NCERT Solutions For Class 11 Mathematics Chapter 4: Principle of Mathematical Induction

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NCERT Solutions for class 11 mathematics Chapter 4 Principles of Mathematical Induction are given in the article. Mathematical Induction is a technique of proving a statement, theorem or formula which is assumed to be true, for each and every natural number n. Important concepts covered in the article are Complex Numbers, Complex Numbers and Quadratic Equations, and Algebraic Operations On Complex Numbers.

Download: NCERT Solutions for Class 11 Mathematics Chapter 4 pdf

Class 11 Maths NCERT Solutions Chapter 4 Principles of Mathematical Induction

Class 11 Maths NCERT Solutions Chapter 4 Principles of Mathematical Induction are as below:

Also check: Principles of Mathematical Induction Important Questions

Important Topics: Class 11 Maths Chapter 4 Principles of Mathematical Induction

Class 11 Maths NCERT Solutions Chapter 4 Principles of Mathematical Induction cover the key steps to prove a theorem. These are as follows:

Base step: To prove P(1) is true.
Assumption step: Assume that P(k) is true for some k in N.
Induction step: Prove that P(k+1) is true.

After proving these 3 steps, it can be concluded that "By the principle of mathematical induction, P(n) is true for all n in N". The assumption that we make in the second step that P(n) holds for some natural number n = k is called induction hypothesis.

Please note: As per Class 11 Maths Updated Syllabus 2022-23, Chapter 4 Principles of Mathematical Induction has been omitted.

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CBSE CLASS XII Related Questions

1.
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 :
2.
Using integration, find the area of the region bounded by the curve $ y = x|x| $, the x-axis, and the vertical lines $ x = -2 $ and $ x = 2 $.
View Solution
3.
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
4.
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 $k$.
- $0$
- $-2$
- $-1$
- $2$
View Solution
5.
Find:

The principal value of \[ \sec^{-1}(\sqrt{2})+2\csc^{-1}(-2) \] is:
- $-\frac{\pi}{2}$
- $-\frac{\pi}{4}$
- $\frac{\pi}{4}$
- $\frac{\pi}{2}$
View Solution
6.
A relation $R$ on set $A=\{1,2,3\}$ defined as $R=\{(1,2),(2,1),(2,2)\}$ is
- Reflexive only
- Reflexive and Transitive
- Symmetric and Transitive
- Symmetric only
View Solution

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You can also check

Principle of Mathematical Induction

NCERT Solutions For Class 11 Mathematics Chapter 4: Principle of Mathematical Induction

Class 11 Maths NCERT Solutions Chapter 4 Principles of Mathematical Induction

Important Topics: Class 11 Maths Chapter 4 Principles of Mathematical Induction

CBSE CLASS XII Related Questions

1.
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 :

2.
Using integration, find the area of the region bounded by the curve \( y = x|x| \), the x-axis, and the vertical lines \( x = -2 \) and \( x = 2 \).

3.
Find:

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

4.
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 \(k\).

5.
Find:

The principal value of \[ \sec^{-1}(\sqrt{2})+2\csc^{-1}(-2) \] is:

6.
A relation $R$ on set $A=\{1,2,3\}$ defined as $R=\{(1,2),(2,1),(2,2)\}$ is

Comments

SUBSCRIBE TO OUR NEWS LETTER

NCERT Solutions For Class 11 Mathematics Chapter 4: Principle of Mathematical Induction

Class 11 Maths NCERT Solutions Chapter 4 Principles of Mathematical Induction

Important Topics: Class 11 Maths Chapter 4 Principles of Mathematical Induction

CBSE CLASS XII Related Questions

1.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 :

2.Using integration, find the area of the region bounded by the curve \( y = x|x| \), the x-axis, and the vertical lines \( x = -2 \) and \( x = 2 \).

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

4. 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 \(k\).

5. Find: The principal value of \[ \sec^{-1}(\sqrt{2})+2\csc^{-1}(-2) \] is:

6.A relation $R$ on set $A=\{1,2,3\}$ defined as $R=\{(1,2),(2,1),(2,2)\}$ is

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
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 :

2.
Using integration, find the area of the region bounded by the curve \( y = x|x| \), the x-axis, and the vertical lines \( x = -2 \) and \( x = 2 \).

3.
Find:

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

4.
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 \(k\).

5.
Find:

The principal value of \[ \sec^{-1}(\sqrt{2})+2\csc^{-1}(-2) \] is:

6.
A relation $R$ on set $A=\{1,2,3\}$ defined as $R=\{(1,2),(2,1),(2,2)\}$ is