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.
XAT Binomial Theorem — practice questions
Explore 88 free Binomial Theorem questions in XAT Mathematics. 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 1–30 of 88.
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 →Complete the definition of conditional probabilityRead the answer and worked solution →True or false: conditional probabilityRead the answer and worked solution →Independent or mutually exclusive?Read the answer and worked solution →Match each rule to its nameRead the answer and worked solution →IndependenceRead the answer and worked solution →Order the steps for a Bayes' theorem questionRead the answer and worked solution →Complete the conditions for a partitionRead the answer and worked solution →True or false: independence versus exclusivityRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Tap every statement that follows from independenceRead the answer and worked solution →The multiplication ruleRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Complete the theorem of total probabilityRead 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
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