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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.

In the expansion f (7

^{1/3}+ 11^{1/9})^{6561}, the number of terms free from radical is ?If the coeffients of 5th, 6th & 7th terms in expansion of (1+x)

^{n}are in AP, then find values of n???Q:fnd the coeff of x

^{9}y^{-3}inthe expansion of (2x^{2}/y + y/3x)^{12}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

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

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..^{9}in the expansion of (1+ 3x + 3x^{2}+x^{3 })^{15}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

^{99}-19^{93}is divisible by 162 using binomial theorem.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.

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_{2 , }prove that mc_{2}= 3^{n+1}c_{4 }(1+2x+x^2)^20

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 !

^{3})((3/2)x^{2}- 1/3x)^{9.}_{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 tousing binomial therorem, 3

^{2n+2}-8n-9 is divisible by 64, n belongs to N_{1}/C_{0}) + (2C_{2}/C_{1}) + ( 3C_{3}/ C_{2}) +.... + nC_{n}/C_{n-1}= ? Pls solve using summation method. ThanksFind the value of nC0 - nC1 + nC2 - nC3 +.................+(-1)^n nCn

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

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

^{n}C_{1}+ 2.^{n}C2 + 3.^{n}C_{3}+...+^{}n.^{n}C_{n}= n.2^{n}^{2}-x^{3}/6)^{7}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.The cofficient of three consecutive terms in the expansion of (1+x)

^{n}are in the ratio 1:7:42.find n?^{12}.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 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}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 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

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})Show that 2

^{4n}-15n-1 is divisible by 225 by using binomial theorem.Find the coefficient of x^{9}in the expansion of [x^{2}-(1/3x)]^{9 Plz help}using binomial theorem prove that 6

^{n}-5n always remender -1when divided by 25_{0}) - ( C_{1}/2) + ( C_{2}/3) - (C_{3}/ 4) + ...... n terms = ? Pls solve using summation formulaFind the fifth term from the end in the expansion of (x

^{3}/2 - 2/x^{2})^{9}Expand the Binomial (1-3x)

^{5}find the coefficient of x

^{n}in the expansion of(1+x)(1-x)^{n}(a) 2

^{2n}(b) 2^{n}(c) 2^{2n}+ ${}^{2n}{C}_{n}$ (d) $\frac{1}{2}({2}^{2n}+{}^{2n}{C}_{n})$find the [n+1]th term from the end in the expansion of [x-1/x]^3n

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.

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

SOLVE

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

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

find the value of

^{50}C_{0}-^{50}C_{1 }+^{50}C_{2 }-.........+^{50}C_{50}The 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 first 3 terms in the expansion of (1+ax)

^{n}are 1, 12x, 64x^{2}respectively, Find n and 'a' .1. Find the total no. of terms in the expansion of (x+a)^100 + (x-a)^100after simplification

if x is very nearly equal to1 ,show that

1) (mx

^{m}-nx^{n})/(m-n )=x^{m+n}^{th}term in the expansion of (x/3-2/x^{2})^{10}contains x^{4}, then find the value of r