Advertisements
Advertisements
प्रश्न
Find the 4th term from the end in the expansion of `(x^3/2 - 2/x^2)^9`
Advertisements
उत्तर
Since rth term from the end in the expansion of (a + b)n is (n – r + 2)th term from the beginning.
Therefore 4th term from the end is 9 – 4 + 2
i.e., 7th term from the beginning
Which is given by T7 = `""^9"C"_6 (x^3/2) ((-2)/x^2)^6`
= `""^9"C"_3 x^9/8 * 64/x^12`
= `(9 xx 8 xx 7)/(3 xx 2 xx 1) xx 64/x^3`
= `672/x^3`
APPEARS IN
संबंधित प्रश्न
Expand the expression (1– 2x)5
Expand the expression: `(2/x - x/2)^5`
Expand the expression: (2x – 3)6
Expand the expression: `(x/3 + 1/x)^5`
Expand the expression: `(x + 1/x)^6`
Using Binomial Theorem, evaluate of the following:
(102)5
Using binomial theorem, evaluate f the following:
(101)4
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`
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`
If n is a positive integer, prove that \[3^{3n} - 26n - 1\] is divisible by 676.
Using binomial theorem determine which number is larger (1.2)4000 or 800?
Evaluate: `(x^2 - sqrt(1 - x^2))^4 + (x^2 + sqrt(1 - x^2))^4`
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`
Find the coefficient of x50 after simplifying and collecting the like terms in the expansion of (1 + x)1000 + x(1 + x)999 + x2(1 + x)998 + ... + x1000 .
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)`
If the coefficients of x7 and x8 in `2 + x^n/3` are equal, then n is ______.
If (1 – x + x2)n = a0 + a1 x + a2 x2 + ... + a2n x2n , then a0 + a2 + a4 + ... + a2n equals ______.
Find the coefficient of x in the expansion of (1 – 3x + 7x2)(1 – x)16.
Find the coefficient of x15 in the expansion of (x – x2)10.
In the expansion of (x + a)n if the sum of odd terms is denoted by O and the sum of even term by E. Then prove that O2 – E2 = (x2 – a2)n
In the expansion of (x + a)n if the sum of odd terms is denoted by O and the sum of even term by E. Then prove that 4OE = (x + a)2n – (x – a)2n
The number of terms in the expansion of (x + y + z)n ______.
The coefficient of a–6b4 in the expansion of `(1/a - (2b)/3)^10` 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 ______.
