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Syllabus

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

^{10}find the first three terms in the expansion of [2+x(3+4x)]^5 in ascending power of x.

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.

^{n}C_{1}+ 2.^{n}C2 + 3.^{n}C_{3}+...+^{}n.^{n}C_{n}= n.2^{n}If the coeffients of 5th, 6th & 7th terms in expansion of (1+x)

^{n}are in AP, then find values of n???^{2})^{4}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

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

_{1}/C_{0}) + (2C_{2}/C_{1}) + ( 3C_{3}/ C_{2}) +.... + nC_{n}/C_{n-1}= ? Pls solve using summation method. ThanksThe coefficients of three consecutive terms in the expansion of(1+x)

^{n}are in the ratio 1:7:42. find n.Prove that nc

_{r}/nc_{r-1}=n-r+1/rShow 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_{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(1+2x+x^2)^20

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

^{2n+2}-8n-9 is divisible by 64, n belongs to NQ26. â€‹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.

Find the value of nC0 - nC1 + nC2 - nC3 +.................+(-1)^n nCn

^{2}/3+3/2x^{2})^{10}is??if three successive coefficients in the expressions of (1+x)

^{n}are 220, 495 and 792 respectively, find the value of n?^{2}+1/x]^{12}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 ofQ. What is the sum of the coefficients of odd powers of x in the expansion of ${\left(1+x\right)}^{50}$?

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

^{2}-x^{3}/6)^{7}Find the term independent of x in the expansion of (2x +3/x

^{2})^{9},x^{r-1}in the binomial expansion ofx^{r }, x^{r+1 }are in A.P. , prove that(1+x)^{n}.n^{2}- n(4r + 1) + 4r^{2}- 2 = 0The cofficient of three consecutive terms in the expansion of (1+x)

^{n}are in the ratio 1:7:42.find n?^{-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}find the [n+1]th term from the end in the expansion of [x-1/x]^3n

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.

What is the coefficient of x

^{11}in the expansion of (x^{3 }- 2/x^{2})^{12}?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.))))))))))))

find the value of

^{50}C_{0}-^{50}C_{1 }+^{50}C_{2 }-.........+^{50}C_{50}Using binomial theoram ,show that 9

^{n+1}-8n-9 is divisible by 64 ,whr n is a positive integer.write down the expansion of (3x-y/2)^4 by giving suitable values of x and y deduce the value of (29.5)^4 correct to 4 decimal places?

Find the coefficient of x^{9}in the expansion of [x^{2}-(1/3x)]^{9 Plz help}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})_{0}/2 ) - ( C_{1}/3) + (C_{2}/4) - ( C_{3}/5) +...... =? Pls solve using summation method. Thanks.if the 21st and 22nd terms in the expansion of (1+x)^44 are equal then find the value of x.

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

^{4n}-15n-1 is divisible by 225 by using binomial theorem.Answer is (C10 - B10)

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}( 3x + y )^8 - ( 3x-y )^8

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

a) 10

b) 20

c) 210

d) none of these

please give the blueprint of annual examination of maths paper.

SOLVE

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

^{n}C_{0}+ 2.^{n}C_{1}+ 3.^{n}C_{2}+ ........... +(n+1).^{n}C_{n}= (n+2).2^{(}^{n-1)}.^{10}The no of irrational terms in the expansion of (4

^{1/5}+ 7^{1/10})^{45 }are??????_{0}) - ( C_{1}/2) + ( C_{2}/3) - (C_{3}/ 4) + ...... n terms = ? Pls solve using summation formulaFind the coefficient of x

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

^{1000}+ 2x(1+x)^{999}+3x^{2}(1+x)^{998}+…………………..+1001x^{1000}Using Binomial theorem, expand:( Root x + Root y)

^{10}...1. Find the total no. of terms in the expansion of (x+a)^100 + (x-a)^100after simplification

_{o}C_{r}+ C_{1}C_{r+1}+ .... + C_{n-r}C_{n}= (2n)! / (n-r)! (n+r)!The first 3 terms in the expansion of (1+ax)

^{n}are 1, 12x, 64x^{2}respectively, Find n and 'a' .Write the no of terms in the expansion of (1-3x+3x

^{2}-x^{3})^{8}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.in a binomial expansion (x+a),the first three terms are 1,56,1372 respectively,find the values of a and x.