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Test: JEE Previous Year Questions- Binomial Numbers - Question 1

If in the expansion of (1 + x)^{m} (1 – x)^{n}, the co-efficients of x and x^{2} are 3 and – 6 respectively, then m is [JEE 99,2 ]

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Test: JEE Previous Year Questions- Binomial Numbers - Question 3

Find the largest co-efficient in the expansion of (1 + x)^{n}, given that the sum of co-efficients of the terms in its expansion is 4096. [REE 2000 (Mains)]

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Test: JEE Previous Year Questions- Binomial Numbers - Question 4

In the binomial expansion of (a - b)^{n}, n ³ 5, the sum of the 5th and 6th terms is zero. Then equals.

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Test: JEE Previous Year Questions- Binomial Numbers - Question 5

Find the coefficient of x^{49} in the polynomial [REE 2001 (Mains), 3] where C_{r} = ^{50}C_{r}

Test: JEE Previous Year Questions- Binomial Numbers - Question 6

The sum , (where = O if P < q) is maximum when m is [JEE 2002 (Scr.), 3]

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Test: JEE Previous Year Questions- Binomial Numbers - Question 7

(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]

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Test: JEE Previous Year Questions- Binomial Numbers - Question 8

^{n_1}C_{r} = (k^{2} – 3). ^{n}C_{r + 1}^{, }if k Î [JEE 2004 (Scr.)]

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Test: JEE Previous Year Questions- Binomial Numbers - Question 9

^{n-1}C_{r} = (k^{2} - 3). ^{n}C_{r + 1} [JEE 2004 (Scr.)]

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Test: JEE Previous Year Questions- Binomial Numbers - Question 10

The value of

is, where = ^{n}C_{r } [JEE 2005 (Scr.)]

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Test: JEE Previous Year Questions- Binomial Numbers - Question 11

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]

Test: JEE Previous Year Questions- Binomial Numbers - Question 12

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]

Test: JEE Previous Year Questions- Binomial Numbers - Question 13

Let a_{n} denote the number of all n-digit 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 n-digit integers ending with digit 1 and c_{n} = the number of such n-digit integers ending with digit 0. [JEE 2012]

Which of the following is correct ?

Test: JEE Previous Year Questions- Binomial Numbers - Question 14

Let a_{n} denote the number of all n-digit 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 n-digit integers ending with digit 1 and c_{n} = the number of such n-digit integers ending with digit 0. [JEE 2012]

The value of b_{6} is

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