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Syllabus

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

^{10}^{2}-x^{3}/6)^{7}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.

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

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

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.the first three terms in the expansion of (x+y)^n are 1,56,1372 respectively.Find x and y

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.

^{2})^{4}Using Binomial theoram, prove that 2

^{3n }- 7n^{}-1 is divisible by 49 where n is a Natural number^{n}are respectively 112,7 and 1/4,find x, a and 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 N^{3})((3/2)x^{2}- 1/3x)^{9.}^{2})^{4}(1+x^{3})^{7}(1+x^{4})^{12 }??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

_{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 toFind

a,bandnin the expansion of (a+b)^{n}if the first three terms of the expansion are 729, 7290 and 30375, respectively.^{n}C_{1}+ 2.^{n}C2 + 3.^{n}C_{3}+...+^{}n.^{n}C_{n}= n.2^{n}Find

n, if the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of( 3x + y )^8 - ( 3x-y )^8

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.SOLVE

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

_{o}C_{r}+ C_{1}C_{r+1}+ .... + C_{n-r}C_{n}= (2n)! / (n-r)! (n+r)!The cofficient of three consecutive terms in the expansion of (1+x)

^{n}are in the ratio 1:7:42.find n?^{n}C_{0}+^{n}C_{2}+^{n}C_{4}= 2^{n -1}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.}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}^{1/5}+y^{1/10})^{55},and what is meant by radical sign here?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.

C1/(C1+C2) + C3/(C3+C4) = 2*C2/(C2+C3)

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

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

Using binomial theoram ,show that 9

^{n+1}-8n-9 is divisible by 64 ,whr n is a positive integer.^{2}+1/x^{2})^{9 .}in the binomial expansion of (a + b)

^{n}, the coefficient of the 4th and the 13th terms are equal to each other. find n?^{9}in the expansion of (1+ 3x + 3x^{2}+x^{3 })^{15}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. =)

Find the term independent of x in the expansion of {x+ 1/x}

^{12}_{1}/C_{0}) + (2C_{2}/C_{1}) + ( 3C_{3}/ C_{2}) +.... + nC_{n}/C_{n-1}= ? Pls solve using summation method. ThanksThe 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})Show that 2

^{4n}-15n-1 is divisible by 225 by using binomial theorem.using binomial theorem prove that 6

^{n}-5n always remender -1when divided by 25If 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.Find the fifth term from the end in the expansion of (x

^{3}/2 - 2/x^{2})^{9}show 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.

find the coefficient of x

^{n}in the expansion of(1+x)(1-x)^{n}Prove that nc

_{r}/nc_{r-1}=n-r+1/rplease give the blueprint of annual examination of maths paper.

Find (

a+b)^{4}– (a–b)^{4}. Hence, evaluate.any 3 successive coefficient in the expansion of (1+x)^n where n is a positive integer are 28,56,70 then n is

^{5}- (root2- 1)^{5}.if the 21st and 22nd terms in the expansion of (1+x)^44 are equal then find the value of x.

Answer is (C10 - B10)

The no of irrational terms in the expansion of (4

^{1/5}+ 7^{1/10})^{45 }are??????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 = 01. Find the total no. of terms in the expansion of (x+a)^100 + (x-a)^100after simplification

_{0}+c_{1}+c_{2}+........+c_{n}=2^{n}Find the coefficient of x

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

^{1000}+ 2x(1+x)^{999}+3x^{2}(1+x)^{998}+…………………..+1001x^{1000}^{}^{2n-1}C_{n-1}+^{2n-1}C_{n }=^{2n}C_{n but not by directly using properties of combination but by actual combination formula}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