Advertisements
Advertisements
प्रश्न
Find the coefficient of x5 in the product (1 + 2x)6 (1 – x)7 using binomial theorem.
Advertisements
उत्तर
Using Binomial Theorem, the expressions, (1 + 2x)6 and (1 – x)7, can be expanded as

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`
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
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 if the coefficients of x2 and x3 in the expansion of (3 + ax)9 are equal.
Evaluate `(sqrt3 + sqrt2)^6 - (sqrt3 - sqrt2)^6`
Find an approximation of (0.99)5 using the first three terms of its expansion.
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?
Find the value of (1.01)10 + (1 − 0.01)10 correct to 7 places of decimal.
Expand the following (1 – x + x2)4
Find the coefficient of x11 in the expansion of `(x^3 - 2/x^2)^12`
Show that `2^(4n + 4) - 15n - 16`, where n ∈ N is divisible by 225.
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 (1 – x + x2)n = a0 + a1 x + a2 x2 + ... + a2n x2n , then a0 + a2 + a4 + ... + a2n equals ______.
If z = `sqrt(3)/2 + i^5/2 + sqrt(3)/2 - i^5/2`, then ______.
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.
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.
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
Let the coefficients of x–1 and x–3 in the expansion of `(2x^(1/5) - 1/x^(1/5))^15`, x > 0, be m and n respectively. If r is a positive integer such that mn2 = 15Cr, 2r, then the value of r is equal to ______.
The sum of the last eight coefficients in the expansion of (1 + x)16 is equal to ______.
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 ______.
