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RD Sharma Solution Class 11 Mathematics Chapter 12 Mathematical Induction

Chapter 12 – Mathematical Induction Exercise Ex. 12.1

Question 1

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 1

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Question 2

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 2

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Question 3

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 3

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Question 4

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 4

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Question 5

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 5

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Question 6

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 6

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Chapter 12 – Mathematical Induction Exercise Ex. 12.2

Question 1

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 1

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Question 2

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 2

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Question 3

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 3

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Question 4

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 4

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Question 5

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 5

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Question 6

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 6

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Question 7

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 7

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction
Question 8

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 8

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction
Question 9

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 9

 

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction
Question 10

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 10

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Question 11

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 11

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Question 12

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 12

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Question 13

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 13

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction
Question 14

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 14

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Question 15

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 15

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Question 16

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 16

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction
Question 17

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 17

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Question 18

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 18

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Question 19

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 19

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Question 20

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 20

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Question 21

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 21

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Question 22

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 22

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Question 23

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 23

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Question 24

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 24

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Question 25

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 25

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Question 26

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 26

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Question 27

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 27

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Question 28

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 28

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Question 29

Prove by the principle of mathematical induction

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

Solution 29

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Question 30

Prove by the principle of mathematical induction

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

Solution 30

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Question 31

Prove by the principle of mathematical induction

 Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction 

Solution 31

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Question 32

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 32

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Question 33

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 33

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Question 34

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 34

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction
Question 35

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 35

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Question 36

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 36

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction
Question 37

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 37

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Question 38

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 38

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Question 39

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

for all nRd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical InductionN

Solution 39

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Question 40

Prove that

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

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 40

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Question 41

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 41

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Question 42

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 42

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Question 43

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 43

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Question 44

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 44

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Question 45

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

Solution 45

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

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

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Question 47

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction 

Solution 47

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

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

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Question 49

Using principle of mathematical induction prove that

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction 

Solution 49

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

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

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Chapter 12 – Mathematical Induction Exercise Ex. 12VSAQ

Question 1

State the first principle of mathematical induction.

Solution 1

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

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

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Question 4

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

Solution 4

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Mathematical Induction

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