Advertisements
Advertisements
प्रश्न
If the coefficients of x7 and x8 in `2 + x^n/3` are equal, then n is ______.
विकल्प
56
55
45
15
Advertisements
उत्तर
If the coefficients of x7 and x8 in `2 + x^"n"/3` are equal, then n is 55.
Explanation:
Since `"T"_("r" + 1) = ""^"n""C"_"r" "a"^("n" - "r") x^"r"` in expansion of (a + x)n
Therefore, T8 = `""^"n""C"_7 (2)^("n" - 7) (x/3)^7`
= `""^"n""C"_7 (2^("n" - 7))/3^7 x^7`
And T9 = `""^"n""C"_8 (2)^("n" - 8) (x/3)^8`
= `""^"n""C"_8 (2^("n" - 8))/3^8 x^8`
Therefore, `""^"n""C"_7 (2^("n" - 7))/3^7`
= `""^"n""C"_8 (2^("n" - 8))/3^8` ....(Since it is given that coefficient of x7 = coefficient x8)
⇒ `"n"/((7)("n" - 7)) xx (8("n" - 8))/"n" = (2^("n" - 8))/3^8 * 3^7/(2^("n" - 7))`
⇒ `8/("n" - 7) = 1/6`
⇒ n = 55
APPEARS IN
संबंधित प्रश्न
Expand the expression (1– 2x)5
Expand the expression: (2x – 3)6
Expand the expression: `(x/3 + 1/x)^5`
Using binomial theorem, evaluate f the following:
(101)4
Find (a + b)4 – (a – b)4. Hence, evaluate `(sqrt3 + sqrt2)^4 - (sqrt3 - sqrt2)^4`
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`
Find a, b and n in the expansion of (a + b)n if the first three terms of the expansion are 729, 7290 and 30375, respectively.
Find the coefficient of x5 in the product (1 + 2x)6 (1 – x)7 using binomial theorem.
Find an approximation of (0.99)5 using the first three terms of its expansion.
Expand using Binomial Theorem `(1+ x/2 - 2/x)^4, x != 0`
Find the expansion of (3x2 – 2ax + 3a2)3 using binomial theorem.
Using binomial theorem determine which number is larger (1.2)4000 or 800?
Find the rth term in the expansion of `(x + 1/x)^(2r)`
Find the 4th term from the end in the expansion of `(x^3/2 - 2/x^2)^9`
Find the coefficient of x11 in the expansion of `(x^3 - 2/x^2)^12`
Find the term independent of x in the expansion of `(sqrt(x)/sqrt(3) + sqrt(3)/(2x^2))^10`.
If n is a positive integer, find the coefficient of x–1 in the expansion of `(1 + x)^2 (1 + 1/x)^n`
If a1, a2, a3 and a4 are the coefficient of any four consecutive terms in the expansion of (1 + x)n, prove that `(a_1)/(a_1 + a_2) + (a_3)/(a_3 + a_4) = (2a_2)/(a_2 + a_3)`
The number of terms in the expansion of (a + b + c)n, where n ∈ N is ______.
Find the coefficient of x15 in the expansion of (x – x2)10.
Find the sixth term of the expansion `(y^(1/2) + x^(1/3))^"n"`, if the binomial coefficient of the third term from the end is 45.
If the coefficient of second, third and fourth terms in the expansion of (1 + x)2n are in A.P. Show that 2n2 – 9n + 7 = 0.
Find the coefficient of x4 in the expansion of (1 + x + x2 + x3)11.
The total number of terms in the expansion of (x + a)100 + (x – a)100 after simplification is ______.
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 ______.
The coefficient of a–6b4 in the expansion of `(1/a - (2b)/3)^10` is ______.
Number of terms in the expansion of (a + b)n where n ∈ N is one less than the power n.
If the coefficients of (2r + 4)th, (r – 2)th terms in the expansion of (1 + x)18 are equal, then r is ______.
The positive integer just greater than (1 + 0.0001)10000 is ______.
