jee/cbse 2021: binomial theorem l-2
TRANSCRIPT
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JEE/CBSE 2021: Binomial Theorem L-2 General term
JEE/CBSE 2021: Binomial Theorem L-2
General term
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JEE/CBSE 2021: Binomial Theorem L-2 General term
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JEE/CBSE 2021: Binomial Theorem L-2 General term
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
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JEE/CBSE 2021: Binomial Theorem L-2 General term
Q1. Find general term in expansion of (2 + x) 10
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JEE/CBSE 2021: Binomial Theorem L-2 General term
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 :
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JEE/CBSE 2021: Binomial Theorem L-2 General term
Q2. Find 5th term in expansion of (2 + x) 7
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JEE/CBSE 2021: Binomial Theorem L-2 General term
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 :
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JEE/CBSE 2021: Binomial Theorem L-2 General term
Q3. Find the 7th term from the end in expansion of
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JEE/CBSE 2021: Binomial Theorem L-2 General term
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 :
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JEE/CBSE 2021: Binomial Theorem L-2 General term
Q4. If 21st and 22nd terms in the expansion of (1 + x)44 are equal then find ‘x’
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JEE/CBSE 2021: Binomial Theorem L-2 General term
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 :
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JEE/CBSE 2021: Binomial Theorem L-2 General term
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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JEE/CBSE 2021: Binomial Theorem L-2 General term
Solution :
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JEE/CBSE 2021: Binomial Theorem L-2 General term
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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JEE/CBSE 2021: Binomial Theorem L-2 General term
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
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JEE/CBSE 2021: Binomial Theorem L-2 General term
Solution :
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JEE/CBSE 2021: Binomial Theorem L-2 General term
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
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JEE/CBSE 2021: Binomial Theorem L-2 General term
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
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JEE/CBSE 2021: Binomial Theorem L-2 General term
Solution :
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JEE/CBSE 2021: Binomial Theorem L-2 General term
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
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JEE/CBSE 2021: Binomial Theorem L-2 General term
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
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JEE/CBSE 2021: Binomial Theorem L-2 General term
Solution :
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JEE/CBSE 2021: Binomial Theorem L-2 General term
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JEE/CBSE 2021: Binomial Theorem L-2 General term
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JEE/CBSE 2021: Binomial Theorem L-2 General term
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JEE/CBSE 2021: Binomial Theorem L-2 General term
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