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Syllabus

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

^{10}T?_{r+1}=^{n}Cr .a^{n-r} .b^{r}And when should you use this formula-

T?_{r+1}= (-1)^{n}C_{r }.a^{n-r}.(+b)^{r}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???Expand the Binomial (1-3x)

^{5}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

prove nPr=

n!(n-r)!

and deduce it to nCr answere fast important for test

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 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.

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.

^{10}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 rIf (1+x)

^{n}= C_{0}+ C_{1}x + C_{2}x^{2}+ …..+C_{n}x^{n}. Prove that C_{1}+ 2C_{2}+ 3C_{3}+ ……+ nC_{n}= n.2^{n-1 }(1+2x+x^2)^20

7. If the coefficient of r

^{th},(r+1)^{th}and (r+12^{th}terms in the binomial expansion of (1+y)^{m}are in AP, then m and r satisfy the equation:(1) m

^{2}-m(4r-1)+4r^{2}+2=0 (2) m^{2}-m(4r+1)+4r^{2}-2=0(3) m

^{2}-m(4r+1)+4r^{2}+2=0 (4) m^{2}-m(4r-1)+4r^{2}-2=08. The Value of ${C}_{4}^{50}+\sum _{r=1}^{6}{C}_{3}^{56-1}$ is

$\left(1\right){C}_{4}^{56}\left(2\right){C}_{3}^{56}\left(3\right){C}_{3}^{55}\left(4\right){C}_{4}^{55}$

^{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

^{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}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 ofShow 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 !

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.^{2}+1/x]^{12}the first three terms in the expansion of (x+y)^n are 1,56,1372 respectively.Find x and y

^{n}C_{0}+^{n}C_{1}+^{n}C_{2}+...........+^{n}C_{n}= 2^{n}^{2}-x^{3}/6)^{7}in the second example, just by finding n2=9, we can conclude that n=3. so why did we have to find n3=27?

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

^{n}are in the ratio 1:7:42.find n?prove that

^{n}C_{r}+^{n}C_{r-1}=^{n+1}C_{r}^{-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.}^{10}in the copyThe 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.

Using binomial theoram ,show that 9

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

For solving the combination part in the expansion are there any specific formulas or we have to solve it each and every time?

in the binomial expansion of (a + b)

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

^{34}, the coeffients of the (2r+1)^{th}and (r+2)^{th}terms are equal. Find r?^{2})^{4}Find n if the coefficient of 5th, 6th& 7th terms in the expansion of (1+x)

^{n}are in A.P.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. =)

i dnt understand binomial ncert Q10

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})for questions such as to find that which is greater of (1.01)^1000000 or 10000

in ncert solution it is given that

^{1000000C}_{1}=1000000 BUT atq formula it shd hv been 1000000!/99999!*1pls help why??? reply soon :/

_{}_{}_{}_{}^{10}_{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.C1/(C1+C2) + C3/(C3+C4) = 2*C2/(C2+C3)

using binomial theorem prove that 6

^{n}-5n always remender -1when divided by 25_{}Find 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}_{0}^{2}- 2C_{1}^{2}^{}+ 3C_{2}^{2}-....+(-1)^{n}(n+1)C_{n}WHERE n IS A POSITIVE EVEN NUMBER IS :(-1)

^{n/2}(n+2)(-1)

^{n}(n+1)(-1)

^{n/2}(n+1)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

^{9}please give the blueprint of annual examination of maths paper.

^{9}in the expansion of (1+ 3x + 3x^{2}+x^{3 })^{15}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.

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}Q6. If ${}^{\mathrm{n}+1}\mathrm{C}_{2}+2\left({}^{2}\mathrm{C}_{2}+{}^{3}{\mathrm{C}}_{2}{+}^{4}{\mathrm{C}}_{2}+........+{}^{\mathrm{n}}{\mathrm{C}}_{2}\right)={1}^{2}+{2}^{2}+{3}^{2}+...........+{100}^{2}$, then find n.

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.