Recent questions tagged ch8

The expression $P(x)$ = $\big(\sqrt {x^5-1}+x\big)^7$ - $\big(\sqrt {x^5-1}-x\big)^7$ is a polynomial of what degree?

asked Oct 15, 2013 by rvidyagovindarajan_1

1 answer

The digit at unit place in the number $17^{1995}+11^{1995}-7^{1995}$ is ?

asked Oct 14, 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

If $P_n$ denotes the product of binomial coeff. in the expansion of $(1+x)^n$, then $\large\frac{P_{n+1}}{P_n}$=?

asked Oct 14, 2013 by rvidyagovindarajan_1

1 answer

The coeff. of $x^n$ in the expansion of $(1+x)(1-x)^n$ is ?

asked Oct 14, 2013 by rvidyagovindarajan_1

1 answer

$^nC_0^2$ + $^nC_1^2$ + $^nC_2^2$ + ...... + $^nC_n^2$ = ?

asked Oct 14, 2013 by rvidyagovindarajan_1

1 answer

The coefficient of the term independent of $x$ in the expansion of

$(1+x+2x^3)\bigg(\large\frac{3}{2}$$x^2-\large\frac{1}{3x}$$\bigg)^9$ is

asked Oct 12, 2013 by rvidyagovindarajan_1

1 answer

If the sum of the coefficients in the expansion of $(x+y)^n $ is 4096, then the greatest coefficient in the expansion is ?

asked Oct 12, 2013 by rvidyagovindarajan_1

1 answer

The value of $^nC_0-^nC_1$ + $^nC_2-......$ + $(-1)^n$ $^n C_n$ = ?

asked Oct 12, 2013 by rvidyagovindarajan_1

1 answer

The coefficient of $x^m$ in the expansion 1 + $(1+x)$ + $(1+x)^2$ + ..... + $(1+x)^n$ is

asked Oct 12, 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

The number of integral terms in the expansion of $(5^{\large\frac{1}{2}}$$+7^{\large\frac{1}{8}}$$)^{1024}$ is ?

asked Oct 5, 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 $\large\frac{T_2}{T_3}$ in the expansion of $(a+b)^n$ and $\large\frac{T_3}{T_4}$ in the expansion of $(a+b)^{n+3}$ are equal, then $n=?$

asked Sep 26, 2013 by rvidyagovindarajan_1

1 answer

The coefficients of $x^p$, and $x^q$ in the expansion of $(1+x)^{p+q}$ are

asked Sep 26, 2013 by rvidyagovindarajan_1

1 answer

In the binomial expansion of $(1+ax)^n$, the first three terms are $1+12x+64x^2$, then $n=?$

asked Sep 26, 2013 by rvidyagovindarajan_1

1 answer

$^nC_0$ - $\large\frac{^nC_1}{2}$ + $\frac{^nC_2}{3}$ - ...... = ?

asked Sep 26, 2013 by rvidyagovindarajan_1

1 answer

$^nC_1$ + $2.^nC_2$ + $3.^nC_3$ + ..... + $n.^nC_n$ = ?

asked Sep 24, 2013 by rvidyagovindarajan_1

1 answer

The sum of coefficients of odd powers of $x$ in the expansion $(1+x)^{50}$ is ?

asked Sep 24, 2013 by rvidyagovindarajan_1

1 answer

If the sum of odd numbered terms and even numbered terms in the expansion of $(x+a)^n$ are $A,B$, then $(x^2-a^2)^n=?$

asked Sep 24, 2013 by rvidyagovindarajan_1

1 answer

The no. of terms in the expansion $(x+y+z)^{10}$ is ?

asked Sep 24, 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

If the third term in the expansion of $\bigg(\large\frac{1}{x}$$+ x^{log_{10}x}\bigg)^5$ is 1000, then $x$ = ?

