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Syllabus

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

^{10}^{10}in the copythe 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.

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 !

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

^{n}are in AP, then find values of n???^{2}+1/x)^{n}is 1024. Find the coefficient of x^{11}in the binomial expansion.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..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 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

The 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

^{21}C_{0}+^{21}C_{1}+^{21}C_{2}+^{21}C_{3}+^{21}C_{4}+ .......... +^{21}C_{10}.^{3})((3/2)x^{2}- 1/3x)^{9.}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

Prove that nc

_{r}/nc_{r-1}=n-r+1/r^{9}in the expansion of (1+ 3x + 3x^{2}+x^{3 })^{15}if three successive coefficients in the expressions of (1+x)

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

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

Find

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

r=1 to n

Find

n, if the ratio of the fifth term from the beginning to the fifth term from the end in the expansion ofFind 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.^{2})^{20}.the first three terms in the expansion of (x+y)^n are 1,56,1372 respectively.Find x and y

^{2}-x^{3}/6)^{7}Q:fnd the coeff of x

^{9}y^{-3}inthe expansion of (2x^{2}/y + y/3x)^{12}^{4}in the expansion of (1+ x -2x^{2})^{7.}The cofficient of three consecutive terms in the expansion of (1+x)

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

^{-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.}Answer is (C10 - B10)

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}find the value of

^{50}C_{0}-^{50}C_{1 }+^{50}C_{2 }-.........+^{50}C_{50}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 theorem prove that 6

^{n}-5n always remender -1when divided by 25if 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.))))))))))))

Using binomial theoram ,show that 9

^{n+1}-8n-9 is divisible by 64 ,whr n is a positive integer.the coefficients of x^2y^2,yzt^2 and xyzt in the expansion of (x+y+z+t)^4 are in the ratio

(a) 4:2:1 (b)1:2:4

(c)2:4:1 (d)1:4:2

in the binomial expansion of (a + b)

^{n}, the coefficient of the 4th and the 13th terms are equal to each other. find n?Expand 2nCn. How does it happen and why?

^{2})^{4}Using Binomial theorem, expand:( Root x + Root y)

^{10}...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 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})_{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_{1}/C_{0}) + (2C_{2}/C_{1}) + ( 3C_{3}/ C_{2}) +.... + nC_{n}/C_{n-1}= ? Pls solve using summation method. ThanksShow that 2

^{4n}-15n-1 is divisible by 225 by using binomial theorem.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.For what value of

mthe coefficients of (2m+1)^{th}and (4m+5)^{th}terms, in the expansion of (1+x)^{th}, are equal?find the tem independent of x in (2x^2-1x)^12

find the coefficient of x

^{n}in the expansion of(1+x)(1-x)^{n}_{2 , }prove that mc_{2}= 3^{n+1}c_{4 }any 3 successive coefficient in the expansion of (1+x)^n where n is a positive integer are 28,56,70 then n is

please give the blueprint of annual examination of maths paper.

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??????( 3x + y )^8 - ( 3x-y )^8

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

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

^{n}are 1, 12x, 64x^{2}respectively, Find n and 'a' .^{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}USING BINOMIAL THEOREM, EXPAND(999)^{4}