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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.

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

^{n}are in AP, then find values of n???FIND THE GREATEST term in the expansion of (3x+4y)

^{28 }when x=6 ,y=3..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..(1+2x+x^2)^20

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.^{3}in the expansion of (1+3x)^{2}/1-2x will be1)8 2)32 3)50 4)46

(answer in detail please)

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.

_{1}/C_{0}) + (2C_{2}/C_{1}) + ( 3C_{3}/ C_{2}) +.... + nC_{n}/C_{n-1}= ? Pls solve using summation method. ThanksUsing Binomial theoram, prove that 2

^{3n }- 7n^{}-1 is divisible by 49 where n is a Natural numberAnswer is (C10 - B10)

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^{n}C_{1}+ 2.^{n}C2 + 3.^{n}C_{3}+...+^{}n.^{n}C_{n}= n.2^{n}^{21}C_{0}+^{21}C_{1}+^{21}C_{2}+^{21}C_{3}+^{21}C_{4}+ .......... +^{21}C_{10}.^{3})((3/2)x^{2}- 1/3x)^{9.}^{n}C_{0}+^{n}C_{2}+^{n}C_{4}= 2^{n -1}using binomial therorem, 3

^{2n+2}-8n-9 is divisible by 64, n belongs to 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.}_{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 the value of nC0 - nC1 + nC2 - nC3 +.................+(-1)^n nCn

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

^{n}are 220, 495 and 792 respectively, find the value of n?Find the coefficient of x

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

^{1000}+ 2x(1+x)^{999}+3x^{2}(1+x)^{998}+…………………..+1001x^{1000}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 of^{2})^{4}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}-x^{3}/6)^{7}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?if the 21st and 22nd terms in the expansion of (1+x)^44 are equal then find the value of x.

^{n}E_{r=0}^{n}C_{r}sin2rx /^{n}E_{r=0}^{n}C_{r}cos2rx = tan nxE--->Sigma(summation).

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}in the expansion of (1+x)^nProvr that-(C0+C1)(C1+C2)(C2+C3) - - - - - (Cn-1+Cn)=

{(C0*C1*C2* - - - Cn-1)(n+1)^n} / n!

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.

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}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.))))))))))))

Using binomial theoram ,show that 9

^{n+1}-8n-9 is divisible by 64 ,whr n is a positive integer.in the binomial expansion of (a + b)

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

a+b)^{4}– (a–b)^{4}. Hence, evaluate.SOLVE

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

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. =)

Find the remainder when 27

^{10}+7^{51 }divided by 10.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})If (1+ x - 2x^2)^6 = 1+ a1x + a2x^2 +.........+ a(12)x^12, then prove that a2+a4+a6+........+a12 = 31

Prove that nc

_{r}/nc_{r-1}=n-r+1/rQ26. 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.

Show that 2

^{4n}-15n-1 is divisible by 225 by using binomial theorem.find the [n+1]th term from the end in the expansion of [x-1/x]^3n

using binomial theorem prove that 6

^{n}-5n always remender -1when divided by 25^{2})^{10}is 405 ,then k is equal to??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}Q8. The coefficient of x

^{53}in the following expansions $\sum _{\mathrm{in}=0}^{100}{100}_{{\mathrm{C}}_{\mathrm{n}}}{\left(\mathrm{x}-3\right)}^{100\mathrm{m}}.{2}^{\mathrm{m}}$ is$\left(\mathrm{a}\right){100}_{{\mathrm{C}}_{47}}\left(\mathrm{b}\right){100}_{{\mathrm{C}}_{53}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\left(\mathrm{c}\right)-{100}_{\mathrm{C}53}\left(\mathrm{d}\right)-{100}_{{\mathrm{C}}_{100}}$

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

Q=write the sum of the coffeicients in the expansion of (1-3x+ x^{2})^{111}.Ans=(-1)Q2=If a and b denote the sum of coefficients in the expansions of (1-3x-+10x^{2})^{n}and (1+x)^{2}respectively ,then write the relation b/w a and b.Ans= a=b^{3}.please give the blueprint of annual examination of maths paper.

^{9}in the expansion of (1+ 3x + 3x^{2}+x^{3 })^{15}$ThecorrectformultocalculatethehydroxylionconcentrationofanaqueoussolutionofN{H}_{4}N{O}_{3}is:\phantom{\rule{0ex}{0ex}}\left(a\right)\sqrt{\frac{C\times {K}_{w}}{{K}_{b}}}\phantom{\rule{0ex}{0ex}}\left(b\right)\sqrt{\frac{{K}_{w}\times {K}_{b}}{C}}\phantom{\rule{0ex}{0ex}}\left(c\right)\sqrt{\frac{C\times {K}_{w}}{{K}_{a}}}\phantom{\rule{0ex}{0ex}}\left(d\right)\sqrt{\frac{{K}_{a}\times {K}_{w}}{C}}$

The no of irrational terms in the expansion of (4

^{1/5}+ 7^{1/10})^{45 }are??????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' .^{10}in (1-x^{2})^{10}and the term independent of x in (x-2/x)^{10}is 1 :32 .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 the expansion f (7

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