asked Sep 23, 2013 by rvidyagovindarajan_1

1 answer

If the coefficient of $x^2$ and $x^3$ in the expansion of $(3+ax)^9$ are same, then the value of $a$ is ?

asked Sep 19, 2013 by rvidyagovindarajan_1

1 answer

The $5^{th}$ term from the end in the expansion of $\bigg(\large\frac{x^3}{2}-\frac{2}{x}\bigg)^{12}$ is ?

asked Sep 19, 2013 by rvidyagovindarajan_1

1 answer

The middle term in the expansion $(1+x)^{2n}$ is ?

asked Sep 19, 2013 by rvidyagovindarajan_1

1 answer

The term independent of $x$ in the expansion $(2x-\large\frac{1}{3x})^6$ is ?

asked Sep 17, 2013 by rvidyagovindarajan_1

1 answer

If $x=\large\frac{1}{3}$, the greatest term in the expansion of $(1+4x)^8$ is ?

asked Sep 17, 2013 by rvidyagovindarajan_1

1 answer

If the coefficient of middle terms in $(1+\alpha x)^4$ and $(1-\alpha x)^6$ is same then $\alpha =?$

asked Sep 17, 2013 by rvidyagovindarajan_1

1 answer

The coefficient of $x^7$ in the expansion $(1-x-x^2+x^3)^6$ is ?

asked Sep 17, 2013 by rvidyagovindarajan_1

1 answer

In the binomial expansion of $(a-b)^n,\:n\geq 5$ the sum of $5^{th}$ and $6^{th}$ term is $0$, then $\large\frac{a}{b}$=?

asked Sep 16, 2013 by rvidyagovindarajan_1

1 answer

If the coefficient of $x^7$ in $\big(ax^2+\large\frac{1}{bx}\big)^{11}$ is equal to coefficient of $x^{-7}$ in $\big(ax-\large\frac{1}{bx^2}\big)^{11}$, then $a$ and $b$ satisfy the relation

asked Sep 15, 2013 by rvidyagovindarajan_1

1 answer

The coefficient of $x^n$ in the expansion $(1+x)(1-x)^n$ is

asked Sep 15, 2013 by rvidyagovindarajan_1

1 answer

The total no. of terms in the expansion $(x+y)^{100}+(x-y)^{100} $ is ?

asked Sep 15, 2013 by rvidyagovindarajan_1

2 answers

Solve the following differential equation;$(D^{2}-13D+12)$y$=e^{-2x}+5e^x$

asked Sep 5, 2013 by sreemathi.v

1 answer

Find the area under the given curves and given lines: $ (ii)\:y = x^4, x = 1, x = 5 \: and\: x - axis$

asked Aug 16, 2013 by sreemathi.v

1 answer

A radioactive substance disintegrates at a rate proportional to its mass. When its mass is $10 $mgm, the rate of disintegration is $0.051$ mgm per day. How long will it take for the mass to be reduced from $10$mgm to $5$mgm.$ [\log_{e}$$2=0.6931]$

asked Apr 17, 2013 by poojasapani_1

1 answer

The rate at which the population of a city increases at any time is propotional to the population at that time. If there were $1,30,000$ people in the city in $1960 $ and $1,60,000$ in $1990$ what population may be anticipated in $2020$.$[\log_{e}(\large\frac{16}{13})=$$.2070;$$e^{.42}=1.52]$

asked Apr 17, 2013 by poojasapani_1

1 answer

A cup of coffee at temperature $100^{\circ}$$C$ is placed in a room whose temperature is $15^ {\circ}$$C$ and it cools to $60^{\circ}$$C$ in $5$ minutes . Find its temperature after a further interval of $5$ minutes.

asked Apr 17, 2013 by poojasapani_1

1 answer

The sum of Rs $1000$ is compounded continuously, the nominal rate of interest being four percent per annum. In how many years will the amount be twice the original principal ? $(\log_{e}$$2=0.6931)$

asked Apr 17, 2013 by poojasapani_1

1 answer