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# Combination Revision Notes - JEE Main & Advanced Mock Test Series

• If certain objects are to be arranged in such a way that the order of objects is not important, then the concept of combinations is used.
• The number of combinations of n things taken r (0 < r < n) at a time is given by nCr= n!/r!(n-r)!
• The relationship between combinations and permutations is nCr = nPr/r!
• The number of ways of selecting r objects from n different objects subject to certain condition like:
1. k particular objects are always included =  n-kCr-k
2. k particular objects are never included =  n-kCr
• The number of arrangement of n distinct objects taken r at a time so that k particular objects are
1. Always included = n-kCr-k.r!,
2. Never included = n-kCr.r!.
• In order to compute the combination of n distinct items taken r at a time wherein, the chances of occurrence of any item are not fixed and may be one, twice, thrice, …. up to r times is given by n+r-1Cr
• If there are m men and n women (m > n) and they have to be seated or accommodated in a row in such a way that no two women sit together then total no. of such arrangements
= m+1Cn. m! This is also termed as the Gap Method.
• If there is a problem that requires n number of persons to be accommodated in such a way that a fixed number say ‘p’ are always together, then that particular set of p persons should be treated as one person. Hence, the total number of people in such a case becomes (n-m+1). Therefore, the total number of possible arrangements is (n-m+1)! m! This is also termed as the String Method.
• Let there be n types of objects with each type containing at least r objects. Then the number of ways of arranging r objects in a row is nr.
• The number of selections from n different objects, taking at least one
= nC1 + nC2 + nC+ ... + nCn = 2n - 1.
• Total number of selections of zero or more objects from n identical objects is n+1.
• Selection when both identical and distinct objects are present:
• The number of selections, taking at least one out of a1 + a2 + a3 + ... an + k objects, where a1 are alike (of one kind), a2 are alike (of second kind) and so on ... an are alike (of nth kind), and k are distinct
= {[(a1 + 1)(a2 + 1)(a3 + 1) ... (an + 1)]2k} - 1.
• Combination of n different things taken some or all of n things at a time is given by 2– 1.
• Combination of n things taken some or all at a time when p of the things are alike of one kind, q of the things are alike and of another kind and r of the things are alike of a third kind
= [(p + 1) (q + 1)(r + 1)….] – 1
• Combination of selecting s1 things from a set of n1 objects and sthings from a set of nobjects where combination of s1 things and s2 things are independent is given by n1Cs1 x n2Cs2
• Some results related to nC
1. nC= nCn-r
2. If nC= nCk, then r = k or n-r = k
3. nC+ nCr-1 = n+1Cr
4. nCr = n/r  n-1Cr-1
5. nCr/nCr-1 = (n-r+1)/ r
6. If n is even nCr is greatest for r = n/2
7. If n is odd, is greatest for r = (n-1) /2, (n+1)/2
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## FAQs on Combination Revision Notes - JEE Main & Advanced Mock Test Series

 1. What is the JEE exam and why is it important?
Ans. The Joint Entrance Examination (JEE) is a national level engineering entrance exam conducted in India. It is the gateway for admission to prestigious engineering colleges, including the Indian Institutes of Technology (IITs). The JEE exam is important as it determines the eligibility of candidates for admission to undergraduate engineering programs.
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Ans. Here are some effective tips to prepare for the JEE exam: 1. Understand the exam pattern and syllabus thoroughly. 2. Create a study schedule and stick to it. 3. Practice solving previous years' question papers and sample papers. 4. Join a coaching institute or take online courses for guidance. 5. Revise regularly and focus on weak areas. 6. Stay calm and confident during the exam.
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Ans. Yes, it is possible to crack the JEE exam without coaching. However, coaching institutes provide structured guidance, study materials, and regular mock tests that can be beneficial for many students. Self-study and online resources are also available for those who choose to prepare on their own. It ultimately depends on an individual's dedication, hard work, and understanding of the exam syllabus.
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Ans. As per the current guidelines, candidates can attempt the JEE exam a maximum of two times in consecutive years. However, the number of attempts may vary from year to year, so it is advisable to check the official notification for the most accurate information.
 5. What are some important topics to focus on for the JEE exam?
Ans. The JEE exam covers a wide range of topics from physics, chemistry, and mathematics. Some important topics to focus on include: - Physics: Mechanics, Thermodynamics, Electromagnetism. - Chemistry: Organic Chemistry, Inorganic Chemistry, Physical Chemistry. - Mathematics: Algebra, Calculus, Coordinate Geometry. It is important to have a strong foundation in these topics and practice solving various types of problems to excel in the JEE exam.

## JEE Main & Advanced Mock Test Series

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## JEE Main & Advanced Mock Test Series

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