MCQ (Previous Year Questions) - Binomial Solution (Competition Level 1) - JEE MCQ

The number of integral terms in the expansion of 

[AIEEE- 2003]

The coefficient of the middle term in the binomial expansion in powers of x of  the same if a equals-

[AIEEE 2004]

The coefficient of xⁿ in expansion of (1+x)(1–x)ⁿ is

[AIEEE 2004]

[AIEEE 2004]

If the coefficients of rth, (r + 1)^th and (r + 2)^th terms in the binomial expansion of (1 + y)^m are in A.P., then m and r satisfy the equation-

[AIEEE-2005]

If the coefficient of   equals the coefficient of  then a and b satisfythe relation

-[AIEEE-2005]

For natural numbers m, n if 

In the binomial expansion of (a - b)ⁿ, n ≥ 5, the sum of 5^th and 6^th terms is zero, then a/b  equals-

The sum of the series  

[AIEEE 2007]

[AIEEE-2008]

The remainder left out when 8²ⁿ –(62)²ⁿ⁺¹ is divided by 9 is  -

[AIEEE-2009]

[AIEEE-2010]

 The coefficient of x⁷ in the expansion of (1 – x – x² + x³)⁶ is :

[AIEEE-2011]

If n is an positive integer, then 

 [JEE-MAIN 2013]

The term independent of x in expression of 

[JEE-MAIN 2013]

If in the expansion of (1 + x) ^m ( 1 – x )ⁿ, the co-efficients of x and x² are 3 and – 6 respectively, then m is

[JEE 99,2 ]

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)]

In the binomi al expansion of (a – b)ⁿ, n ≥ 5, the sum of the 5th and 6th terms is zero. Then a/b  equals.

Find the coefficient of x⁴⁹ in the polynomial 

[REE 2001 (Mains), 3]

 is maximum when m is

[JEE 2002 (Scr.)]

 Coefficient of t²⁴ in the expansion of (1 + t²)¹² (1 + t¹²) (1 + t²⁴) is

[JEE 2003 (Scr.), 3]

[JEE 2004 (Scr.)]

[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 l et A r, Br, Cr denote, respectivel y, the coeffi ci ent of x ^r in the expansions of (1 + 

[JEE 2010]

Paragraph for Question Nos. 13 to 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     bn = 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.

Which of the following is correct ?

[JEE 2012]