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Write the General Term in the Expansion of (X2 – Yx)12, X ≠ 0 - Mathematics

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प्रश्न

Write the general term in the expansion of (x2 – yx)12x ≠ 0

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उत्तर

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अध्याय 8: Binomial Theorem - Exercise 8.2 [पृष्ठ १७१]

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एनसीईआरटी Mathematics [English] Class 11
अध्याय 8 Binomial Theorem
Exercise 8.2 | Q 4 | पृष्ठ १७१

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संबंधित प्रश्न

Write the general term in the expansion of (x2 – y)6


In the expansion of (1 + a)m + n, prove that coefficients of am and an are equal.


Find a positive value of m for which the coefficient of x2 in the expansion

(1 + x)m is 6


Find the middle term in the expansion of: 

(i)  \[\left( \frac{2}{3}x - \frac{3}{2x} \right)^{20}\]

 


Find the middle term in the expansion of: 

(ii)  \[\left( \frac{a}{x} + bx \right)^{12}\]

 


Find the middle terms in the expansion of: 

(i)  \[\left( 3x - \frac{x^3}{6} \right)^9\]

 


Find the middle terms in the expansion of: 

(iii) \[\left( 3x - \frac{2}{x^2} \right)^{15}\]

 


Find the middle terms(s) in the expansion of:

(ii)  \[\left( 1 - 2x + x^2 \right)^n\]


Find the middle terms(s) in the expansion of: 

(vi)  \[\left( \frac{x}{3} + 9y \right)^{10}\]

 


If the coefficients of \[\left( 2r + 4 \right)\text{ th and } \left( r - 2 \right)\] th terms in the expansion of  \[\left( 1 + x \right)^{18}\]  are equal, find r.

 
 
 

Prove that the term independent of x in the expansion of \[\left( x + \frac{1}{x} \right)^{2n}\]  is \[\frac{1 \cdot 3 \cdot 5 . . . \left( 2n - 1 \right)}{n!} . 2^n .\]

 
 

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

 

If in the expansion of (1 + x)n, the coefficients of three consecutive terms are 56, 70 and 56, then find n and the position of the terms of these coefficients.


If 3rd, 4th 5th and 6th terms in the expansion of (x + a)n be respectively a, b, c and d, prove that `(b^2 - ac)/(c^2 - bd) = (5a)/(3c)`.


If a, b, c and d in any binomial expansion be the 6th, 7th, 8th and 9th terms respectively, then prove that \[\frac{b^2 - ac}{c^2 - bd} = \frac{4a}{3c}\].


If the coefficients of three consecutive terms in the expansion of (1 + x)n be 76, 95 and 76, find n.


If the 6th, 7th and 8th terms in the expansion of (x + a)n are respectively 112, 7 and 1/4, find xan.


Write the middle term in the expansion of  \[\left( x + \frac{1}{x} \right)^{10}\]

 

Write the coefficient of the middle term in the expansion of \[\left( 1 + x \right)^{2n}\] . 

 

If in the expansion of \[\left( x^4 - \frac{1}{x^3} \right)^{15}\] ,  \[x^{- 17}\]  occurs in rth term, then

 

If in the expansion of (1 + y)n, the coefficients of 5th, 6th and 7th terms are in A.P., then nis equal to


In the expansion of \[\left( \frac{1}{2} x^{1/3} + x^{- 1/5} \right)^8\] , the term independent of x is

 

The middle term in the expansion of \[\left( \frac{2x}{3} - \frac{3}{2 x^2} \right)^{2n}\] is 

 

If rth term is the middle term in the expansion of \[\left( x^2 - \frac{1}{2x} \right)^{20}\]  then \[\left( r + 3 \right)^{th}\]  term is

 

 

Find the middle term in the expansion of `(2ax - b/x^2)^12`.


The ratio of the coefficient of x15 to the term independent of x in `x^2 + 2^15/x` is ______.


If p is a real number and if the middle term in the expansion of `(p/2 + 2)^8` is 1120, find p.


If xp occurs in the expansion of `(x^2 + 1/x)^(2n)`, prove that its coefficient is `(2n!)/(((4n - p)/3)!((2n + p)/3)!)`


The position of the term independent of x in the expansion of `(sqrt(x/3) + 3/(2x^2))^10` is ______.


If n is the number of irrational terms in the expansion of `(3^(1/4) + 5^(1/8))^60`, then (n – 1) is divisible by ______.


The term independent of x in the expansion of `[(x + 1)/(x^(2/3) - x^(1/3) + 1) - (x - 1)/(x - x^(1/2))]^10`, x ≠ 1 is equal to ______.


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