Class 11 • Maths • Chapter 7
BINOMIAL THEOREM
True & False Quiz
Expand. Simplify. Discover.
✓True
✗False
25
Questions
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Ch.7
Chapter
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XI
Class
Why True & False for BINOMIAL THEOREM?
How this format sharpens your conceptual clarity
🔵 The Binomial Theorem gives a formula to expand any power of a binomial without repeated multiplication.
✅ T/F tests the general term Tᵣ₊₁ = ⁿCᵣ aⁿ−ᵣ bᵣ and coefficient sums — high-frequency CBSE objectives.
🎯 Critical insight: (a+b)ⁿ has (n+1) terms — a perennially tested true/false trap.
📋
Read each statement carefully. Click True or False — instant feedback with explanation appears. Submit anytime; unattempted questions are marked Skipped.
Q 1
The expansion of \((a+b)^n\) contains exactly \(n+1\) terms when \(n\) is a non-negative integer.
Q 2
The first term of the expansion of \((x+y)^n\) is \(^{n}C_{0}x^n\).
Q 3
The last term of the expansion of \((a+b)^n\) is \(^{n}C_{n}b^n\).
Q 4
In the expansion of \((a+b)^n\), the powers of \(a\) decrease while the powers of \(b\) increase successively.
Q 5
The binomial coefficient \(^{n}C_{r}\) is equal to \(^{n}C_{n-r}\).
Q 6
The middle term of \((a+b)^n\) is always unique.
Q 7
The sum of all binomial coefficients in the expansion of \((1+1)^n\) is \(2^n\).
Q 8
The coefficient of \(x^r\) in the expansion of \((1+x)^n\) is \(^{n}C_{r}\).
Q 9
The coefficient of \(x^2\) in \((1+x)^5\) is equal to 10.
Q 10
The expansion of \((a-b)^n\) contains only positive terms for all values of \(n\).
Q 11
The constant term in the expansion of \((x+\frac{1}{x})^n\) exists only when \(n\) is even.
Q 12
The middle term of \((a+b)^{10}\) is the 6th term.
Q 13
The coefficient of \(x^3\) in \((2+x)^5\) is \(80\).
Q 14
The sum of coefficients of all odd-powered terms in \((1+x)^n\) is \(2^{n-1}\).
Q 15
If \(n\) is a positive integer, then \((1+x)^n=(1-x)^n\) for all real \(x\).
Q 16
The general term of \((a+b)^n\) is \(T_{r+1}=\,^{n}C_{r}a^{\,n-r}b^{\,r}\).
Q 17
The coefficient of the middle term in \((1+x)^{2n}\) is always the greatest coefficient.
Q 18
The term independent of \(x\) in \((x^2+\frac{1}{x})^9\) exists.
Q 19
In \((a+b)^n\), the ratio of successive coefficients is \(\frac{^{n}C_{r+1}}{^{n}C_{r}}=\frac{n-r}{r+1}\).
Q 20
The number of terms in the expansion of \((a+b)^{2n+1}\) is even.
Q 21
The coefficient of \(x^k\) in \((1+x)^n\) is zero if \(k>n\).
Q 22
The greatest term in the expansion of \((1+x)^n\) for \(x>0\) is always the middle term.
Q 23
The sum of coefficients of terms with even powers of \(x\) in \((1+x)^n\) equals the sum of coefficients of odd-powered terms.
Q 24
The coefficient of \(x^r\) in \((ax+b)^n\) is \(^{n}C_{r}a^rb^{\,n-r}\).
Q 25
The number of positive integral solutions of \(r\) for which the term independent of \(x\) exists in \((x^p+\frac{1}{x^q})^n\) is at most one.
Key Takeaways — BINOMIAL THEOREM
Core facts for CBSE Boards & JEE
1
(a+b)ⁿ has (n+1) terms — count starts from r=0 to r=n.
2
General term: Tᵣ₊₁ = ⁿCᵣ · aⁿ−ᵣ · bᵣ (r starts from 0).
3
Sum of all binomial coefficients = 2ⁿ (substitute x=1 in (1+x)ⁿ).
4
Sum of odd-indexed = Sum of even-indexed = 2ⁿ−¹.
5
Middle term: (n/2+1)th if n is even; two middle terms if n is odd.
6
Binomial coefficients are symmetric: ⁿCᵣ = ⁿCⁿ−ᵣ always.