Mathematics JEE Advanced Binomial Theorem Sample Paper with Answer & Solution 2019
Sub-topic of Binomial Theorem
Binomial expansion | Identifying terms independent of “x” | Ratio of two terms | Middle term of binomial expansion | Binomial coefficients | Sum of different combinations of binomial coefficients | Application of binomial expansion | Problems on multinomial expansion
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Binomial Theorem JEE Formulas 2018-2019
- Binomial Theorem. …
- General Term in a expansion: …
- Combinations or groups formula: …
- Middle term in a expansion: …
- Coefficient of xm in (axp + b / xq ) …
- Independent Term of x in (axp + b / xq ) …
- Greatest Coefficients:
If n is a positive integer, then binomial theorem is
(x+y)n = nc0.xn + nc1xn-1y + nc2xn-2y2 + nc3.xn-3y3 + ……. + ncrxn-ryr + …. + ncn.yn
General Term in a binomial expansion:
In the binomial expansion of (x+y)n, general term is denoted by Tr + 1 and it is
Tr + 1 = ncr.xn – r.yr
Combinations or groups formula:
ncr= n!/[( n – r ) !].[r!]
Middle term in a binomial expansion:
In the binomial expansion of (x+y)n, middle term is T( n/2 + 1)if n is even, and T(n + 1)/2and T( n + 3)/2 , if n is odd.
Binomial Coefficients in the binomial expansion (x+y)n
nC0, nC1, nC2, nC3,….. nCr… nCn are called Binomial Coefficients.
Binomial Coefficient of xmin (axp+ b / xq )
The value of r of the term which contains the coefficient of xm is
(np – m )/( p + q)
Independent Term of x in (axp+ b / xq)
The value of r of the term which does not contain x is
( np ) / (p + q)
Greatest Binomial Coefficients:
In the binomial expansion of (x + y)n, the greatest binomial coefficient is
nc(n+1)/2 , nc( n + 3 )/2 , when n is an odd integer, and nc( n/2 + 1) , when n is an even integer.
Numerically Greatest term in the binomial expansion: (1 + x)n
In the binomial expansion of (1 + x)n, the numerically greatest term is found by the following method:
If [( n + 1 ) | x | ] / [| x | + 1] = K + f,
Where K is an integer and f is a positive proper fraction, then
( K + 1)thterm is the numerically greatest fraction.
And if [( n + 1 ) | x | ] / [| x | + 1] = K,
Where K is an integer, then
Kth term and ( K + 1 )th terms are the two numerically greatest terms.
In the binomial expansion of (x+y)n:
1. Sum of the binomial coefficients is 2n
nc0 + nc1 + nc2 + …………. + ncn = 2n
2. Sum of the odd binomial coefficients is 2n – 1
c1 + c3 + c5 + …………. = 2n – 1
3. Sum of the even binomial coefficients is 2n – 1
c0 + c2 + c4 +……….. = 2n – 1
Number of terms in various expansions:
Number of terms in the expansion of
1. ( x + y )nis n + 1
2. ( x + y + z ) n is [( n + 1 ) ( n + 2 )]/2
3. ( x + y + z + w) n = [ ( n + 1)(n + 2 ) ( n + 3 )]/ 1. 2.3
IIT Advanced 2016-17 Syllabus
IIT-JEE Advanced syllabus has largely remained unchanged for the last 16 years! It is the same as the syllabus for IIT IIT-JEE in the previous years. This is the reason, we bring you 16 years of IIT IIT-JEE and IIT-JEE Advanced past year question Papers, as they cover same topics as specified in the IIT. IIT-JEE syllabus 2016. Ezyexams experts suggest that IIT-JEE Adv. 2016 Syllabus for Chem, Phy, Maths should have been the starting point of your IIT-JEE preparation. Even if you have not paid enough attention to it until now, pick up the IIT syllabus, now and check whether you have covered all the topics well or not.
JEE Advanced 2016 Complete Syllabus
There are only minor changes between the IIT-JEE Mains syllabus 2016 and the IIT-JEEadv. syllabus. While the former is more tuned to the CBSE syllabi of Class XIth and Class XIIth, the latter includes topics from a wider range of boards.
You can download the subject-wise IIT-JEEadvanced syllabus pdf in an easy-to-read format by clicking on the links below:
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Last (past) year papers which are helpful to good score…
Absolutely yes, solving the last 3 to 8 years Q. papers are not only makes the students you stronger, but this also gives a confidence of questions which are coming in our JEE mains & Advanced exams. So try these papers as a BRAHMASTRA for your preparation of your JEE Advanced exams, because these given Question Papers will be helpful for getting full marks in JEE Advanced examination.
Past 10 year Q. Paper of 2006, 7, 8….. 16 and also available in the attached sheet for candidates and teachers. Last years Q. paper for Mains and Advanced Mathematics, Physics and Chemistry are a smart way to revise for main & advanced exams. Specially are helpful for those appearing for Advanced exam as they familiarize students with the patterns of the Solved Q.paper and the method of marking.
JEE Advanced Q. Papers are top revision tools and must be made an important part of exam preparation. Chemistry are issued by JEE Main/Advanced 2016-17. Chemistry Advanced syllabus 2015-16 was Chemical Bonding, Ionic Equilibrium, s-Block Elements, Solid State, p-Block elements, Surface Chemistry etc…… important question bank for JEE. How to score 90+ per-cent on JEE Advanced examination practice the last 10 years question paper this Board for sure will prove to be the special tool in getting a high score end success in CBSE class XIIth Examinations,