle term is the (n/2 + 1)th term.
• If n is odd, there are two middle terms, at positions (n+1)/2 and (n+3)/2.
5. For what values of x is the binomial expansion of (1 + x)n valid?
The binomial expansion of (1 + x)n is valid for all real values of x when n is a positive integer. For non-integer or negative n, the expansion is valid for |x| < 1 (convergent for infinite series).
6. Find the coefficient of x4 in the expansion of (2 + 3x)6.
The general term in (2 + 3x)6 is Tr+1 = 6Cr × (2)6–r × (3x)r. For x4, put r = 4:
Coefficient = 6C4 × 22 × 34 = 15 × 4 × 81 = 4860.
7. What is a simple application of the Binomial Theorem in probability?
In probability, the Binomial Theorem helps calculate the probability of getting a certain number of successes in n independent Bernoulli trials, such as tossing coins or drawing balls from a bag, by expanding (p + q)n.
8. How is the Binomial Theorem applied to compute values like 996?
To calculate expressions like 996 using the Binomial Theorem, express 99 as (100 – 1) and expand (100 – 1)6 using binomial expansion, then substitute and simplify.
9. What is the sum of coefficients in the expansion of (x + y)n?
The sum of the coefficients in the expansion of (x + y)n is found by substituting x = 1 and y = 1 into the expansion, resulting in 2n.
10. What is the term independent of x in the expansion of (x3 + 1/x)8?
The general term is Tr+1 = 8Cr × (x3)8–r × (1/x)r = 8Cr × x24–4r. For the term without x, set exponent zero: 24 – 4r = 0 ⇒ r = 6.
So the required term is 8C6 × x0 = 28.
11. What are Pascal’s Triangle and its relation to the Binomial Theorem?
Pascal’s Triangle is a triangular arrangement of numbers, where each number is the sum of the two directly above it. Its rows correspond to the binomial coefficients for the expansion of (a + b)n in the Binomial Theorem.
12. How can the Binomial Theorem help in finding approximate values?
The Binomial Theorem can be used to quickly estimate values of powers and roots for numbers close to a reference value. By expressing numbers in the form (a + x) and applying the theorem, approximate values are obtained by considering only a few leading terms.
