alleryThe number of terms in the expansion of $(a+b)^n$ is:
- $2n$
- $n+1$
- $n$
- $n-1$
Show answer and solution
Correct answer: B. $n+1$
The expansion of (a+b)ⁿ has n+1 terms (one more than the index).
GRE Binomial Theorem — practice questions
Explore 31 free Binomial Theorem questions in GRE Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
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Showing questions 1–30 of 31.
The number of terms in the expansion of $(a+b)^n$ is:Read the answer and worked solution →The general term $T_{r+1}$ in the expansion of $(a+b)^n$ is:Read the answer and worked solution →In the expansion of $(x+y)^8$, the middle term is the:Read the answer and worked solution →The coefficient of $x^3$ in the expansion of $(1+x)^{10}$ is:Read the answer and worked solution →The term independent of $x$ in the expansion of $\left(x+\dfrac{1}{x}\right)^6$ is:Read the answer and worked solution →The value of $\binom{n}{0}+\binom{n}{1}+\cdots+\binom{n}{n}$ is:Read the answer and worked solution →The constant term in the expansion of $\left(x^2+\dfrac{1}{x}\right)^6$ is:Read the answer and worked solution →The coefficient of $x$ in the expansion of $(1+2x)^5$ is:Read the answer and worked solution →The greatest binomial coefficient in the expansion of $(1+x)^{10}$ is:Read the answer and worked solution →The number of middle terms in the expansion of $(a+b)^7$ is:Read the answer and worked solution →If $\binom{10}{3}=\binom{10}{k}$ (with $k\neq 3$), then $k$ equals:Read the answer and worked solution →The coefficient of $x^3$ in the expansion of $(2+x)^5$ is:Read the answer and worked solution →The sum of all the coefficients in the expansion of $(2x+3)^4$ is:Read the answer and worked solution →The number of terms in the binomial expansion of (a + b)^n, n a positive integer, isRead the answer and worked solution →The general term T_(r+1) in the expansion of (a + b)^n isRead the answer and worked solution →The sum of all binomial coefficients ⁿC_0 + ⁿC_1 + … + ⁿC_n equalsRead the answer and worked solution →Pascal's triangle gives, for index n, the rowRead the answer and worked solution →The expansion of (x + 1)^4 isRead the answer and worked solution →The coefficient of x⁴ in the expansion of (1 + x)^7 isRead the answer and worked solution →In the expansion of (a + b)^n, the sum of the indices of a and b in every term isRead the answer and worked solution →The binomial coefficients ⁿC_r and ⁿC_(n−r) areRead the answer and worked solution →Which identity is the basis for constructing Pascal's triangle row by row?Read the answer and worked solution →The term independent of x in the expansion of (x + 1/x)^6 isRead the answer and worked solution →The coefficient of x^5 in (1 + x)^8 isRead the answer and worked solution →Expanding (2x + 3y)^5 using Pascal's row 1 5 10 10 5 1, the coefficient of x²y³ isRead the answer and worked solution →The middle term of (a + b)^8 isRead the answer and worked solution →(1.01)^5 evaluated using the binomial expansion to first two terms only is approximatelyRead the answer and worked solution →The sum of coefficients of ODD powers of x in (1 + x)^10 equalsRead the answer and worked solution →The expansion of $(a + b)^n$ contains how many terms?Read the answer and worked solution →The general term in the expansion of $(x + 2)^{10}$ is:Read the answer and worked solution →
Worked practice questions
The general term $T_{r+1}$ in the expansion of $(a+b)^n$ is:
- $\binom{n}{r} a^{n-r} b^{r-1}$
- $\binom{n}{r+1} a^{n-r} b^{r}$
- $\binom{n}{r} a^{r} b^{n-r}$
- $\binom{n}{r} a^{n-r} b^{r}$
Show answer and solution
Correct answer: D. $\binom{n}{r} a^{n-r} b^{r}$
The general term is T_{r+1} = C(n,r) a^{n−r} b^{r}.
In the expansion of $(x+y)^8$, the middle term is the:
- 9th term
- 8th term
- 5th term
- 4th term
Show answer and solution
Correct answer: C. 5th term
For (x+y)⁸, n=8 is even, so there is one middle term: the (n/2 + 1) = 5th term.
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