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Syllabus

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

^{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.

^{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

Find the number of terms in the expansion of [(x+y)^3(x-y)^3]^2.

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..Expand the Binomial (1-3x)

^{5}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.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 numberif the coefficient of (r-1)th, rth and (r+1)th terms in the expansion of (1+x)^n are in the ratio 1:7:42, find n and r

solve 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

correct option is D

^{3})((3/2)x^{2}- 1/3x)^{9.}^{50}>(greater than) 100^{50}>(greater than) 99^{50}using binomial therorem, 3

^{2n+2}-8n-9 is divisible by 64, n belongs to N^{n}C_{0}+^{n}C_{1}+^{n}C_{2}+...........+^{n}C_{n}= 2^{n}^{10}Find the value of nC0 - nC1 + nC2 - nC3 +.................+(-1)^n nCn

^{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?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 of^{-15}in the expansion of (3x^{2}- a/3x^{3})^{10}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.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}Using Binomial theorem, expand:( Root x + Root y)

^{10}...prove that

^{n}C_{r}+^{n}C_{r-1}=^{n+1}C_{r}The cofficient of three consecutive terms in the expansion of (1+x)

^{n}are in the ratio 1:7:42.find n?^{2}-2x+1)^{35}is equal to the sum of the coefficients of the expansion (x-ay)^{35}prove that a=1^{-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}^{n}C_{0}+^{n}C_{2}+^{n}C_{4}= 2^{n -1}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

(Summation) of r.r!

r=1 to n

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

correct option is A

Using binomial theoram ,show that 9

^{n+1}-8n-9 is divisible by 64 ,whr n is a positive integer.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 !

in the binomial expansion of (a + b)

^{n}, the coefficient of the 4th and the 13th terms are equal to each other. find n?how we will suppose d 3 consecutive terms in expansion of (1+a) raise to power n if d coefficients of these terms r in ratio 1;7;42?also find n?

^{2})^{4}1. Find the coefficient of x^3in(√(x^5 )+3/√(x^3))^6

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. =)

suppose for (a+b)^6, how to easily and quickly identify it's terms??

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})The coefficient of 3 consecutive terms in the expansion of (1+x)

^{n}are inthe ratio 3 : 8 :14. Find n.if the first three terms in the expansion of (1+ax)^n in ascending power of x are 1+12x+64x^2 find the values of n and a??

_{1}/C_{0}) + (2C_{2}/C_{1}) + ( 3C_{3}/ C_{2}) +.... + nC_{n}/C_{n-1}= ? Pls solve using summation method. ThanksUsing binomial theorem prove that (3

^{2n+2}- 8n - 9) is divisible by 64,where n is a positive integer. Please give me the solution of this as soon as possible. Thank u.Show that 2

^{4n}-15n-1 is divisible by 225 by using binomial theorem.^{2}+x^{3})^{6},the coefficient of x^{14}^{}is ??using binomial theorem prove that 6

^{n}-5n always remender -1when divided by 25^{1/4}+ 1/(3^{1/4})}^{n}is 6^{1/2}: 1Find the fifth term from the end in the expansion of (x

^{3}/2 - 2/x^{2})^{9}find the coefficient of x

^{n}in the expansion of(1+x)(1-x)^{n}correct answer is 50

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.

SOLVE

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

Q.31. The total number of terms which are dependent on the value of x in the expansion of ${\left({x}^{2}-2+\frac{1}{{x}^{2}}\right)}^{n}$ is equal to

a. 2n + 1

b. 2n

c. n

d. n + 1

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??????Pl answer Q 4 (multi answer type)

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

^{st}and 22^{nd}terms in the expansion of (1+x)^{44}are equal , find x(a)7/6 (b)5/8 (c)7/8 (d)6/8

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

^{n}are 1, 12x, 64x^{2}respectively, Find n and 'a' .In the expansion f (7

^{1/3}+ 11^{1/9})^{6561}, the number of terms free from radical is ?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.iam not able to view the ncert solutions of alll subjects