Advertisements
Advertisements
प्रश्न
Given the integers r > 1, n > 2, and coefficients of (3r)th and (r + 2)nd terms in the binomial expansion of (1 + x)2n are equal, then ______.
विकल्प
n = 2r
n = 3r
n = 2r + 1
None of these
उत्तर
Given the integers r > 1, n > 2, and coefficients of (3r)th and (r + 2)nd terms in the binomial expansion of (1 + x)2n are equal, then n = 2r.
Explanation:
Given that r > 1 and n > 2
Then `"T"_(3r) = "T"_(3r - 1 + 1)`
= `""^(2n)"C"_(3r - 1) * x^(3r - 1)`
And `"T_(r + 2) = "T"_(r + 1 + 1)`
= `""^(2n)"C"_(r + 1) x^(r + 1)`
We have `""^(2n)"C"_(3r - 1) = ""^(2n)"C"_(r + 1)`
⇒ 3r – 1 + r + 1 = 2n `....[because ""^n"C"_p = ""^n"C"_q ⇒ n = p + q]`
⇒ 4r = 2n
n = 2r
APPEARS IN
संबंधित प्रश्न
Expand the expression: (1– 2x)5
Expand the expression: (2x – 3)6
Expand the expression: `(x + 1/x)^6`
Using Binomial Theorem, evaluate the following:
(96)3
Using Binomial Theorem, evaluate of the following:
(102)5
Using binomial theorem, evaluate f the following:
(101)4
Using binomial theorem, evaluate the following:
(99)5
Using Binomial Theorem, indicate which number is larger (1.1)10000 or 1000.
Find (x + 1)6 + (x – 1)6. Hence or otherwise evaluate `(sqrt2 + 1)^6 + (sqrt2 -1)^6`
Show that 9n+1 – 8n – 9 is divisible by 64, whenever n is a positive integer.
Prove that `sum_(r-0)^n 3^r ""^nC_r = 4^n`
If a and b are distinct integers, prove that a – b is a factor of an – bn, whenever n is a positive integer.
[Hint: write an = (a – b + b)n and expand]
Using binomial theorem determine which number is larger (1.2)4000 or 800?
Expand the following (1 – x + x2)4
Find the 4th term from the end in the expansion of `(x^3/2 - 2/x^2)^9`
Determine whether the expansion of `(x^2 - 2/x)^18` will contain a term containing x10?
If n is a positive integer, find the coefficient of x–1 in the expansion of `(1 + x)^2 (1 + 1/x)^n`
If (1 – x + x2)n = a0 + a1 x + a2 x2 + ... + a2n x2n , then a0 + a2 + a4 + ... + a2n equals ______.
The coefficient of xp and xq (p and q are positive integers) in the expansion of (1 + x)p + q are ______.
The number of terms in the expansion of (a + b + c)n, where n ∈ N is ______.
Find the coefficient of x in the expansion of (1 – 3x + 7x2)(1 – x)16.
The total number of terms in the expansion of (x + a)100 + (x – a)100 after simplification is ______.
If the coefficients of (2r + 4)th, (r – 2)th terms in the expansion of (1 + x)18 are equal, then r is ______.
Let `(5 + 2sqrt(6))^n` = p + f where n∈N and p∈N and 0 < f < 1 then the value of f2 – f + pf – p is ______.
The positive integer just greater than (1 + 0.0001)10000 is ______.
