If in the expansion of (1 + x)^{m} (1 – x)^{n}, the coefficients of x and x^{2} are 3 and – 6 respectively, then m is [JEE 99,2 ]
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Find the largest coefficient in the expansion of (1 + x)^{n}, given that the sum of coefficients of the terms in its expansion is 4096. [REE 2000 (Mains)]
In the binomial expansion of (a  b)^{n}, n ³ 5, the sum of the 5th and 6th terms is zero. Then equals.
Find the coefficient of x^{49} in the polynomial [REE 2001 (Mains), 3] where C_{r} = ^{50}C_{r}
The sum , (where = O if P < q) is maximum when m is [JEE 2002 (Scr.), 3]
(a) Coefficient of t^{24} in the expansion of (1 + t^{2})^{12} (1 + t^{12}) (1 + t^{24}) is [JEE 2003 (Scr.), 3]
(b) Prove that :
[JEE 2003 (Mains),2]
^{n_1}C_{r} = (k^{2} – 3). ^{n}C_{r + 1}^{, }if k Î [JEE 2004 (Scr.)]
^{n1}C_{r} = (k^{2}  3). ^{n}C_{r + 1} [JEE 2004 (Scr.)]
The value of
is, where = ^{n}C_{r } [JEE 2005 (Scr.)]
The number of seven digit integers, with sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only, is [JEE 2009]
For r = 0, 1, ...., 10 let A_{r}, B_{r}, C_{r} denote, respectively, the coefficient of x^{r} in the expansions of (1 + x)^{10}, (1 + x)^{20} and (1 + x)^{30}. Then is equal to [JEE 2010]
Let a_{n} denote the number of all ndigit positive integers formed by the digits 0, 1 or both such that no consecutive digits in them are 0. Let b_{n} = the number of such ndigit integers ending with digit 1 and c_{n} = the number of such ndigit integers ending with digit 0. [JEE 2012]
Which of the following is correct ?
Let a_{n} denote the number of all ndigit positive integers formed by the digits 0, 1 or both such that no consecutive digits in them are 0. Let b_{n} = the number of such ndigit integers ending with digit 1 and c_{n} = the number of such ndigit integers ending with digit 0. [JEE 2012]
The value of b_{6} is
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447 docs930 tests

JEE Advanced (Single Correct Type): Mathematical induction & Binomial Theorem Doc  8 pages 
JEE Advanced (One or More Correct Option): Mathematical induction & Binomial Theorem Doc  3 pages 
JEE Advanced (Subjective Type Questions): Mathematical Induction & Binomial Theorem Doc  23 pages 
JEE Advanced (Fill in the Blanks): Mathematical Induction & Binomial Theorem Doc  2 pages 
Integer Answer Type Questions for JEE: Mathematical induction & Binomial Theorem Doc  5 pages 