Binomial Theorem questions
776 published questions with worked solutions.
- If the coefficients of the second, third and fourth terms in the expansion of (1+x)^n are in AP, then n is equal to
- If a_r is the coefficient of x^ r-1 in (1+x)^n+(1+x)^ n+1 + +(1+x)^ n+k (n<r-1 n+k), then _ r=0 ^ n+k+1 (-1)^ra_r is equal to
- The largest term in the expansion of (3+2x)^ 50 , where x= 15 is
- Statement 1: The coefficient of x^n in the binomial expansion of (1-x)^ -2 is (n+1). Statement 2: The coefficient of x^r in...
- The number of irrational terms in the expansion of (5^ 1/6 +2^ 1/8 )^ 100 is
- If the sum of the coefficients in the expansion of (a^2x^2-2ax+1 )^ 51 vanishes, then the value of a is
- The coefficient of x^ 2^ m+1 in the expansion of E= 1 (1+x)(1+x^2)(1+x^4)(1+x^8) (1+x^ 2^m ) , |x|<1 is
- The coefficient of ^n ^n in the expansion of [(1+ )(1+ )( + ) ]^n is
- C_0C_r+C_1C_ r+1 +C_2C_ r+2 + +C_ n-r C_n is equal to
- In the expansion of (1+x+x^2+x^3)^6, the coefficient of x^ 14 is Statement 1: 130. Statement 2: 120.
- The coefficient of x^4 in the expansion of (1+x+x^2+x^3 )^n is
- The coefficient of x^r [0 r (n-1)] in the expansion of (x+3)^ n-1 +(x+3)^ n-2 (x+2)+(x+3)^ n-3 (x+2)^2+ +(x+2)^ n-1 is
- If sum of the coefficients of the first, second and third terms of the expansion of (x^2+ 1x )^m is 46, then the coefficient of...
- The sum of the series _ r=0 ^n(-1)^r , ^nC_r ( 1 2^r + 3^r 2^ 2r + 7^r 2^ 3r + 15^r 2^ 4r + +m terms ) is
- If (1+x)^n= ^nC_0+ ^nC_1x+ ^nC_2x^2+ + ^nC_nx^n, then ^nC_1 ^nC_0 + 2 , ^nC_2 ^nC_1 + 3 , ^nC_3 ^nC_2 + + n , ^nC_n ^nC_ n-1 is...
- If the 4^ th term in the expansion of ( 23x- 3 2x )^n is independent of x, then n is equal to
- Statement 1: If n is even, then ^ 2n C_1+ ^ 2n C_3+ + ^ 2n C_ n-1 =2^ 2n-1 . Statement 2: ^ 2n C_1+ ^ 2n C_3+ + ^ 2n C_ 2n-1 =2^...
- If the coefficients of T_r, T_ r+1 , T_ r+2 terms of (1+x)^ 14 are in AP, then the value of r is
- If (1-3x)^ 1/2 +(1-x)^ 5/3 4-x is approximately equal to a+bx for small values of x, (a,b) is equal to
- If a_1,a_2,a_3,a_4 are the coefficients of any four consecutive terms in the expansion of (1+x)^n, then a_1 a_1+a_2 + a_3 a_3+a_4...
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