JEE/CBSE 2021: Binomial Theorem L-2

JEE/CBSE 2021: Binomial Theorem L-2 General term

JEE/CBSE 2021: Binomial Theorem L-2

General term


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General term :

Lets observe

(a + b)n = nC0 + nC1 + nC2 + …….. nCnanb0 an–1b1 an–2b2 a0bn

Lets observe termsFirst term = T1 = nC0 a

nb0

Second term = T2 = nC1 an – 1 b1

Third term = T3 = nC2 an – 2 b2

From above we can write general term asTr + 1 = nCr a

n–r br


Q1. Find general term in expansion of (2 + x) 10


Find general term in expansion of (2 + x)10

In this a = 2, b = x, n = 10

Tr+

1

= nCran–r br

= 10Cr (2)10–r (x)r

Solution :


Q2. Find 5th term in expansion of (2 + x) 7


Find 5th term in expansion of (2 + x)7

As we need T5

r + 1 = 5

r = 4

a = 2, b = x, n = 7

Tr+

1

= nCr (a)n–r br

T5 = T4+1 = 7C4(2)7– 4 (x)4

= 7C4(2)3 x4

Solution :


Q3. Find the 7th term from the end in expansion of


a = x , b =– 2x2 , n = 10

Total number of terms = 10 + 1 = 11

7th term from end = 5th term from start

General term Tr+1 = nC (a)n – r (b)r

r

T5 = T4 + 1 = 10C4 (x)10 – 4 – 2x2

4=

10C4(2)4

x2

Solution :


Q4. If 21st and 22nd terms in the expansion of (1 + x)44 are equal then find ‘x’


Tr + 1 = nCr (x)n – r (y)r

T21 = T22

In the problema = 1, b = x, n = 44

44C20 (1)44 – 20 (x)20 = 44C21 (1)44 – 21 (x)21

44C2044C21

44 !20 ! 24 !

44 !21 ! 23 !

⇒ x = 2124

= 78

= x ⇒ x =

Solution :


Q5. The sum of coefficients of integral powers of x in the binomial expansion of

JEE Main 2015A

B

D

C


Solution :


Q5. The sum of coefficients of integral powers of x in the binomial expansion of

JEE Main 2015A

B

D

C

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Q6. If the coefficients of x3 and x4 in the expansion of (1 + ax + bx2) (1 - 2x)18 in powers of x are both zero, then (a, b) is equal to

A

B

D

C

JEE Main 2014


Solution :


Q6. If the coefficients of x3 and x4 in the expansion of (1 + ax + bx2) (1 - 2x)18 in powers of x are both zero, then (a, b) is equal to

A

B

D

C

JEE Main 2014


Q7. The coefficient of x7 in the expansion of ( 1-x-x2+x3)6 is

A

B

D

C

-132

-144

144

132

AIEEE 2011


Solution :


Q7. The coefficient of x7 in the expansion of ( 1-x-x2+x3)6 is

A

B

D

C

-132

-144

144

132

AIEEE 2011


Q8. If sum of the coefficients of the first, second and third terms of the expansion of is 46, then find the coefficient of the term

that does not contain x


Solution :





Thank You

Documents

JEE/CBSE 2021: Binomial Theorem L-2