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Syllabus

Find the term independent of x in the expansion of (2x - 1/x)

^{10}If the coeffients of 5th, 6th & 7th terms in expansion of (1+x)

^{n}are in AP, then find values of n???the second, third and fourth term of the binomial expansion (x+a)n (n is actually (x+a)raised to the power n) are 240, 720 and 1080. find x, a and n.

^{-17 }on the expansion of (x^{4}-1/x^{3})^{15.}.^{1/3}+x^{-1/5)}^{8.}^{8}*y16 in the expansion of (x+y)^{18.}the coefficient of x

^{4}in the expansion of (1+x+x^{2}+x^{3})^{11}is :a) 900 b)909

c) 990 d)999

(1+2x+x^2)^20

If 3rd,4th,5th,6th term in the expansion of (x+alpha)

^{n}be respectively a,b,c and d, prove that b^{2}-ac/c^{2}-bd=4a/3c..if 4th term in the expansion of ( ax+1/x)

^{n }is 5/2, then the values of a and n :a) 1/2,6 b) 1,3

c) 1/2,3

^{2})^{4}Show that the middle term in the expansion of(1+x)raise to power 2n is = 1.3.5.......(2n-1) . 2n.xraise to power n upon n! , where nis a +ve integer.

^{n}are respectively 112,7 and 1/4,find x, a and n.The coefficients of three consecutive terms in the expansion of(1+x)

^{n}are in the ratio 1:7:42. find n.^{3})((3/2)x^{2}- 1/3x)^{9.}Using Binomial theoram, prove that 2

^{3n }- 7n^{}-1 is divisible by 49 where n is a Natural numberif three successive coefficients in the expressions of (1+x)

^{n}are 220, 495 and 792 respectively, find the value of n?solve this

if the coefficients of (r-5)

^{th}and (2r-1)^{th}term in the expansion of (1+x)^{34}are equal, fiind rusing binomial therorem, 3

^{2n+2}-8n-9 is divisible by 64, n belongs to Nin the binomial expansion of (a + b)

^{n}, the coefficient of the 4th and the 13th terms are equal to each other. find n?^{2}-x^{3}/6)^{7}Find

a,bandnin the expansion of (a+b)^{n}if the first three terms of the expansion are 729, 7290 and 30375, respectively.The first 3 terms in the expansion of (1+ax)

^{n}are 1, 12x, 64x^{2}respectively, Find n and 'a' .Find the value of nC0 - nC1 + nC2 - nC3 +.................+(-1)^n nCn

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.Find

n, if the ratio of the fifth term from the beginning to the fifth term from the end in the expansion ofFor what value of

mthe coefficients of (2m+1)^{th}and (4m+5)^{th}terms, in the expansion of (1+x)^{th}, are equal?_{0}/2 ) - ( C_{1}/3) + (C_{2}/4) - ( C_{3}/5) +...... =? Pls solve using summation method. Thanks.The cofficient of three consecutive terms in the expansion of (1+x)

^{n}are in the ratio 1:7:42.find n?Find the coefficient of

x^{5}in the product (1 + 2x)^{6}(1 –x)^{7}using binomial theorem.if the 21st and 22nd terms in the expansion of (1+x)^44 are equal then find the value of x.

Using binomial theoram ,show that 9

^{n+1}-8n-9 is divisible by 64 ,whr n is a positive integer.prove that the term independent of x in the expansion of (x+1/x)^2n is 1.3.5......(2n-1)/n! .2^n

the coefficients of 2nd, third and fourth terms in the expansion of (1+n)^2n are in AP.Prove that 2n^2-9n+7=0

a) 10

b) 20

c) 210

d) none of these

The sum of the coefficients of the first three terms in the expansion of (x-3/x. (NCERT PG 174 EXAMPLE NO 16). The steps in the NCERTbook are not clear..^{2})^{m}, x is not equal to 0,m being a natural number, is 559. Find the term of the wxpansion containing x^{3}the first three terms in the expansion of (x+y)^n are 1,56,1372 respectively.Find x and y

find the [n+1]th term from the end in the expansion of [x-1/x]^3n

The 3rd, 4th and 5th terms in the expansion of (x + a)n are respectively 84, 280 and 560, find the values of x, a and n.

