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.
Find:

The shortest distance between the lines: \[ \vec{r}=(4+\lambda)\hat{i}+(2\lambda-1)\hat{j}-3\lambda\hat{k} \] and \[ \vec{r}=(1+2\mu)\hat{i}+(4\mu-1)\hat{j}+(2-5\mu)\hat{k} \]
View Solution
2.
Find:

If the function \[ f(x)= \begin{cases} \frac{\sin x}{x}+\cos x, & x\neq0\\ k, & x=0 \end{cases} \] is continuous at \(x=0\), then find the value of \(k\).
- \(0\)
- \(-2\)
- \(-1\)
- \(2\)
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3.
Find:

The principal value of \[ \sec^{-1}(\sqrt{2})+2\csc^{-1}(-2) \] is:
- \(-\frac{\pi}{2}\)
- \(-\frac{\pi}{4}\)
- \(\frac{\pi}{4}\)
- \(\frac{\pi}{2}\)
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4.
An NGO organises a charity event in which they decide to distribute woollen caps to protect children from winter. The caps to be distributed are in three separate boxes, Box I has 30 red caps, Box II has 20 red and 10 green caps, and Box III has 30 green caps. The probability that a Box i is selected and a cap picked out is i/6, where i = 1, 2, 3.
Based on the above information, answer the following questions :
5.
If \( xy = e^{x - y} \), then find \( \frac{dy}{dx} \).
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6.
At a birthday party, children are being served orange juice in conical cups, as shown in the figure.

Each cup is 15 cm deep and has a radius 5 cm. The juice is being poured into this cup at a rate of 0·1 cm3/s.
On the basis of the above information, answer the following questions :