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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.

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

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

^{n}are in AP, then find values of n???^{2}-x^{3}/6)^{7}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

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

^{2})^{n}in a series of ascending powers of x upto and including the terms in x^{2}The coefficients of three consecutive terms in the expansion of(1+x)

^{n}are in the ratio 1:7:42. find n.^{10}C_{1}+ 2.10C2 - 22.10C3 + ....+29.10C10 is equal toShow 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.

Experts the above image is the question & the image below is the solution of the way ''I'' have solved the question.... Just check my solution & working.... I know the correct solution & correct answer also..... I JUST WANT TO KNOW WHERE HAVE I GONE WRONG? IN MY OWN METHOD ????? ....??? In my method I have taken the index of denominator and subtracted it with the index of numerator ..(becoz the number on which power was equal)...

Using Binomial theoram, prove that 2

^{3n }- 7n^{}-1 is divisible by 49 where n is a Natural numberfind the [n+1]th term from the end in the expansion of [x-1/x]^3n

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^{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

^{2}- 3/2x]^{20}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.If T

_{r}denotes the rth term in the expansion of (1+x)^{n}in ascending powers of x ( n being a natural number), prove thatr(r+1)T

_{r+2}=(n-r+1)(n-r)x^{2}T_{r}given hint T

_{r}=^{n}C_{r-1}x^{r-1}and T_{r+2}=^{n}C_{r+1}x^{r+1}Q. Equation of hyperbola? Foci are (0, $\pm $ 12) and length of latus rectum is 36.

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

The cofficient of three consecutive terms in the expansion of (1+x)

^{n}are in the ratio 1:7:42.find n?_{1}/C_{0}) + (2C_{2}/C_{1}) + ( 3C_{3}/ C_{2}) +.... + nC_{n}/C_{n-1}= ? Pls solve using summation method. Thanks^{-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}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.

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.

^{2}and higher powers of x can be neglected, prove that(1-2x)

^{2/3 }/ (4+5x)^{3/2 }(1-x) =(approx.)(1/8 - 53x/192) .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

In the expansion f (7

^{1/3}+ 11^{1/9})^{6561}, the number of terms free from radical is ?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.(1-3x+3x^2-x^3)^6

in the binomial expansion of (a + b)

^{n}, the coefficient of the 4th and the 13th terms are equal to each other. find n?Q. What is the sum of the coefficients of odd powers of x in the expansion of ${\left(1+x\right)}^{50}$?

^{2})^{4}Q7. Show that

^{n}C_{0}^{n}C_{0 }–^{n+1}C_{1}.^{n}C_{1}+^{n+2}C_{2}^{n}C_{2}– ...... = ( – 1)^{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. =)

^{nd}, 3^{rd}and 4^{th}terms in the expansion of (1+x)^{n}are in A.P. then find the value of n. Hence find the middle termsThe 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})^{2})^{10}is 405 ,then k is equal to??^{n}C_{1}+ 2.^{n}C2 + 3.^{n}C_{3}+...+^{}n.^{n}C_{n}= n.2^{n}^{10}Show 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}any 3 successive coefficient in the expansion of (1+x)^n where n is a positive integer are 28,56,70 then n is

Q26. If first three terms in the expansion of a positive integral power of a binomial are 729, 7290

and 30375 respectively, find the binomial expansion.

please give the blueprint of annual examination of maths paper.

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.

Show that is divisible by 64, whenever

nis a positive integer.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}a) 10

b) 20

c) 210

d) none of these

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' .Find the coefficient of x^{9}in the expansion of [x^{2}-(1/3x)]^{9 Plz help}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.Findthe 13

^{th}term in the expansion of.