The sum of two numbers is 6 times their geometric mean show that the numbers are in the ratio

(3+2.2^{1/2}):(3-2.2^{1/2})^{2})^{n}in a series of ascending powers of x upto and including the terms in x^{2}if C1, C2, c3, C4 are the coefficient of 2nd, 3rd , 4th , and 5th , term in the expansion of (1+x)raise to "n" then prove that

C1/C1+c2 + c3/c3+c4 = 2c2/c2+c3 ((((((((((((((((((((( where c1+c2 , c3 +c4 and c2 + c3 are together under the division THAT IS C1 BY C1 +C2 etc.))))))))))))

find the first three terms in the expansion of [2+x(3+4x)]^5 in ascending power of x.

This is my doubt:

Find a if the coefficients of x

^{2}and x^{3}in the expansion of (3+ax)^{9 }are equal.Thanks a lot. =)

_{1}/C_{0}) + (2C_{2}/C_{1}) + ( 3C_{3}/ C_{2}) +.... + nC_{n}/C_{n-1}= ? Pls solve using summation method. Thanksshow that the coefficient of the middle term in the expansion of (1+x)^2n is equal to the sum of the coefficients of two middle terms in the expansion (1+x)^2n-1.

using binomial theorem prove that 6

^{n}-5n always remender -1when divided by 25please give the blueprint of annual examination of maths paper.

prove that there is no term involving x^5 int he expansion of (2x^2-3/x)^11

Show that 2

^{4n}-15n-1 is divisible by 225 by using binomial theorem.Find the fifth term from the end in the expansion of (x

^{3}/2 - 2/x^{2})^{9}SOLVE

1) C1+2C2+3C3+--------+nCn=n2 to power n-1

find the coefficient of x

^{n}in the expansion of(1+x)(1-x)^{n}Q26. If first three terms in the expansion of a positive integral power of a binomial are 729, 7290

and 30375 respectively, find the binomial expansion.

any 3 successive coefficient in the expansion of (1+x)^n where n is a positive integer are 28,56,70 then n is

The no of irrational terms in the expansion of (4

^{1/5}+ 7^{1/10})^{45 }are??????Show that the middle term in the expansion of (1+x)^2n is x^n . 1.3..5----(2n-1)/n! 2^n where 'n' is a +ve integer

^{th}term in the expansion of (x/3-2/x^{2})^{10}contains x^{4}, then find the value of rprove that

^{n}C_{r}+^{n}C_{r-1}=^{n+1}C_{r}$ThecorrectformultocalculatethehydroxylionconcentrationofanaqueoussolutionofN{H}_{4}N{O}_{3}is:\phantom{\rule{0ex}{0ex}}\left(a\right)\sqrt{\frac{C\times {K}_{w}}{{K}_{b}}}\phantom{\rule{0ex}{0ex}}\left(b\right)\sqrt{\frac{{K}_{w}\times {K}_{b}}{C}}\phantom{\rule{0ex}{0ex}}\left(c\right)\sqrt{\frac{C\times {K}_{w}}{{K}_{a}}}\phantom{\rule{0ex}{0ex}}\left(d\right)\sqrt{\frac{{K}_{a}\times {K}_{w}}{C}}$

Prove that the coefficient of

x^{n}in the expansion of (1 +x)^{2}^{n}is twice the coefficient ofx^{n}in the expansion of (1 +x)^{2}^{n}^{–1 }.Find the middle term in the expansion: (1 -2x +x

^{2})^{n }1. Find the total no. of terms in the expansion of (x+a)^100 + (x-a)^100after simplification

^{2})^{4}(1+x^{3})^{7}(1+x^{4})^{12 }??In the expansion of (1 +

a)^{m + n}, prove that coefficients ofa^{m}anda^{n}are equal.If coefficient of X^3 and X^4 in expansion of (1+ax+bX^2)(1-2X)^18 in power of X both are zero, then (a,b) equals to ?