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.
Assertion (A) : In an experiment of throwing an unbiased die, the probability of getting a prime number given that number appearing on the die being odd is \( \frac{2}{3} \).
Reason (R) : For any two events \( A \) and \( B \), \( P(A|B) = \frac{P(A \cup B)}{P(B)} \).
- 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 and Reason (R) is false.
- Assertion (A) is false and Reason (R) is true.
View Solution
2.
Sports car racing is a form of motorsport which uses sports car prototypes.The competition is held on special tracks designed in various shapes.
The equation of a sports car racing track is given as: \[ f(x)= \begin{cases} x^4-4x^2+4, & 0\leq x<3,\\ x^2+40, & x\geq 3 \end{cases} \] Based on this information:
3.
Check whether \[ f:\mathbb{R}-\{3\}\rightarrow\mathbb{R} \] defined as \[ f(x)=\frac{x-2}{x-3} \] is onto or not.
View Solution
4.
For a square matrix \(A\), \[ (3A)^{-1}= \]
- \( 3A^{-1} \)
- \( 9A^{-1} \)
- \( \frac{1}{3} A^{-1} \)
- \( \frac{1}{9} A^{-1} \)
View Solution
5.
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.
View Solution
6.
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.
View Solution

View All

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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.
Assertion (A) : In an experiment of throwing an unbiased die, the probability of getting a prime number given that number appearing on the die being odd is \( \frac{2}{3} \).
Reason (R) : For any two events \( A \) and \( B \), \( P(A|B) = \frac{P(A \cup B)}{P(B)} \).

3.
Check whether \[ f:\mathbb{R}-\{3\}\rightarrow\mathbb{R} \] defined as \[ f(x)=\frac{x-2}{x-3} \] is onto or not.

4.
For a square matrix \(A\), \[ (3A)^{-1}= \]

5.
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.

6.
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): \[ |\vec{a}\times\vec{b}| = (\vec{a}\cdot\vec{b})\tan\theta, \quad \theta\neq\frac{\pi}{2}. \]

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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.Assertion (A) : In an experiment of throwing an unbiased die, the probability of getting a prime number given that number appearing on the die being odd is \( \frac{2}{3} \). Reason (R) : For any two events \( A \) and \( B \), \( P(A|B) = \frac{P(A \cup B)}{P(B)} \).

3.Check whether \[ f:\mathbb{R}-\{3\}\rightarrow\mathbb{R} \] defined as \[ f(x)=\frac{x-2}{x-3} \] is onto or not.

4. For a square matrix \(A\), \[ (3A)^{-1}= \]

5.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.

6.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): \[ |\vec{a}\times\vec{b}| = (\vec{a}\cdot\vec{b})\tan\theta, \quad \theta\neq\frac{\pi}{2}. \]

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Assertion (A) : In an experiment of throwing an unbiased die, the probability of getting a prime number given that number appearing on the die being odd is \( \frac{2}{3} \).
Reason (R) : For any two events \( A \) and \( B \), \( P(A|B) = \frac{P(A \cup B)}{P(B)} \).

3.
Check whether \[ f:\mathbb{R}-\{3\}\rightarrow\mathbb{R} \] defined as \[ f(x)=\frac{x-2}{x-3} \] is onto or not.

4.
For a square matrix \(A\), \[ (3A)^{-1}= \]

5.
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.

6.
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): \[ |\vec{a}\times\vec{b}| = (\vec{a}\cdot\vec{b})\tan\theta, \quad \theta\neq\frac{\pi}{2}. \]