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Syllabus

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

^{10}Show that C_{0}/2 + C_{1}/3 + C_{2}/4 + ......... + C_{n}/n+2 = (1+n.2^{(n+1)})/(n+1)(n+2)Please tell me the answer to this question. Need urgently. Help from meritnation experts would be commendable . Please help !

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.

^{21}C_{0}+^{21}C_{1}+^{21}C_{2}+^{21}C_{3}+^{21}C_{4}+ .......... +^{21}C_{10}.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

In the expansion f (7

^{1/3}+ 11^{1/9})^{6561}, the number of terms free from radical is ?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..^{2}+1/x)^{n}is 1024. Find the coefficient of x^{11}in the binomial expansion.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

^{10}in the copyThe coefficients of three consecutive terms in the expansion of(1+x)

^{n}are in the ratio 1:7:42. find n.Find the fifth term from the end in the expansion of (x

^{3}/2 - 2/x^{2})^{9}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 first three terms in the expansion of [2+x(3+4x)]^5 in ascending power of x.

Using Binomial theoram, prove that 2

^{3n }- 7n^{}-1 is divisible by 49 where n is a Natural numbersolve this

if the coefficients of (r-5)

^{th}and (2r-1)^{th}term in the expansion of (1+x)^{34}are equal, fiind r(1+2x+x^2)^20

^{n}C_{1}+ 2.^{n}C2 + 3.^{n}C_{3}+...+^{}n.^{n}C_{n}= n.2^{n}^{3})((3/2)x^{2}- 1/3x)^{9.}If x+y=1, then Σ(from r=0 to r=n) r

^{ n}C_{r}x^{r}y^{n-r }equalsA) 1

B) n

C) nx

D) ny

Thank You

using binomial therorem, 3

^{2n+2}-8n-9 is divisible by 64, n belongs to NFind 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 toif three successive coefficients in the expressions of (1+x)

^{n}are 220, 495 and 792 respectively, find the value of n?(Summation) of r.r!

r=1 to n

Find

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

n, if the ratio of the fifth term from the beginning to the fifth term from the end in the expansion ofif 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 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.Prove that nc

_{r}/nc_{r-1}=n-r+1/rthe first three terms in the expansion of (x+y)^n are 1,56,1372 respectively.Find x and y

ï»¿ï»¿

^{n}E_{r=0}^{n}C_{r}sin2rx /^{n}E_{r=0}^{n}C_{r}cos2rx = tan nxE--->Sigma(summation).

^{2}-x^{3}/6)^{7}^{2})^{20}.The cofficient of three consecutive terms in the expansion of (1+x)

^{n}are in the ratio 1:7:42.find n?T?_{r+1}=^{n}Cr .a^{n-r} .b^{r}And when should you use this formula-

T?_{r+1}= (-1)^{n}C_{r }.a^{n-r}.(+b)^{r}^{-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}Answer is (C10 - B10)

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.

^{40}in the expansion of (1/x^{2}+ x^{4})^{18}^{st}4 terms in the expansion of ( 1 –x )^{-1/4}^{2}/4)^{9}^{3}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

SOLVE

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

^{n}C_{0}+^{n}C_{2}+^{n}C_{4}= 2^{n -1}Using binomial theoram ,show that 9

^{n+1}-8n-9 is divisible by 64 ,whr n is a positive integer.Expand 2nCn. How does it happen and why?

in the binomial expansion of (a + b)

^{n}, the coefficient of the 4th and the 13th terms are equal to each other. find n?^{2})^{4}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. =)

Using Binomial theorem, expand:( Root x + Root y)

^{10}...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})_{1}/C_{0}) + (2C_{2}/C_{1}) + ( 3C_{3}/ C_{2}) +.... + nC_{n}/C_{n-1}= ? Pls solve using summation method. ThanksQ:fnd the coeff of x

^{9}y^{-3}inthe expansion of (2x^{2}/y + y/3x)^{12}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 25_{o}C_{r}+ C_{1}C_{r+1}+ .... + C_{n-r}C_{n}= (2n)! / (n-r)! (n+r)!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

^{9}in the expansion of (1+ 3x + 3x^{2}+x^{3 })^{15}please give the blueprint of annual examination of maths paper.

^{4}in the expansion of (1+ x -2x^{2})^{7.}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??????expand (x+1/x)

^{6 using binomial theoram}Find the coefficient of x

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

^{1000}+ 2x(1+x)^{999}+3x^{2}(1+x)^{998}+…………………..+1001x^{1000}1. Find the total no. of terms in the expansion of (x+a)^100 + (x-a)^100after simplification

_{2 , }prove that mc_{2}= 3^{n+1}c_{4 }The first 3 terms in the expansion of (1+ax)

^{n}are 1, 12x, 64x^{2}respectively, Find n and 'a' .Q. A committee of seven students is formed selecting from 6 boys and 5 girls such that majority are from boys. How many different committees can be formed?

^{2}+1/x]^{12}