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Syllabus

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

^{10}(1+2x+x^2)^20

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}-x^{3}/6)^{7}If the coeffients of 5th, 6th & 7th terms in expansion of (1+x)

^{n}are in AP, then find values of n???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

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

^{n}are in the ratio 1:7:42. find n.( 3x + y )^8 - ( 3x-y )^8

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.Using Binomial theoram, prove that 2

^{3n }- 7n^{}-1 is divisible by 49 where n is a Natural number^{2})^{4}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 NWrite the no of terms in the expansion of (1-3x+3x

^{2}-x^{3})^{8}^{3})((3/2)x^{2}- 1/3x)^{9.}the first three terms in the expansion of (x+y)^n are 1,56,1372 respectively.Find x and y

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

^{n}are 220, 495 and 792 respectively, find the value of n?Find the value of nC0 - nC1 + nC2 - nC3 +.................+(-1)^n nCn

Find

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

n, if the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of^{n}C_{1}+ 2.^{n}C2 + 3.^{n}C_{3}+...+^{}n.^{n}C_{n}= n.2^{n}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._{n}=^{n}C_{0}.^{n}C_{1}+^{n}C_{1}.^{n}C_{2}+ ..... +^{n}C_{n-1}.^{n}C_{n}and if S_{n+1}/S_{n}= 15/4 then n is equal to^{2})^{4}(1+x^{3})^{7}(1+x^{4})^{12 }??The cofficient of three consecutive terms in the expansion of (1+x)

^{n}are in the ratio 1:7:42.find n?Find the middle term in the expansion: (1 -2x +x

^{2})^{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.}^{1/5}+y^{1/10})^{55},and what is meant by radical sign here?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}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.))))))))))))

^{n}C_{0}+^{n}C_{2}+^{n}C_{4}= 2^{n -1}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 coefficients of 2nd, third and fourth terms in the expansion of (1+n)^2n are in AP.Prove that 2n^2-9n+7=0

Using binomial theoram ,show that 9

^{n+1}-8n-9 is divisible by 64 ,whr n is a positive integer._{1}/C_{0}) + (2C_{2}/C_{1}) + ( 3C_{3}/ C_{2}) +.... + nC_{n}/C_{n-1}= ? Pls solve using summation method. ThanksProve that nc

_{r}/nc_{r-1}=n-r+1/rin the binomial expansion of (a + b)

^{n}, the coefficient of the 4th and the 13th terms are equal to each other. find n?_{o}C_{r}+ C_{1}C_{r+1}+ .... + C_{n-r}C_{n}= (2n)! / (n-r)! (n+r)!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. =)

^{2}+1/x^{2})^{9 .}Find the term independent of x in the expansion of {x+ 1/x}

^{12}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})if the coefficients of a

^{r-1}and a^{r }and a^{r+1}in the binomiaol expansion of (1+a)^{n}are in a.p then prove tht n^{2}-n(4r+1) + 4r^{2}-2 = 0Show that 2

^{4n}-15n-1 is divisible by 225 by using binomial theorem.Find the coefficient of x

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

^{1000}+ 2x(1+x)^{999}+3x^{2}(1+x)^{998}+…………………..+1001x^{1000}If (1+ x - 2x^2)^6 = 1+ a1x + a2x^2 +.........+ a(12)x^12, then prove that a2+a4+a6+........+a12 = 31

using binomial theorem prove that 6

^{n}-5n always remender -1when divided by 25^{1/2}+7^{1/8})^{1024}Find the fifth term from the end in the expansion of (x

^{3}/2 - 2/x^{2})^{9}Q7. Show that

^{n}C_{0}^{n}C_{0 }–^{n+1}C_{1}.^{n}C_{1}+^{n+2}C_{2}^{n}C_{2}– ...... = ( – 1)^{n}.find the coefficient of x

^{n}in the expansion of(1+x)(1-x)^{n}Find (

a+b)^{4}– (a–b)^{4}. Hence, evaluate.please give the blueprint of annual examination of maths paper.

SOLVE

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

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

Answer is (C10 - B10)

if the 21st and 22nd terms in the expansion of (1+x)^44 are equal then find the value of x.

_{0}+c_{1}+c_{2}+........+c_{n}=2^{n}The no of irrational terms in the expansion of (4

^{1/5}+ 7^{1/10})^{45 }are??????^{9}in the expansion of (1+ 3x + 3x^{2}+x^{3 })^{15}1. Find the total no. of terms in the expansion of (x+a)^100 + (x-a)^100after simplification

In the expansion f (7

^{1/3}+ 11^{1/9})^{6561}, the number of terms free from radical is ?prove 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

Write the sum of exponents of x and y in the expansion of ( x +y )

^{n}? Also find the number of terms in the expansion?