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Recent questions tagged binomial-theorem

Evaluate $(\sqrt 3+\sqrt 2)^4-(\sqrt 3-\sqrt 2)^4$

asked Jun 23, 2014 by sreemathi.v

1 answer

Find $(a+b)^4-(a-b)^4$.

asked Jun 23, 2014 by sreemathi.v

1 answer

Using the Binomial theorem indicate which number is larger $(1-1)^{10000}$ or 1000

asked Jun 23, 2014 by sreemathi.v

1 answer

Expand the expression:$(99)^5$

asked Jun 23, 2014 by sreemathi.v

1 answer

Expand the expression:$(101)^4$

asked Jun 23, 2014 by sreemathi.v

1 answer

Expand each of the expressions:$(102)^5$

asked Jun 20, 2014 by sreemathi.v

1 answer

Expand each of the expressions:$(96)^3$

asked Jun 20, 2014 by sreemathi.v

1 answer

Expand each of the expressions:$\big(x+\large\frac{1}{x}\big)^6$

asked Jun 20, 2014 by sreemathi.v

1 answer

Expand each of the expressions:$\big(\large\frac{x}{3}+\frac{1}{x}\big)^5$

asked Jun 20, 2014 by sreemathi.v

1 answer

Expand each of the expressions:$(2x-3)^6$

asked Jun 20, 2014 by sreemathi.v

1 answer

Expand each of the expressions:$\big(\large\frac{2}{x}-\frac{x}{2}\big)^5$

asked Jun 20, 2014 by sreemathi.v

1 answer

Expand each of the expressions:$(1-2x)^5$

asked Jun 20, 2014 by sreemathi.v

1 answer

In the expansion of $(1 + a)^{m+n}$, prove that coefficients of $a^m$ and $a^n$ are equal.

asked Apr 10, 2014 by balaji.thirumalai

1 answer

Find the middle terms in the expansions of $\; \large ( \frac{x}{3}$$+9y \large)$$^{10}$

asked Apr 10, 2014 by balaji.thirumalai

1 answer

Find the middle terms in the expansions of $\;\large ($$ 3 $$- \large\frac{x^3}{6})^7$

asked Apr 10, 2014 by balaji.thirumalai

1 answer

Find the $13th$ term in the expansion of $\large ($$9x$$-\large \frac{1}{3\sqrt x})^{\normalsize 18}$$, x\neq 0$

asked Apr 10, 2014 by balaji.thirumalai

1 answer

Find the $4th$ term in the expansion of $(x - 2y)^{12}$.

asked Apr 10, 2014 by balaji.thirumalai

1 answer

Write the general term in the expansion of $ (x^2 - yx)^{12},\; x\neq 0$

asked Apr 10, 2014 by balaji.thirumalai

1 answer

Write the general term in the expansion of $ (x^2 - y)^6$

asked Apr 10, 2014 by balaji.thirumalai

1 answer

Find the coefficient of $a^5b^7$ in $ (a-2b)^{12}$

asked Apr 10, 2014 by balaji.thirumalai

1 answer

Find the coefficient of $x^5$ in $(x+3)^8$

asked Apr 10, 2014 by balaji.thirumalai

1 answer

Show that $9^{n+1} – 8n – 9$ is divisible by $64$, whenever $n$ is a positive integer.

asked Apr 10, 2014 by balaji.thirumalai

1 answer

Find $(x+1)^6 + (x – 1)^6$. Hence, evaluate $( \sqrt2 + 1)^6+(\sqrt 2 –1)^6$.

asked Apr 10, 2014 by balaji.thirumalai

1 answer

Find $ (a + b)^4 - (a - b)^4.$ Hence, evaluate $( \sqrt3 + \sqrt2)^4 - (\sqrt 3 - \sqrt 2)^4$.

asked Apr 10, 2014 by balaji.thirumalai

1 answer

Using Binomial Theorem, indicate which number is larger $(1.1)^{10000}$ or $1000$.

asked Apr 10, 2014 by balaji.thirumalai

1 answer

Using Binomial Theorem, evaluate $101^4$

asked Apr 10, 2014 by balaji.thirumalai

1 answer

Using Binomial Theorem, evaluate $99^5$

asked Apr 10, 2014 by balaji.thirumalai

1 answer

Using Binomial Theorem, evaluate $102^6$

asked Apr 10, 2014 by balaji.thirumalai

1 answer

Using Binomial Theorem, evaluate $96^3$.

