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Syllabus

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

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

Q:fnd the coeff of x

^{9}y^{-3}inthe expansion of (2x^{2}/y + y/3x)^{12}If the coeffients of 5th, 6th & 7th terms in expansion of (1+x)

^{n}are in AP, then find values of n???In the expansion f (7

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

^{9}in the expansion of (1+ 3x + 3x^{2}+x^{3 })^{15}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..find the first three terms in the expansion of [2+x(3+4x)]^5 in ascending power of x.

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.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.

^{99}-19^{93}is divisible by 162 using binomial theorem.Using Binomial theoram, prove that 2

^{3n }- 7n^{}-1 is divisible by 49 where n is a Natural number( 3x + y )^8 - ( 3x-y )^8

solve this

if the coefficients of (r-5)

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

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

_{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^{3})((3/2)x^{2}- 1/3x)^{9.}_{2 , }prove that mc_{2}= 3^{n+1}c_{4 }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

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

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

a,bandnin the expansion of (a+b)^{n}if the first three terms of the expansion are 729, 7290 and 30375, respectively._{1}/C_{0}) + (2C_{2}/C_{1}) + ( 3C_{3}/ C_{2}) +.... + nC_{n}/C_{n-1}= ? Pls solve using summation method. ThanksFind

n, if the ratio of the fifth term from the beginning to the fifth term from the end in the expansion ofIf 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

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.^{12}.the first three terms in the expansion of (x+y)^n are 1,56,1372 respectively.Find x and y

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

^{n}are in the ratio 1:7:42.find n?Find the remainder when 27

^{10}+7^{51 }divided by 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 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}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 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

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

Using binomial theoram ,show that 9

^{n+1}-8n-9 is divisible by 64 ,whr n is a positive integer.^{2})^{4}^{n}C_{1}+ 2.^{n}C2 + 3.^{n}C_{3}+...+^{}n.^{n}C_{n}= n.2^{n}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 [n+1]th term from the end in the expansion of [x-1/x]^3n

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

Show that 2

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

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

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

^{3}/2 - 2/x^{2})^{9}The first 3 terms in the expansion of (1+ax)

^{n}are 1, 12x, 64x^{2}respectively, Find n and 'a' .find the coefficient of x

^{n}in the expansion of(1+x)(1-x)^{n}if x is very nearly equal to1 ,show that

1) (mx

^{m}-nx^{n})/(m-n )=x^{m+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

^{th}term in the expansion of (x/3-2/x^{2})^{10}contains x^{4}, then find the value of rplease give the blueprint of annual examination of maths paper.

SOLVE

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

prove nPr=

n!(n-r)!

and deduce it to nCr answere fast important for test

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

^{50}are equalThe no of irrational terms in the expansion of (4

^{1/5}+ 7^{1/10})^{45 }are??????Find the coefficient of x

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

^{1000}+ 2x(1+x)^{999}+3x^{2}(1+x)^{998}+…………………..+1001x^{1000}the last digit of 3 ^ 3 ^ 4n+1 where n belongs to natural numbers is

1. Find the total no. of terms in the expansion of (x+a)^100 + (x-a)^100after simplification

Find the coefficient of x

^{32 }and x^{-17 }in the expansion of (x^{4}-^{1}/x^{3})^{15.}^{n}C_{0}+ 2.^{n}C_{1}+ 3.^{n}C_{2}+ ........... +(n+1).^{n}C_{n}= (n+2).2^{(}^{n-1)}.