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Syllabus

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

^{10}^{-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 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.

^{2})^{4}If the coeffients of 5th, 6th & 7th terms in expansion of (1+x)

^{n}are in AP, then find values of n???^{2}-x^{3}/6)^{7}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

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

if three successive coefficients in the expressions of (1+x)

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

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.The coefficients of three consecutive terms in the expansion of(1+x)

^{n}are in the ratio 1:7:42. find n.Using Binomial theoram, prove that 2

^{3n }- 7n^{}-1 is divisible by 49 where n is a Natural numbershow 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.

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 N^{3})((3/2)x^{2}- 1/3x)^{9.}Find

a,bandnin the expansion of (a+b)^{n}if the first three terms of the expansion are 729, 7290 and 30375, respectively.(1+2x+x^2)^20

$ThecorrectformultocalculatethehydroxylionconcentrationofanaqueoussolutionofN{H}_{4}N{O}_{3}is:\phantom{\rule{0ex}{0ex}}\left(a\right)\sqrt{\frac{C\times {K}_{w}}{{K}_{b}}}\phantom{\rule{0ex}{0ex}}\left(b\right)\sqrt{\frac{{K}_{w}\times {K}_{b}}{C}}\phantom{\rule{0ex}{0ex}}\left(c\right)\sqrt{\frac{C\times {K}_{w}}{{K}_{a}}}\phantom{\rule{0ex}{0ex}}\left(d\right)\sqrt{\frac{{K}_{a}\times {K}_{w}}{C}}$

Find the value of nC0 - nC1 + nC2 - nC3 +.................+(-1)^n nCn

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

^{2})^{n}in a series of ascending powers of x upto and including the terms in x^{2}Find

n, if the ratio of the fifth term from the beginning to the fifth term from the end in the expansion ofThe 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.Using binomial theoram ,show that 9

^{n+1}-8n-9 is divisible by 64 ,whr n is a positive integer.the first three terms in the expansion of (x+y)^n are 1,56,1372 respectively.Find x and y

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

in the binomial expansion of (a + b)

^{n}, the coefficient of the 4th and the 13th terms are equal to each other. find n?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 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.

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

If the coefficient of x

^{r}in the expansion of (1-x)^{2n-1}is denoted by a_{r}then prove that a_{r-1}+ a_{2n-r}= 0.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})Q26. â€‹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.

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.))))))))))))

For what value of

mthe coefficients of (2m+1)^{th}and (4m+5)^{th}terms, in the expansion of (1+x)^{th}, are equal?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. =)

The first 3 terms in the expansion of (1+ax)

^{n}are 1, 12x, 64x^{2}respectively, Find n and 'a' .a) 10

b) 20

c) 210

d) none of these

Write the no of terms in the expansion of (1-3x+3x

^{2}-x^{3})^{8}SOLVE

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

using binomial theorem prove that 6

^{n}-5n always remender -1when divided by 25Show that 2

^{4n}-15n-1 is divisible by 225 by using binomial theorem._{1}/C_{0}) + (2C_{2}/C_{1}) + ( 3C_{3}/ C_{2}) +.... + nC_{n}/C_{n-1}= ? Pls solve using summation method. Thanksplease give the blueprint of annual examination of maths paper.

prove that the term independent of x in the expansion of (x+1/x)^2n is 1.3.5......(2n-1)/n! .2^n

^{2}/3+3/2x^{2})^{10}is??Find the fifth term from the end in the expansion of (x

^{3}/2 - 2/x^{2})^{9}find the coefficient of x

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

Find the coefficient of x

^{50 }in the expansion :(1+x)

^{1000}+ 2x(1+x)^{999}+3x^{2}(1+x)^{998}+…………………..+1001x^{1000}^{2}+1/x^{2})^{9 .}if the 21st and 22nd terms in the expansion of (1+x)^44 are equal then find the value of x.

The no of irrational terms in the expansion of (4

^{1/5}+ 7^{1/10})^{45 }are??????Prove that nc

_{r}/nc_{r-1}=n-r+1/rprove that

^{n}C_{r}+^{n}C_{r-1}=^{n+1}C_{r}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

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 }.^{2})^{4}(1+x^{3})^{7}(1+x^{4})^{12 }??1. Find the total no. of terms in the expansion of (x+a)^100 + (x-a)^100after simplification

^{10}in (1-x^{2})^{10}and the term independent of x in (x-2/x)^{10}is 1 :32 .In the expansion of (1 +

a)^{m + n}, prove that coefficients ofa^{m}anda^{n}are equal._{0}/2 ) - ( C_{1}/3) + (C_{2}/4) - ( C_{3}/5) +...... =? Pls solve using summation method. Thanks.