asked Apr 10, 2014 by balaji.thirumalai

1 answer

Expand the expression: $(x + \large\frac{1}{x}$$)^6$

asked Apr 9, 2014 by balaji.thirumalai

1 answer

Expand the expression: $\large(\frac{x}{3} + \frac{1}{x})$$^5$

asked Apr 9, 2014 by balaji.thirumalai

1 answer

Expand the expression: $(2x-3)^6$

asked Apr 9, 2014 by balaji.thirumalai

1 answer

Expand the expression: $\large(\frac{2}{x} - \frac{x}{2})$$^5$

asked Apr 9, 2014 by balaji.thirumalai

1 answer

Expand the expression: $(1-2x)^5$

asked Apr 9, 2014 by balaji.thirumalai

1 answer

The ratio of the coefficient of $x^{10}$ in $(1-x^2)^{10}$ and the term independent of $x$ in $(x-\large\frac{2}{x}$$)^{10}$ is ?

asked Jan 21, 2014 by rvidyagovindarajan_1

1 answer

$ \displaystyle\sum_ {i=o} ^{{m} ^{10}} C_i ^{20}C_{m-i}$ is maximum when $m=?$

asked Jan 21, 2014 by rvidyagovindarajan_1

1 answer

The term independent of $x$ in the expansion $\bigg(\large\frac{x+1}{x^{\large\frac{2}{3}}-x^{\large\frac{1}{3}}+1}-\frac{x-1}{x-\sqrt x}\bigg)^{10}$ is ?

asked Dec 1, 2013 by rvidyagovindarajan_1

1 answer

If in the expansion of $(x+a)^{15},$ the $11^{th}$ term is $G.M.$ of $8^{th} $ & $12^{th}$ terms, then which term is the greatest term?

asked Nov 24, 2013 by rvidyagovindarajan_1

1 answer

If the sum of $5^{th}\:and\:6^{th}$ terms in the expansion of $(a-b)^n$, $n\geq5$, is 0, then $\large\frac{a}{b}$ = ?

asked Nov 24, 2013 by rvidyagovindarajan_1

1 answer

If the sum of the coefficients of $(1+x)^n=4096$, then the largest coefficient is ?

asked Nov 24, 2013 by rvidyagovindarajan_1

1 answer

The value of $^nC_0.^{2n}C_r$ - $^nC_1^{2-2}C_r$ + $^nC_2.^{2n-4}C_r$ - ...., if $r \lt n$ is

asked Nov 24, 2013 by rvidyagovindarajan_1

1 answer

Coeff. of $x^{50}$ in $(1+x)^{1000}$ + $x(1+x)^{999}$ + $x^2(1+x)^{998}$ + .... + $x^{1000}$ is

asked Nov 23, 2013 by rvidyagovindarajan_1

1 answer

$53^{53} - 33^{33}$ is divisible by

asked Nov 22, 2013 by rvidyagovindarajan_1

1 answer

A student is allowed to select at the most n books from a collection of $2n+1$ books. The no. of ways in which he can select at least one book is 63, then $n$ = ?

asked Oct 28, 2013 by rvidyagovindarajan_1

1 answer

$^nC_0.^nC_1$ + $^nC_1.^nC_2$ + $....^nC_{n-1}.^nC_n$ = ?

asked Oct 27, 2013 by rvidyagovindarajan_1

1 answer

If the $4^{th}$ term in the expansion of $\big(x^2-\large\frac{1}{x^3}\big)^n$ is independent of $x$, then $n=?$

asked Oct 26, 2013 by rvidyagovindarajan_1

1 answer

The remainder when $5^{99}$ is divided by $13$ is

asked Oct 26, 2013 by rvidyagovindarajan_1

1 answer

$\large\frac{^8C_0}{6}$ - $^8C_1$ + $^8C_2.6$ + $....$ + $^8C_8.6^7$ = ?

asked Oct 26, 2013 by rvidyagovindarajan_1

1 answer

If $(1+\sqrt 2)^n=x_n+y_n\sqrt 2$, where $x_n,y_n$ are integers, then

asked Oct 23, 2013 by rvidyagovindarajan_1

1 answer

If the sum of the coefficients in the expansion of $(b+c)^{20}[1+(a-2)x]^{20}$ is square of the sum of the coefficients in the expansion $[2bcx-(b+c)y]^{10}$ where $a,b,c$ are positive constants, then $a,b,c$ satisfies the equation?

asked Oct 23, 2013 by rvidyagovindarajan_1

1 answer

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