# RD SHARMA Solutions for Class 11-science Maths Chapter 12 - Mathematical Induction

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Question 2

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## Chapter 12 - Mathematical Induction Exercise Ex. 12.2

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

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Question 7

Solution 7

Question 8

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Question 9

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Question 10

Solution 10

Question 11

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Question 12

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Question 13

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Question 14

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Question 15

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Question 16

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Question 17

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Question 18

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Question 19

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Question 20

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Question 21

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Question 22

Solution 22

Question 23

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Question 24

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Question 25

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Question 26

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Question 27

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Question 32

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Question 33

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Question 34

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Question 36

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Question 37

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Question 38

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Question 39

for all nN

Solution 39

Question 42

Solution 42

Question 43

Solution 43

Question 29

Prove by the principle of mathematical induction

n3 - 7n + 3 is divisible by 3 for all n Î N

Solution 29

Question 30

Prove by the principle of mathematical induction

1 + 2 + 22 +…. + 2n = 2n + 1 -1 for all n Î N

Solution 30

Question 31

Prove by the principle of mathematical induction

Solution 31

Question 40

Prove that

cos a + cos (a + b) + cos (a + 2b) + …..+ cos (a + (n - 1)b)

Solution 40

Question 41

Solution 41

Question 44

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Question 45

Prove that the number of subsets of a set containing n distinct elements is 2n for all n Î N.

Solution 45

Question 46

A sequence a1, a2, a3, …….. is defined by letting a1 = 3 and ak = 7 ak-1 for all natural numbers k ³ 2. Show that an = 3.7n-1 for all n Î N.

Solution 46

Question 47

Solution 47

Question 48

A sequence x0, x1, x2, x3, ……. is defined by letting x0 = 5 and xk = 4 + xk -1 for all natural number k. show that xn = 5 + 4n for all n Î N using mathematical induction.

Solution 48

Question 49

Using principle of mathematical induction prove that

Solution 49

Question 50

The distributive law from algebra states that for all real numbers c, a1 and a2, we have c (a1 + a2) = ca1 + ca2

Use this law and mathematical induction to prove that, for all natural numbers, n ³ 2, if c (a1 + a2 + …. + an) = ca1 + ca2 + …+ can.

Solution 50

Question 28

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Question 35

Solution 35

## Chapter 12 - Mathematical Induction Exercise Ex. 12VSAQ

Question 1

State the first principle of mathematical induction.

Solution 1

Question 2

Write the set of value of n for which the statement P(n):2n

Solution 2

N-{1,2,3} Where N is the set of all natural numbers

Question 3

State the second principle of mathematical induction.

Solution 3

Question 4

Solution 4

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