alleryStart learning →The number of terms in the binomial expansion of (a + b)^n, n a positive integer, is
- n − 1
- n + 1
- 2n
- n
Show answer and solution
Correct answer: B. n + 1
There are (n + 1) terms — one for each power of b from 0 to n.
MICAT Binomial Theorem — practice questions
Explore 29 free Binomial Theorem questions in MICAT Quantitative Aptitude. Open each question or exercise to read its content, reference answers and available explanation.
Practise Binomial Theorem with Quill →Binomial Theorem questions and exercises with answers
Showing questions 1–29 of 29.
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 →By the Binomial Theorem, the expansion of $(a+b)^n$ for positive integer $n$ isRead the answer and worked solution →The sum of all binomial coefficients in the expansion of $(1+x)^n$ isRead the answer and worked solution →The $(r+1)^\text{th}$ term (the GENERAL term) in the expansion of $(a+b)^n$ isRead the answer and worked solution →Find the coefficient of $x^7$ in the expansion of $(1+x)^{11}$.Read the answer and worked solution →The MIDDLE TERM in the expansion of $(a+b)^{2n}$ (where the power is EVEN) isRead the answer and worked solution →Use the binomial theorem to compute $(101)^4$.Read the answer and worked solution →Find the term INDEPENDENT of $x$ in the expansion of $\left(x^2 + \dfrac{3}{x}\right)^6$.Read the answer and worked solution →How many terms are in the expansion of $(a + b)^{15}$?Read the answer and worked solution →The coefficient of $x^4$ in the expansion of $(1 + 2x)^6$ isRead the answer and worked solution →The expansion of $(1+x)^n$ at $x = -1$ gives the valueRead the answer and worked solution →Pascal's triangle row 6 (corresponding to $(a+b)^6$) isRead the answer and worked solution →Find the value of $\sum_{r=0}^{10} \binom{10}{r}\cdot 3^r$.Read the answer and worked solution →How many terms are in the expansion of $(a + b + c)^4$?Read the answer and worked solution →GMAT · Quantitativeaptitude · Coordinate Geometry — Memory FlipRead the answer and worked solution →
Worked practice questions
The general term T_(r+1) in the expansion of (a + b)^n is
- ⁿC_r · a^r · b^(n−r)
- ⁿC_r · a^(n−r) · b^r
- ⁿC_r · a^n · b^r
- ⁿC_r · a^(n+r) · b^r
Show answer and solution
Correct answer: B. ⁿC_r · a^(n−r) · b^r
T_(r+1) = ⁿC_r · a^(n−r) · b^r.
The 'r' index moves on b and complement on a.
The sum of all binomial coefficients ⁿC_0 + ⁿC_1 + … + ⁿC_n equals
- n!
- n + 1
- n²
- 2^n
Show answer and solution
Correct answer: D. 2^n
Substituting a = b = 1 in (a + b)^n gives 2^n = Σ ⁿC_r.
How to practise
- Choose a Binomial Theorem question and try to work out your answer.
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