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Syllabus

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

^{10}^{4 }(2x^{2}+m/x)^{7}is 896. Find m.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.

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

^{n}are in AP, then find values of 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.))))))))))))

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

(Summation) of r.r!

r=1 to n

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

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.

^{n}C_{0}+^{n}C_{2}+^{n}C_{4}= 2^{n -1}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 rthe 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

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

^{8}^{3})((3/2)x^{2}- 1/3x)^{9.}using binomial therorem, 3

^{2n+2}-8n-9 is divisible by 64, n belongs to NSolve this:Find the coefficient of x

^{49}in the polynomial$\left(x-\frac{{C}_{1}}{{C}_{0}}\right)\left(x-{2}^{2}\frac{{C}_{2}}{{C}_{1}}\right)\left(x-{3}^{2}.\frac{{C}_{3}}{{C}_{2}}\right)................\left(x-{50}^{2}.\frac{{C}_{50}}{{C}_{49}}\right)where{C}_{r}={}^{50}C_{r}.$

In the expansion of (1 +

a)^{m + n}, prove that coefficients ofa^{m}anda^{n}are equal.Find the value of nC0 - nC1 + nC2 - nC3 +.................+(-1)^n nCn

Write the sum of exponents of x and y in the expansion of ( x +y )

^{n}? Also find the number of terms in the expansion?if three successive coefficients in the expressions of (1+x)

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

a,bandnin the expansion of (a+b)^{n}if the first three terms of the expansion are 729, 7290 and 30375, respectively.^{21}C_{0}+^{21}C_{1}+^{21}C_{2}+^{21}C_{3}+^{21}C_{4}+ .......... +^{21}C_{10}.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 first three terms in the expansion of (x+y)^n are 1,56,1372 respectively.Find x and y

show that the coefficient of the middle term in the expansion of (1+x)^2n is equal to the sum of the coefficients of two middle terms in the expansion (1+x)^2n-1.

^{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?Q.6. If the coefficients of rth and (r + 1)th terms in the expansion of ${\left(3+7x\right)}^{29}$ are equal, then r equals

a. 15

b. 21

c. 14

d. none of these

^{-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.}Find the terms independent of x , x ≠ 0 , in the expansion of :

(a) (A)(x-1/x)

^{14}(b)[(3x^{2}/2)-(1/3x)]^{6}(c)(x^{2}+ 1/x)^{12}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}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.

Can you pls solve this question quickly in detail :-

Show that the middle term in the expansion of (1+x)

^{2n}is[{1*3*5...(2n-1)} /n! ] *2n x

^{n}Please solve this quickly.....................

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

Can anyone explain the binomial expansion of terms raised to negative or fractional powers?

Find a if the coefficients of x

^{2}and x^{3}in the expansion of (3+ax)^{9}are equal.Using binomial theoram ,show that 9

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

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

in the binomial expansion of (a + b)

^{n}, the coefficient of the 4th and the 13th terms are equal to each other. find n?Show that the middle term in the expansion of (1+x)

^{2n}is-1.3.5...(2n-1)/n! 2nx^{n},where n is a positive integer.Here n is even so the middle term is (n+1) th term.So the n+1 th term is^{2n}C_{n}a^{2n-n}b^{n}i.e^{2n}C_{n}1^{2n-n}x^{n}i.e^{2n}C_{n}x^{n}.I'm i correct till this step???^{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 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. ThanksShow 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 25Find 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}find the specified term in the expansion in the following binomials

fifth term of (2a+3b)^12. evaluate it when a=1/3 b=1/4

any 3 successive coefficient in the expansion of (1+x)^n where n is a positive integer are 28,56,70 then n is

For what value of

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

^{m}and x^{n}in the expansion of (1+x)^{m+n}are equal .2. using binomial theorem prove that 2

^{3n}- 7 - 1 , n belong t N is divisible by 49 .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}correct option is D

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' .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.Expand the Binomial (1-3x)

^{5}