Question (i) Expand in ascending powers of y as far as the term in y2. (ii) In the expansion of the coefficient of x2 is 48. Find the value of the positive constant . Solution i. We are required to expand . Expression for the Binomial expansion of is: In the given […]
Question The coefficient of in the expansion of is 3. Find the value of the constant a. Solution i. First, we expand . Expression for the Binomial expansion of is: In the given case: Hence; Now can we find the coefficient of in the expansion of . We write only terms […]
Question Find the term independent of in the expansion of . Solution Expression for the general term in the Binomial expansion of is: In the given case: Hence; Since we are looking for the coefficient of the term independent of i.e. , so we can equate; Hence, substituting ; Becomes; Hence coefficient of the term […]
Question Find the coefficient of x in the expansion of . Solution We are required to find the coefficient of in the expansion of given expression. We are given expression as; Expression for the general term in the Binomial expansion of is: First rewrite the given expression in standard form. In the given case: […]
Question The term independent of x in the expansion of , where k is a constant, is 540. (i) Find the value of k. (ii) For this value of k, find the coefficient of x2 in the expansion. Solution (i) Expression for the general term in the Binomial expansion of is: In the given […]
Question The coefficient of in the expansion of is -2160. Find the value of the constant . Solution We are given expression as; Expression for the general term in the Binomial expansion of is: First rewrite the given expression in standard form. In the given case: Hence; Since we are looking for the coefficient of […]
Question Find the coefficient of in the expansion of . Solution We are required to expand; We can write it in standard form; Expression for the general term in the Binomial expansion of is: In the given case: Hence; Since we are looking for the coefficient of the term : we can equate; Finally substituting […]
Question Find the coefficient of in the expansion of . Solution We are required to expand; Expression for the general term in the Binomial expansion of is: In the given case: Hence; Since we are looking for the coefficient of the term : we can equate; Finally substituting in: Therefore, the coefficient of is 840. […]
Question i. Find the coefficients of and in the expansion of . ii. Hence find the coefficient of in the expansion of . Solution i. Expression for the general term in the Binomial expansion of is: First we rewrite the expression in the standard form; In the given case: Hence; Since we […]
Question Find the coefficient of in the expansion of . Solution We are required to find the coefficient of in the expansion of . We are given expression as; Expression for the general term in the Binomial expansion of is: First rewrite the given expression in standard form. In the given case: Hence; Since […]
Question The coefficient of in the expansion of is 330. Find the value of the constant a. Solution We can find the coefficient of in the expansion of given expression by finding coefficients of in the expansion of individual terms of expression and then adding them. Let us first find the coefficient of in the […]
Question i. Find the first three terms in the expansion, in ascending powers of , of . ii. Given that the coefficient of in the expansion of is 12, find the value of the constant a. Solution i. Expression for the Binomial expansion of is: First rewrite the given expression in standard […]
Question i. Find the term independent of x in the expansion of . ii. Find the value of a for which there is no term independent of x in the expansion of Solution i. Expression for the general term in the Binomial expansion of is: For the given case: Hence; Since we are looking for the coefficient […]
Question Find the term independent of x in the expansion of . Solution Expression for the general term in the Binomial expansion of is: For the given case: Hence; Since we are looking for the coefficient of the term independent of i.e. , so we can equate Hence, substituting ; Becomes; Hence coefficient of the term independent of i.e. is .
Question The coefficients of and in the expansion of are equal. Find the value of the non-zero constant a. Solution We need to equate the coefficients of and in the expansion of given expression. We are given expression as; Expression for the general term in the Binomial expansion of is: In the given case: Hence; Since we are looking for the coefficients […]
Question i. Find the coefficient of x in the expansion of . ii. Hence find the coefficient of x in the expansion of . Solution i. We are required to find the coefficient of in the expansion of given expression. We are given expression as; Expression for the general term in the Binomial expansion of is: First rewrite […]
Question In the expansion of , the coefficient of x is 5. Find the value of the constant a. Solution We are given expression as; Expression for the general term in the Binomial expansion of is: In the given case: Hence; Since we are looking for the terms with i.e. we can equate; Now we can find the term with; Substituting ; […]
Question The coefficients of and in the expansion of are and respectively. Find the value of . . Solution We can find the coefficients of and in the expansion of given expression. Let us first find the coefficient of in the expansion of . We are given expression as; Expression for the general term in the Binomial expansion of is: First rewrite the […]
Question The coefficient of in the expansion of is 100. Find the value of the constant a. Solution We can find the coefficient of in the expansion of given expression by finding coefficients of in the expansion of individual terms of expression and then adding them. Let us first find the coefficient of in the expansion of . We are given […]
Question Find the coefficient of in the expansion of . Solution First rewrite the given expression in standard form. Expression for the Binomial expansion of is: In the given case: Hence; Hence the coefficient of is .