Binomial Theorem questions
776 published questions with worked solutions.
- For an integer n ≥ 2, if the arithmetic mean of all coefficients in the binomial expansion of (x+y)^ 2n-3 is 16, then the...
- The number of integral terms in the expansion of (5^ 1 2 + 7^ 1 8 )^ 1016 is
- If 1^2 ( ^ 15 C_1) + 2^2 ( ^ 15 C_2) + 3^2 ( ^ 15 C_3) + + 15^2 ( ^ 15 C_ 15 ) = 2^m 3^n 5^k, where m, n, k N , then m + n + k is...
- The sum of the series 2 1 ^ 20 C_4 - 3 2 ^ 20 C_5 + 4 3 ^ 20 C_6 - 5 4 ^ 20 C_7 + + 18 17 ^ 20 C_ 20 , is equal to _______.
- If the coefficients of x^3 and x^4 in the expansion of (1 + ax + bx^2)(1 - 2x)^ 18 in powers of x are both zero, then (a, b) is...
- The value of ( ^ 21 C_1 - ^ 10 C_1) + ( ^ 21 C_2 - ^ 10 C_2) + ( ^ 21 C_3 - ^ 10 C_3) + ( ^ 21 C_4 - ^ 10 C_4) + + ( ^ 21 C_ 10 -...
- The sum of the co-efficients of all odd degree terms in the expansion of (x + x^3 - 1 )^5 + (x - x^3 - 1 )^5, (x > 1) is
- The coefficient of x^2 in the expansion of the product (2 - x^2) ((1 + 2x + 3x^2)^6 + (1 - 4x^2)^6 ) is -
- The sum of the co-efficients of all even degree terms in x in the expansion of (x + x^3-1 )^6 + (x - x^3-1 )^6, (x > 1) is equal...
- The sum of the series 2 ^ 20 C_0 + 5 ^ 20 C_1 + 8 ^ 20 C_2 + 11 ^ 20 C_3 + + 62 ^ 20 C_ 20 is equal to:
- If the fourth term in the binomial expansion of ( x^ 1 1+ _ 10 x + x^ 1 12 )^6 is equal to 200, and x > 1, then the value of x is:
- If the fourth term in the Binomial expansion of ( 2x + x^ _8x )^6 (x > 0) is 20 8^7, then a value of x is:
- The smallest natural number n, such that the coefficient of x in the expansion of (x^2 + 1 x^3 )^n is ^nC_ 23 , is:
- If n is the degree of the polynomial, [ 1 5x^3 + 1 - 5x^3 - 1 ]^8 + [ 1 5x^3 + 1 + 5x^3 - 1 ]^8 and m is the coefficient of x^n...
- The coefficient of x^ 10 in the expansion of (1 + x)^2(1 + x^2)^3(1 + x^3)^4 is equal to -
- If some three coefficients in the binomial expansion of (x + 1)^n in powers of x are in the ratio 2 : 15 : 70, then the average...
- If the coefficients of x^2 and x^3 are both zero, in the expansion of the expression (1 + ax + bx^2)(1 - 3x)^ 15 in powers of x,...
- The coefficient of t^4 in the expansion of ( 1 - t^6 1 - t )^3 is:
- The coefficient of x^ 18 in the product (1 + x)(1 - x)^ 10 (1 + x + x^2)^9 is:
- The total number of irrational terms in the binomial expansion of (7^ 1/5 - 3^ 1/10 )^ 60 is:
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