English

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.

Advertisements
Advertisements

Question

Find ab and n in the expansion of (a + b)n if the first three terms of the expansion are 729, 7290 and 30375, respectively.

Advertisements

Solution

shaalaa.com
  Is there an error in this question or solution?

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Expand the expression (1– 2x)5


Expand the expression: `(2/x - x/2)^5`


Expand the expression: (2x – 3)6


Expand the expression: `(x + 1/x)^6`


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.


Find the coefficient of x5 in the product (1 + 2x)6 (1 – x)7 using binomial theorem.


Evaluate `(sqrt3 + sqrt2)^6 - (sqrt3 - sqrt2)^6`


Expand using Binomial Theorem `(1+ x/2 - 2/x)^4, x != 0`


Find the expansion of (3x2 – 2ax + 3a2)3 using binomial theorem.


Find the value of (1.01)10 + (1 − 0.01)10 correct to 7 places of decimal.

 

Find the rth term in the expansion of `(x + 1/x)^(2r)`


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`


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)`


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 ______.


Find the coefficient of x in the expansion of (1 – 3x + 7x2)(1 – x)16.


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.


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 


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 two successive terms in the expansion of (1 + x)24 whose coefficients are in the ratio 1:4 are ______.


Number of terms in the expansion of (a + b)n where n ∈ N is one less than the power n.


The sum of the last eight coefficients in the expansion of (1 + x)16 is equal to ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×