Binomial Theorem questions
776 published questions with worked solutions.
- The coefficient of x^ 100 in the expansion of _ j=0 ^ 200 (1+x)^j is
- In the expansion of (2-3x^3 )^ 20 , if the ratio of 10^ th term to 11^ th term is 45 22 , then x is equal to
- The total number of terms in the expansion of (x+y)^ 100 +(x-y)^ 100 after simplification is
- If the expansion of ( 3 x 7- 5 2x x )^ 13n contains a term independent of x in 14^ th term, then n should be
- The coefficient of x^4 in the expansion of ( x2- 3 x^2 )^ 10 is
- The coefficient of x in the expansion of (1+x)(1+2x)(1+3x) (1+100x) is
- The coefficient of x^n in the expansion of (1+2x+3x^2+ )^ 1/2 is
- If the coefficient of (2r+1)^ th term and (r+2)^ th term in the expansion of (1+x)^ 43 are equal, then r is equal to
- If (1+2x+x^2)^5= _ k=0 ^ 15 a_kx^k, then _ k=0 ^7a_ 2k is equal to
- Sum of the infinite series 1+ 23 12+ 23 56 1 2^2 + 23 56 89 1 2^3 + is
- If the r^ th term in the expansion of ( x3- 2 x^2 )^ 10 contains x^4, then r is equal to
- The coefficient of x^ -10 in (x^2- 1 x^3 )^ 10 is
- The coefficient of x^2 term in the binomial expansion of ( x 3+x^ -1/4 )^ 10 is
- If the expansion in power of x of the function 1 (1-ax)(1-bx) is a_0+a_1x+a_2x^2+a_3x^3+ , then a_n is
- If in the expansion of (1+x)^m(1-x)^n, the coefficient of x and x^2 are 3 and -6 respectively, then m is
- The sum of the series 1+ 15+ 1 3 5 10 + 1 3 5 5 10 15 + is equal to
- If the magnitude of the coefficient of x^7 in the expansion of (ax^2+ 1 bx )^8, where a,b are positive numbers, is equal to the...
- Coefficient of x in the expansion of (x^2+ ax )^5 is
- The sum of the rational terms in the expansion of ( 2+3^ 1/5 )^ 10 is
- If x is so small that x^3 and higher powers of x may be neglected, then (1+x)^ 3/2 - (1+ 12x )^3 (1-x)^ 1/2 may be approximated as
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