English

Find a If the Coefficients of X2 and X3 in the Expansion of (3 + Ax)9 Are Equal. - Mathematics

Advertisements
Advertisements

Question

Find a if the coefficients of x2 and x3 in the expansion of (3 + ax)9 are equal.

Advertisements

Solution

shaalaa.com
  Is there an error in this question or solution?
Chapter 8: Binomial Theorem - Miscellaneous Exercise [Page 175]

APPEARS IN

NCERT Mathematics [English] Class 11
Chapter 8 Binomial Theorem
Miscellaneous Exercise | Q 1 | Page 175

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/3 + 1/x)^5`


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


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


Find (x + 1)6 + (x – 1)6. Hence or otherwise evaluate `(sqrt2 + 1)^6 + (sqrt2 -1)^6`


Prove that `sum_(r-0)^n 3^r  ""^nC_r = 4^n`


If a and b are distinct integers, prove that a – b is a factor of an – bn, whenever n is a positive integer.

[Hint: write an = (a – b + b)n and expand]


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


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.

 
 

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 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`


Determine whether the expansion of `(x^2 - 2/x)^18` will contain a term containing x10?


Find the term independent of x in the expansion of `(sqrt(x)/sqrt(3) + sqrt(3)/(2x^2))^10`.


Show that `2^(4n + 4) - 15n - 16`, where n ∈ N is divisible by 225.


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 .


The coefficient of xp and xq (p and q are positive integers) in the expansion of (1 + x)p + q are ______.


Find the coefficient of x15 in the expansion of (x – x2)10.


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 ______.


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.


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 ______.


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 ______. 


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×