Daily Practice Problems undefined Principle of Mathematical Induction

Question 1:

Using mathematical induction, prove that [Level: Difficult]

Question 2:

For a positive integer n,

let a(n) = . Then [Level: Moderate]

(a) a(100) > 100

(b) a(100) < 100

(d) a(200) 100

Question 3:

Show that n N. [Level: Moderate]

Question 4:

When is a natural number, then is divisible by [Level: Moderate]

(a)

(b)

(d) 1

Question 5:

Which of the following statements best describes the principle of mathematical induction ? [Level: Easy]

(a) It is a method to prove theorems by using calculus.

(b) It is a method to prove theorems by using graphical representations.

(d) It is a method to prove theorems by using algebraic manipulations.

Question 6:

Statement-1: For all natural numbers n, is divisible by 24.

Statement-2: If f(x) is divisible by x, then f(x + 1) – f(x) is divisible by x + 1, x N. [Level: Moderate]

(a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1

(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1

(d) Statement-1 is false, Statement-2 is true

Question 7:

Which of the following statements best describes the principle of mathematical induction ? [Level: Easy]

(a) It is a method to prove theorems by using calculus.

(b) It is a method to prove theorems by using graphical representations.

(d) It is a method to prove theorems by using algebraic manipulations.

Question 8:

Show that . [Level: Difficult]

Question 9:

Consider the statement: “P(n) : n2-n+41 is prime.” Then which one of the following is true ? [Level: Easy]

(a) P(5) is false but P(3) is true

(b) P(3) is false but P(5) is true

(d) Both P(3) and P(5) are true

Question 10:

Statement-1: For all natural numbers n, 1 + 2 + . . . . + n <

Statement-2: For all natural numbers n, [Level: Moderate]

(a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1

(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1

(d) Statement-1 is false, Statement-2 is true

Question 11:

A = , then for n N, is equal to [Level: Moderate]

(a)

(b)

(c)

(d)

Question 12:

In mathematical induction, what is the step called where we assume the theorem is true for a particular value and prove it for the next value ? [Level: Easy]
(a) Base case

(b) Inductive step

(d) Assumption

Question 13:

Using principle of mathematical induction, prove that for all n N, . [Level: Moderate]

Question 14:

For all n N, (3) is divisible by [Level: Moderate]

(a) 17

(b) 19

(d) 23

Question 15:

When P(n) = is divided by 7, then the remainder is [Level: Moderate]

(a) 2

(b) 3

(d) 7

Question 16:

If = having n radical signs. Then, by mathematical induction which one is true ? [Level: Moderate]

(a)

(b)

(c)

(d)

Question 17:

Statement-1: If

Statement-2: [Level: Difficult]

(a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1

(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1

(d) Statement-1 is false, Statement-2 is true

Question 18:

If A = , then for n N, is equal to [Level: Moderate]

(a)

(b)

(c)

(d) None of these

Question 19:

Show that [Level: Difficult]

Question 20:

The smallest positive integer n for which n! < holds, is: [Level: Easy]

(a) 1

(b) 2

(d) 4

**********

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All About Daily Practice Problems on JEE Maths Principle of Mathematical Induction NCERT Chapter 4

Our Daily Practice Problems (DPPs) offer a diverse range of question types, including Multiple Choice Questions (MCQs) as well as short and long answer types. These questions are categorized into Easy, Moderate, and Difficult levels, allowing students to gradually progress and challenge themselves accordingly. Additionally, comprehensive solutions are provided for each question, available for download in PDF format - Download pdf solutions as well as Download pdf Questions. This approach fosters a holistic learning experience, catering to different learning styles, promoting self-assessment, and improving problem-solving skills. With our well-structured DPPs, students can excel in exams while gaining a deeper understanding of the subject matter. Hope you found the content on JEE Maths Principle of Mathematical Induction NCERT Chapter 4 useful.

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