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

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CBSE CLASS XII Related Questions

1.
For the given Linear Programming Problem, shade the feasible region on the graph and write the coordinates of the corner points.
Minimize \(Z = 5x + 7y\)
subject to constraints
\[ 2x + y \geq 8 \]
\[ x + 2y \geq 10 \]
\[ x,\ y \geq 0. \]
View Solution
2.
The value of \( \left[ \tan^{-1}(-1) + \cos^{-1}\left(-\frac{1}{2}\right) + \sin^{-1}\left(\frac{1}{2}\right) \right] \) is :
- \( \frac{7\pi}{12} \)
- \( \frac{5\pi}{12} \)
- \( -\frac{5\pi}{12} \)
- \( \frac{\pi}{3} \)
View Solution
3.
Find the sum of maximum and minimum values of \(f(x) = \sin x\,(1 + \cos x)\) in the interval \([0, \pi]\).
View Solution
4.
Find the value of \(x\) if \(A = B\), where
\[ A = \begin{bmatrix} 6 & 3x \\ 8 & -6 \end{bmatrix} \text{ and } B = \begin{bmatrix} 6 & x^2+2 \\ 8 & x^2-5x \end{bmatrix}. \]
View Solution
5.
For events A and B, if \(P(B)=\frac{3}{5}\), \(P(A/B)=\frac{1}{2}\) and \(P(A\cup B)=\frac{4}{5}\), then \(P(A)\) is :
- \(\frac{1}{2}\)
- \(\frac{3}{5}\)
- \(\frac{1}{5}\)
- \(\frac{3}{10}\)
View Solution
6.
Find the product of the maximum and minimum values of the function \( f(x) = \cos x - \frac{1}{2}\cos 2x,\ x \in \left[0, \frac{\pi}{2}\right] \).
View Solution

View All

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NCERT Solutions For Class 11 Maths Chapter 8: Binomial Theorem

Class 11 Maths NCERT Solutions Chapter 8 Binomial Theorem

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

CBSE CLASS XII Related Questions

1.
For the given Linear Programming Problem, shade the feasible region on the graph and write the coordinates of the corner points.
Minimize \(Z = 5x + 7y\)
subject to constraints
\[ 2x + y \geq 8 \]
\[ x + 2y \geq 10 \]
\[ x,\ y \geq 0. \]

2.
The value of \( \left[ \tan^{-1}(-1) + \cos^{-1}\left(-\frac{1}{2}\right) + \sin^{-1}\left(\frac{1}{2}\right) \right] \) is :

3.
Find the sum of maximum and minimum values of \(f(x) = \sin x\,(1 + \cos x)\) in the interval \([0, \pi]\).

4.
Find the value of \(x\) if \(A = B\), where
\[ A = \begin{bmatrix} 6 & 3x \\ 8 & -6 \end{bmatrix} \text{ and } B = \begin{bmatrix} 6 & x^2+2 \\ 8 & x^2-5x \end{bmatrix}. \]

5.
For events A and B, if \(P(B)=\frac{3}{5}\), \(P(A/B)=\frac{1}{2}\) and \(P(A\cup B)=\frac{4}{5}\), then \(P(A)\) is :

6.
Find the product of the maximum and minimum values of the function \( f(x) = \cos x - \frac{1}{2}\cos 2x,\ x \in \left[0, \frac{\pi}{2}\right] \).

Similar Mathematics Concepts

Comments

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NCERT Solutions For Class 11 Maths Chapter 8: Binomial Theorem

Class 11 Maths NCERT Solutions Chapter 8 Binomial Theorem

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

CBSE CLASS XII Related Questions

1.For the given Linear Programming Problem, shade the feasible region on the graph and write the coordinates of the corner points.Minimize \(Z = 5x + 7y\)subject to constraints\[ 2x + y \geq 8 \]\[ x + 2y \geq 10 \]\[ x,\ y \geq 0. \]

2.The value of \( \left[ \tan^{-1}(-1) + \cos^{-1}\left(-\frac{1}{2}\right) + \sin^{-1}\left(\frac{1}{2}\right) \right] \) is :

3.Find the sum of maximum and minimum values of \(f(x) = \sin x\,(1 + \cos x)\) in the interval \([0, \pi]\).

4.Find the value of \(x\) if \(A = B\), where\[ A = \begin{bmatrix} 6 & 3x \\ 8 & -6 \end{bmatrix} \text{ and } B = \begin{bmatrix} 6 & x^2+2 \\ 8 & x^2-5x \end{bmatrix}. \]

5.For events A and B, if \(P(B)=\frac{3}{5}\), \(P(A/B)=\frac{1}{2}\) and \(P(A\cup B)=\frac{4}{5}\), then \(P(A)\) is :

6.Find the product of the maximum and minimum values of the function \( f(x) = \cos x - \frac{1}{2}\cos 2x,\ x \in \left[0, \frac{\pi}{2}\right] \).

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
For the given Linear Programming Problem, shade the feasible region on the graph and write the coordinates of the corner points.
Minimize \(Z = 5x + 7y\)
subject to constraints
\[ 2x + y \geq 8 \]
\[ x + 2y \geq 10 \]
\[ x,\ y \geq 0. \]

2.
The value of \( \left[ \tan^{-1}(-1) + \cos^{-1}\left(-\frac{1}{2}\right) + \sin^{-1}\left(\frac{1}{2}\right) \right] \) is :

3.
Find the sum of maximum and minimum values of \(f(x) = \sin x\,(1 + \cos x)\) in the interval \([0, \pi]\).

4.
Find the value of \(x\) if \(A = B\), where
\[ A = \begin{bmatrix} 6 & 3x \\ 8 & -6 \end{bmatrix} \text{ and } B = \begin{bmatrix} 6 & x^2+2 \\ 8 & x^2-5x \end{bmatrix}. \]

5.
For events A and B, if \(P(B)=\frac{3}{5}\), \(P(A/B)=\frac{1}{2}\) and \(P(A\cup B)=\frac{4}{5}\), then \(P(A)\) is :

6.
Find the product of the maximum and minimum values of the function \( f(x) = \cos x - \frac{1}{2}\cos 2x,\ x \in \left[0, \frac{\pi}{2}\right] \).