NCERT Solutions For Class 11 Maths Chapter 8: Binomial Theorem

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NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem are provided in the article below. Binomial theorem is the process of algebraically expanding power of sums of two or more binomials. Chapter 8 Binomial Theorem covers important concepts including Pascal’s Triangle and Binomial Expansion Formula.

Download: NCERT Solutions for Class 11 Mathematics Chapter 8 pdf

Class 11 Maths NCERT Solutions Chapter 8 Binomial Theorem

Class 11 Maths NCERT Solutions Chapter 8 Binomial Theorem are provided below:

Also read: Binomial Theorem

Important Topics for Class 11 Maths NCERT Solutions Chapter 8 Binomial Theorem

Important Topics for Class 11 Maths NCERT Solutions Chapter 8 Binomial Theorem are elaborated below:

Pascal’s Triangle

Pascals triangle (Pascal's triangle) is an arrangement of binomial coefficients in triangular form. This triangle starts with 1 at the top, then 1s at both sides of the triangle until the end.

Let’s understand Pascals Triangle Probability from the following table:

Number of Tosses/Row of Pascals Triangle	Outcomes in Combinations	Elements in Pascals Triangle
1	{H} {T}	1, 1
2	{HH} {HT TH} {TT}	1, 2, 2001
3	{HHH} {HHT, HTH, THH} {HTT, THT, TTH} {TTT}	1, 3, 3, 1
4	{HHHH} {HHHT, HHTH, HTHH, THHH} {HHTT, HTHT, HTTH, THHT, THTH, TTHH} {HTTT, THTT, TTHT, TTTH} {TTTT}	1, 4, 6, 4, 1
...etc...	... etc ...	etc...

Binomial Expansion Formula

inomial expansion formulas are used to find the powers of the binomials which cannot be expanded using the algebraic identities. The binomial expansion formula involves binomial coefficients which are of the form:

\((_{k}^{n}) \) or \(n_{Ck}\)

It is calculated using the formula:

\(\frac{(_{k}^{n}) = n! }{[(n-k)!k!]}\)

NCERT Solutions For Class 11 Maths Chapter 8 Exercises:

The detailed solutions for all the NCERT Solutions for Chapter 8 Binomial Theorem under different exercises are as follows:

Also check:

Important Chapter Related Links
Perfect Square Binomial Formula	Algebra	Real-Valued Function
Important Questions Class 11 Chapter 8 Binomial Theorem	Identities Under Binomial Theorem	Correlation Coeffecient Formula

Also check:

Math Study Guides
Maths Important Formulas	Maths MCQs	Comparison Articles in Maths
Difference Between Topics in Maths	Math Study Material	Arithmetic

CBSE CLASS XII Related Questions

1.
In a school, the probability of holding a debate competition is \( \frac{1}{3} \) and that of a quiz competition is \( \frac{2}{3} \). In the two participating teams, A has 4 girls and 6 boys and B has 7 girls and 3 boys. If a debate competition is held, the students are selected from team A and for the quiz competition they are selected from team B. If only two students are to be chosen from the teams, then find the probability that one will be a girl and the other a boy.
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2.
If \[ \frac{d}{dx}(F(x))=\frac{1}{e^x+1}, \] then find \(F(x)\), given that \[ F(0)=\log\left(\frac{1}{2}\right). \]
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3.
For a square matrix \(A\), \[ (3A)^{-1}= \]
- \( 3A^{-1} \)
- \( 9A^{-1} \)
- \( \frac{1}{3} A^{-1} \)
- \( \frac{1}{9} A^{-1} \)
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4.
Find the domain of \[ q(x)=\cos^{-1}(4x^2-3). \] Hence, find the value of \(x\) for which \[ q(x)=0. \] Also, write the range of \[ 3q(x)-\pi. \]
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5.
For two vectors \(\vec{a}\) and \(\vec{b}\):

Assertion (A): \[ |\vec{a}\times\vec{b}|^2+(\vec{a}\cdot\vec{b})^2 = |\vec{a}|^2|\vec{b}|^2 \] Reason (R): \[ |\vec{a}\times\vec{b}| = (\vec{a}\cdot\vec{b})\tan\theta, \quad \theta\neq\frac{\pi}{2}. \]
- Both Assertion (A) and Reason (R) are true and the Reason (R) is the correct explanation of the Assertion (A).
- Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
- Assertion (A) is true, but Reason (R) is false.
- Assertion (A) is false, but Reason (R) is true.
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6.
Check whether the function \[ f(x)= \begin{cases} \dfrac{|x-3|}{2(x-3)}, & x<3,\\[6pt] \dfrac{x-6}{6}, & x\geq 3 \end{cases} \] is continuous at \(x=3\) or not.
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