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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.

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

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

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

^{40}in the expansion of (1/x^{2}+ x^{4})^{18}^{st}4 terms in the expansion of ( 1 –x )^{-1/4}^{2}/4)^{9}^{3}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.

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 !

Using Binomial theoram, prove that 2

^{3n }- 7n^{}-1 is divisible by 49 where n is a Natural numberIn the expansion f (7

^{1/3}+ 11^{1/9})^{6561}, the number of terms free from radical is ?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

_{2 , }prove that mc_{2}= 3^{n+1}c_{4 }^{3})((3/2)x^{2}- 1/3x)^{9.}Find the remainder when 27

^{10}+7^{51 }divided by 10.using binomial therorem, 3

^{2n+2}-8n-9 is divisible by 64, n belongs to NQ:fnd the coeff of x

^{9}y^{-3}inthe expansion of (2x^{2}/y + y/3x)^{12}^{9}in the expansion of (1+ 3x + 3x^{2}+x^{3 })^{15}Find the value of nC0 - nC1 + nC2 - nC3 +.................+(-1)^n nCn

if three successive coefficients in the expressions of (1+x)

^{n}are 220, 495 and 792 respectively, find the value of n?^{99}-19^{93}is divisible by 162 using binomial theorem.Find

a,bandnin the expansion of (a+b)^{n}if the first three terms of the expansion are 729, 7290 and 30375, respectively._{1}/C_{0}) + (2C_{2}/C_{1}) + ( 3C_{3}/ C_{2}) +.... + nC_{n}/C_{n-1}= ? Pls solve using summation method. ThanksFind

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

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

_{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^{2}-x^{3}/6)^{7}If the numerical coefficient of the pth term in expansion of (2x+3)^6 is 4860,then value of p is/are?

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

^{n}are in the ratio 1:7:42.find n?_{0}) - ( C_{1}/2) + ( C_{2}/3) - (C_{3}/ 4) + ...... n terms = ? Pls solve using summation formulaIf 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

^{-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 value of

^{50}C_{0}-^{50}C_{1 }+^{50}C_{2 }-.........+^{50}C_{50}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}^{12}.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.

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

if x is very nearly equal to1 ,show that

1) (mx

^{m}-nx^{n})/(m-n )=x^{m+n}Using binomial theoram ,show that 9

^{n+1}-8n-9 is divisible by 64 ,whr n is a positive integer._{0}/2 ) - ( C_{1}/3) + (C_{2}/4) - ( C_{3}/5) +...... =? Pls solve using summation method. Thanks.in the binomial expansion of (a + b)

^{n}, the coefficient of the 4th and the 13th terms are equal to each other. find n?^{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. =)

Expand the Binomial (1-3x)

^{5}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})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

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}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

^{n}in the expansion of(1+x)(1-x)^{n}Prove that nc

_{r}/nc_{r-1}=n-r+1/rany 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

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

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 no of irrational terms in the expansion of (4

^{1/5}+ 7^{1/10})^{45 }are??????Find the coefficient of x

^{32 }and x^{-17 }in the expansion of (x^{4}-^{1}/x^{3})^{15.}Find the coefficient of x

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

^{1000}+ 2x(1+x)^{999}+3x^{2}(1+x)^{998}+…………………..+1001x^{1000}^{2}-2x+1)^{35}is equal to the sum of the coefficients of the expansion (x-ay)^{35}prove that a=11. Find the total no. of terms in the expansion of (x+a)^100 + (x-a)^100after simplification

^{8}Answer is (C10 - B10)