# Important Topic Binomial Theorem For Maths NCERT Solutions Class 11 - PowerPoint PPT Presentation

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## Important Topic Binomial Theorem For Maths NCERT Solutions Class 11

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Title: Important Topic Binomial Theorem For Maths NCERT Solutions Class 11

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Binomial Theorem Maths NCERT Solutions Class 11
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Binomial Theorem Maths NCERT Solutions Class 11
• Maths NCERT Solutions Class 11  Suppose you need
to calculate the amount of interest you will get
after 5 years on a sum
• of money that you have invested at the rate of
15 compound interest per year. Or
• suppose we need to find the size of the
population of a country after 10 years if we know
• the annual growth rate. A result that will help
in finding these quantities is the binomial
• theorem. This theorem, as you will see, helps us
to calculate the rational powers of any
• real binomial expression, that is, any expression
involving two terms.
several assertions in the form of sentences. Of
• these assertions, the ones that are either true
or false are called statement or propositions.
• For instance,
• I am 20 years old and If x 3, then x2  9
are statements, but When will you leave? And
• How wonderful! are not statements.
• Notice that a statement has to be a definite
assertion which can be true or false, but not
both.
• For example, x 5 7 is not a statement
because we dont know what x, is. If x 12, it
is
• true, but if x 5, it is not true. Therefore,
x 5 7 is not accepted by mathematicians as
a
• statement.

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Binomial Theorem Maths NCERT Solutions Class 11
• But both x 5 7 ?x 12 and x 5 7 for
any real number x are statements, the first one
• true and the second one false.
• Maths NCERT Solutions Class 11 are available,
click CBSE Class 11th Maths for details.
• For the better and interesting learning through
animated lectures NCERT Maths Class 11 visit
our Maths Section
• Ques. If P (n) denotes 2ngt n1, write P (1), P
(k) and P (k1), where k ? N.
• Solution Replacing n by 1, k and k 1,
respectively in P (n),
• We get P (1) 21gt 2 1, i.e., 2 gt 1
• P (k) 2kgt k 1
• P (k 1) 2k1gt (k 1) 1, i.e., 2k1gt k
• Ques. If P (n) is the statement
• 1 4 7 (3n 2) n(3n - 1)/2
• Write P (1), P(k) and P(k 1).
• Solution To write P(1), the terms on the
left-hand side (LHS) of P(n) continue till
• 3 1 2, i.e., 1. So, P (1) will have only one
term in its LHS, i.e., the first term.
• Also, the right hand side (RHS) of P(1)
1(31-1) / 2
• 1

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Binomial Theorem Maths NCERT Solutions Class 11
• Therefore, P (1) is 1 1.
• Replacing n by 2, we get
• P(2) 1 4 2(32-1) / 2
• i.e., 5 5.
• Replacing n by k and k 1, respectively, we get
• P(k) 1 4 7 . (3k 2)
•   k(3k 1) / 2
• P(k 1) 1 4 7 . (3k 2) 3 (k 1)
2
• (k1)3(k1)-1 / 2
• i.e. , 1 4 7 . (3k 1) (k 1)(3k 2)
/ 2.
• For the better and interesting learning through
animated lectures visit www.takshilalearning.com

5
Binomial Theorem Maths NCERT Solutions Class 11
• After studying this lesson, you will be able to
• state the Principle of (finite) Mathematical
Induction
• verify the truth or otherwise of the statement
P(n) for n 1
• verify if P(k1) is true, assuming that P(k) is
true
• use the principle of mathematical induction to
establish the truth or otherwise of mathematical
statements
• state the binomial theorem for a positive
integral index and prove it using the principle
of mathematical induction
• write the binomial expansion for expressions like
( x y ) n for different values of x and y using
binomial theorem
• write the general term and middle term (s) of a
binomial expansion
• write the binomial expansion for negative as well
as for rational indices
• apply the binomial expansion for finding
approximate values of numbers like 3v9, v2,  3v3
etc and
• apply the binomial expansion to evaluate
algebraic expressions like ( 3 5/x)7, where x
is so small that 2 x and higher powers of x can
be neglected.
•

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Binomial Theorem Maths NCERT Solutions Class 11
• To be continued..
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