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The coefficient of x⁵⁰ in (1 + x)¹⁰⁰ is
Choice (b) is correct. We know that (r + 1) term in the binomial expansion of (1 + x)ⁿ is given by Tᵣ ₊ ₁ = ⁿCᵣ(1)ⁿ ⁻ ʳ xʳ = ⁿCᵣxʳ In the binomial expansion of (1 + x)¹⁰⁰ is given by Tᵣ ₊ ₁ = ¹⁰⁰Cᵣxʳ For coefficient of x⁵⁰, put r = 50 in above, we have T ₅₀ ₊ ₁ = ¹⁰⁰ C₅₀ x⁵⁰ The coefficient x⁵⁰ = Read more
Choice (b) is correct.
We know that (r + 1) term in the binomial expansion of (1 + x)ⁿ is given by
Tᵣ ₊ ₁ = ⁿCᵣ(1)ⁿ ⁻ ʳ xʳ = ⁿCᵣxʳ
In the binomial expansion of (1 + x)¹⁰⁰ is given by
Tᵣ ₊ ₁ = ¹⁰⁰Cᵣxʳ
For coefficient of x⁵⁰, put r = 50 in above, we have T ₅₀ ₊ ₁ = ¹⁰⁰ C₅₀ x⁵⁰
The coefficient x⁵⁰ = ¹⁰⁰ C₅₀
This question related to Chapter 7 maths Class 11th NCERT. From the Chapter 7: Binomial Theorem. Give answer according to your understanding.
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The number of terms in the expansion of (a + b + c)ⁿ, where n ∈ N is
Choice (a) is correct. We have (a + b + c)ⁿ = {a + (b + c)}ⁿ = aⁿ + ⁿC₁aⁿ ⁻ ¹ (b + c) + ⁿC₂aⁿ ⁻ ²(b - c)² + .... + ⁿCₙ(b + c)ⁿ On expanding each term of R.H.S., we get Number of terms in first term = 1 Number of terms in second term = 2 Number of terms in third term = 3 Number of terms in fourth teRead more
Choice (a) is correct.
We have (a + b + c)ⁿ = {a + (b + c)}ⁿ = aⁿ + ⁿC₁aⁿ ⁻ ¹ (b + c) + ⁿC₂aⁿ ⁻ ²(b – c)² + …. + ⁿCₙ(b + c)ⁿ
On expanding each term of R.H.S., we get
Number of terms in first term = 1
Number of terms in second term = 2
Number of terms in third term = 3
Number of terms in fourth term = 4
Number of terms in (n + 1)th term = n + 1
Total number of terms = 1 + 2 + 3 + ….. + (n +1)
= (n – 1) {1 + (n + 1)}/2
= (n + 1)(n + 2) /2
This question related to Chapter 7 maths Class 11th NCERT. From the Chapter 7: Binomial Theorem. Give answer according to your understanding.
For more please visit here:
See lesshttps://www.tiwariacademy.com/ncert-solutions/class-11/maths/#chapter-7
In a sample of ethyl ethanoate (CH3COOC2H5) the two oxygen atoms have the same number of electrons but different number of neutrons. Which of the following is the correct reason for it?
(c) The two oxygen atoms are isotopes. https://www.tiwariacademy.com/ncert-solutions/class-9/science/chapter-4/
(c) The two oxygen atoms are isotopes.
https://www.tiwariacademy.com/ncert-solutions/class-9/science/chapter-4/
See lessIf (1 – x + x²)ⁿ = a₀ + a₁x + a₂x² + a₃x³ + …. + a₂ₙx²ⁿ, then a₁ + a₃ + a₅ …. +a₂ₙ ₋ ₁ equals
Choice (c) is correct. We have, (1 + x + x²)ⁿ = a₀ + a₁x + a₂x² + a₃x³ + .... + a₂ₙx²ⁿ Putting x = 1 and - 1 in (1), we get 1 = a₀ + a₁ + a₂ + a₃ + .... a₂ₙ and 3ⁿ = a₀ + a₁x + a₂x² + a₃x³ + .... + a₂ₙ Subtracting (3) from (2), we get 1 - 3ⁿ = 2(a₁ + a₃ + a₅ .... +a₂ₙ ₋ ₁) ⇒ a₁ + a₃ + a₅ .... +a₂ₙRead more
Choice (c) is correct.
We have, (1 + x + x²)ⁿ = a₀ + a₁x + a₂x² + a₃x³ + …. + a₂ₙx²ⁿ
Putting x = 1 and – 1 in (1), we get
1 = a₀ + a₁ + a₂ + a₃ + …. a₂ₙ
and 3ⁿ = a₀ + a₁x + a₂x² + a₃x³ + …. + a₂ₙ
Subtracting (3) from (2), we get
1 – 3ⁿ = 2(a₁ + a₃ + a₅ …. +a₂ₙ ₋ ₁)
⇒ a₁ + a₃ + a₅ …. +a₂ₙ ₋ ₁ = 1 – 3ⁿ/ 2
This question related to Chapter 7 maths Class 11th NCERT. From the Chapter 7: Binomial Theorem. Give answer according to your understanding.
For more please visit here:
See lesshttps://www.tiwariacademy.com/ncert-solutions/class-11/maths/#chapter-7
The total number of terms in the expansion of (1 + x)¹⁰⁰¹ -x¹⁰⁰¹ is :
Choice (c) is correct. We know that the total number of terms in the expansion of (x + a)ⁿ is (n + 1). Total number of terms in the expansion of (1 + x)¹⁰⁰¹ is (1001 + 1) = 1002. Total number of terms in the expansion of (1 + x) ¹⁰⁰¹ -x¹⁰⁰¹ is 1001 as two terms cancel each other This question relateRead more
Choice (c) is correct.
We know that the total number of terms in the expansion of (x + a)ⁿ is (n + 1).
Total number of terms in the expansion of (1 + x)¹⁰⁰¹ is (1001 + 1) = 1002.
Total number of terms in the expansion of (1 + x) ¹⁰⁰¹ -x¹⁰⁰¹ is 1001 as two terms cancel each other
This question related to Chapter 7 maths Class 11th NCERT. From the Chapter 7: Binomial Theorem. Give answer according to your understanding.
For more please visit here:
See lesshttps://www.tiwariacademy.com/ncert-solutions/class-11/maths/#chapter-7