Advertisements
Advertisements
प्रश्न
Determine whether the expansion of `(x^2 - 2/x)^18` will contain a term containing x10?
Advertisements
उत्तर
Let Tr+1 contain x10.
Then Tr+1 = `""^18"C"_r (x^2)^(18 - r) (-2^r)/x`
= `""^18"C"_r x^(36 - 2r) (-1)^r * 2^r x^(-r)`
= `(-1)^r 2^r ""^18"C"_r x^(36 - 3r)`
Thus, 36 – 3r = 10
i.e., r = `36/3`
Since r is a fraction, the given expansion cannot have a term containing x10.
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 the following:
(96)3
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.
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 a if the coefficients of x2 and x3 in the expansion of (3 + ax)9 are equal.
Find the expansion of (3x2 – 2ax + 3a2)3 using binomial theorem.
If n is a positive integer, prove that \[3^{3n} - 26n - 1\] is divisible by 676.
Find the value of (1.01)10 + (1 − 0.01)10 correct to 7 places of decimal.
Show that \[2^{4n + 4} - 15n - 16\] , where n ∈ \[\mathbb{N}\] is divisible by 225.
Find the rth term in the expansion of `(x + 1/x)^(2r)`
Expand the following (1 – x + x2)4
Find the coefficient of x11 in the expansion of `(x^3 - 2/x^2)^12`
Which of the following is larger? 9950 + 10050 or 10150
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 ______.
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 ______.
If z = `sqrt(3)/2 + i^5/2 + sqrt(3)/2 - i^5/2`, then ______.
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 total number of terms in the expansion of (x + a)100 + (x – a)100 after simplification is ______.
The coefficient of a–6b4 in the expansion of `(1/a - (2b)/3)^10` 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 ______.
