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Recent questions tagged properties-and-applications

$ \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

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

$53^{53} - 33^{33}$ 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

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 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

If $x\in R,$ then the value of $S=1-^nC_1.\large\frac{1+x}{1+nx}$$+^nC_2.\large\frac{1+2x}{(1+nx)^2}$$-^nC_3.\large\frac{1+3x}{(1+nx)^3}$$+..............(n+1) $terms = ?

asked Oct 21, 2013 by rvidyagovindarajan_1

1 answer

The coefficient if $x^{10}$ in the expansion $(1+x^2-x^3)^8$ is ?

asked Oct 21, 2013 by rvidyagovindarajan_1

1 answer

The sum of rational terms in the expansion of $(2^{\large\frac{1}{5}}$$+\sqrt 3)^{20}$ is

asked Oct 19, 2013 by rvidyagovindarajan_1

1 answer

The remainder when $2^{2003}$ is divided by $17$ is ?

asked Oct 16, 2013 by rvidyagovindarajan_1

1 answer

The coefficient of $x^5$ in the expansion of $(1+x)^{21}$ + $(1+x)^{22}$ + ...... + $(1+x)^{30}$ is

asked Oct 14, 2013 by rvidyagovindarajan_1

1 answer

In the expansion of $(1+x)^m.(1-x)^n, $ the coefficients of $x$ and $x^2$ are $3$ and $-6$ respectively, then $m=?$

asked Oct 12, 2013 by rvidyagovindarajan_1

1 answer

If $t_n=\bigg(1+\large\frac{1}{n}\bigg)$$^n$ for $n\in N$, then $t_n$ lies in the interval?

asked Oct 1, 2013 by rvidyagovindarajan_1

1 answer

$8^n-7n-1$ is divisible by ? where $n\in N$

asked Oct 1, 2013 by rvidyagovindarajan_1

1 answer

If the coefficients of $2^{nd},3^{rd}\:and\:4^{th}$ terms in the expansion of $(1+x)^{2n} $ are in A.P., then $n=?$

asked Sep 26, 2013 by rvidyagovindarajan_1

1 answer

If the coefficient of $(2r+4)^{th}$ and $(r-2)^{th}$ terms in the expansion of $(1+x)^{18} $ are equal, then $r=?$

asked Sep 24, 2013 by rvidyagovindarajan_1

1 answer

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