Recent questions in Mathematics

In an AP, the sum of n terms is $n^2+1$ . Find the 16th term.

asked Dec 30, 2013 by yamini.v

1 answer

In an AP, the sum of n terms is a function of n, $S_{n}=3n^2+2n.$ Find the rth term.

asked Dec 30, 2013 by yamini.v

1 answer

In a series -9,-6,-3,----, find the number of terms n to get a sum $S_{n}$ = 66.

asked Dec 30, 2013 by yamini.v

1 answer

If the 7th term of an AP is 23 and the 12th term is 38, find the first term 'a' and common difference 'd'.

asked Dec 30, 2013 by yamini.v

1 answer

Integrate : $\int \large\frac{7}{3} \bigg( \frac{1}{x}-\frac{1}{x^2 }\bigg)$ $\times a (\log x + \large\frac{1}{x} )$ $dx$

asked Dec 30, 2013 by meena.p

1 answer

Find the sum of the series 1, $\frac {7}{5}$ , $\frac {13}{25}$ , $\frac {19}{25}$ ,----, $\infty$ .

asked Dec 30, 2013 by yamini.v

1 answer

Integrate : $\int e^x \bigg( \sin ^{-1} x +\large\frac{1}{\sqrt {1-x^2}}\bigg) dx$

asked Dec 30, 2013 by meena.p

1 answer

Integrate: $\int -cosec ^2 (\log x ) + \cot (\log x) dx$

asked Dec 30, 2013 by meena.p

1 answer

Integrate : $\int e^x. \bigg[\large\frac{1- \sin x}{1- \cos x }\bigg].$ $dx$

asked Dec 30, 2013 by meena.p

1 answer

Given that four positive numbers are in HP, which of the following is true.

asked Dec 30, 2013 by yamini.v

1 answer

The point on $x - axis$ which is equidistant from points $(4,3,1)\:\: and\:\: (-2,-6,-2)$ is?

asked Dec 30, 2013 by rvidyagovindarajan_1

0 answers

If position vector of the points $A,B,C,D$ are given by $7\hat i-4\hat j+7\hat k,\:\hat i-6\hat j+10\hat k,\:-\hat i-3\hat j+4\hat k\:\:and\:\:5\hat i-\hat j+5\hat k$ respectively, then $ABCD$ is ?

asked Dec 30, 2013 by rvidyagovindarajan_1

1 answer

The length of median through $A$ of the $\Delta\:ABC$ where $\overrightarrow {AB}=3\hat i+4\hat k\:\:and\:\:\overrightarrow {AC}=5\hat i-2\hat j+4\hat k$ is ?

asked Dec 30, 2013 by rvidyagovindarajan_1

1 answer

Integrate : $\int x.2^x dx$

asked Dec 30, 2013 by meena.p

1 answer

$\lim\limits_{h\to 0}\large\frac{ln(1+2h)-2ln(1+h)}{h^2}=$

asked Dec 30, 2013 by sreemathi.v

1 answer

Integrate : $\int \large\frac{1+\tan ^2 x }{1+\tan x }$ $dx$

asked Dec 30, 2013 by meena.p

1 answer

Integrate : $\int \large\frac{5}{8}.x.e{^{\Large x^2}}. \sec (e^{\Large x^2}).\tan (e^{x^2})dx$

asked Dec 30, 2013 by meena.p

1 answer

$\lim\limits_{x\to 0}\bigg[\large\frac{1+5x^2}{1+3x^2}\bigg]^{\Large\frac{1}{x^2}}$

asked Dec 30, 2013 by sreemathi.v

1 answer

Integrate : $\int \sqrt {1+\sin x }dx$

asked Dec 30, 2013 by meena.p

1 answer

Let $f(x)=\left\{\begin{array}{1 1}\big[\tan(\large\frac{\pi}{4}\normalsize +x)\big]^{\large\frac{1}{x}}&x\neq 0\\k&x=0\end{array}\right.$ .For what value of k, $f(x)$ is continuous at $x=0$

asked Dec 30, 2013 by sreemathi.v

1 answer

Integrate : $\int \large\frac{\sin ^{-1} x }{(1-x^2)^{3/2}}$ $dx$

asked Dec 30, 2013 by meena.p

1 answer

If $f(x)=\large\frac{1}{1-x}$ ,find the points of discontinuity of the composite function $y=f(f(f(x)))$

asked Dec 30, 2013 by sreemathi.v

1 answer

Integrate : $\int \large\frac{\sin x +\cos x }{\sqrt {\sin 2x}}$ $dx$

asked Dec 30, 2013 by meena.p

1 answer

$\lim\limits_{x\to a}\large\frac{\log(x-a)}{\log(e^x-e^a)}$ is

asked Dec 30, 2013 by sreemathi.v

1 answer

Integrate : $\int \large\frac{\cos 2 x}{\sin ^2 x \cos ^2 x }$ $dx$

asked Dec 30, 2013 by meena.p

1 answer

Integrate : $\int \large\frac{1- x \sin x +\cos x }{x(1- \cos x )}$ $dx$

asked Dec 30, 2013 by meena.p

1 answer

If $f(x)=\large\frac{1}{\sqrt{18-x^2}}$ then $\lim\limits_{x\to 3}\large\frac{f(x)-f(3)}{x-3}$ is

asked Dec 30, 2013 by sreemathi.v

1 answer

Integrate : $\int \large\frac{\sec x cosec x}{\log (\tan x )}$ $dx$

asked Dec 30, 2013 by meena.p

1 answer

$\lim\limits_{x\to {-1}}\large\frac{\sqrt{\pi}-\sqrt{\cos^{-1}x}}{\sqrt{x+1}}$ is given by

asked Dec 30, 2013 by sreemathi.v

1 answer

Integrate : $\int \sqrt {\large\frac{1-x}{1+x}}.\frac{1}{x}$ $dx$

asked Dec 30, 2013 by meena.p

1 answer

If $f(9)=9,f'(9)=4$ then $\lim\limits_{x\to 9}\large\frac{\sqrt{f(x)}-3}{\sqrt x-3}$ is

asked Dec 30, 2013 by sreemathi.v

1 answer

$\lim\limits_{x\to 0}\big(\large\frac{a^x+b^x+c^x}{3}\big)^{1/x}$ is

asked Dec 30, 2013 by sreemathi.v

1 answer

$\lim\limits_{x\to \large\frac{\pi}{4}}\large\frac{\cos x-\sin x}{(\Large\frac{\pi}{4}-\normalsize x)(\large\cos x+\sin x)}$ is

asked Dec 30, 2013 by sreemathi.v

1 answer

Integrate : $\int \sqrt {\tan \theta} . d \theta$

asked Dec 30, 2013 by meena.p

1 answer

If $f(x)=\large\frac{x^2-10x+25}{x^2-7x+10}$ for $x\neq 5$ and $f$ is continuous at $x=5$ then $f(5)=$

asked Dec 30, 2013 by sreemathi.v

1 answer

Among 5 numbers a, b, c, d and e the relationships are: a, b, c are in AP and b, c, d are in GP and c, d, e are in HP. Find b, c, d if a = 2 and e = 18.

asked Dec 30, 2013 by yamini.v

2 answers

$\lim\limits_{x\to \large\frac{\pi}{4}}\big(\large\frac{1-\tan x}{1\sqrt 2\sin x}\big)$ =

asked Dec 30, 2013 by sreemathi.v

1 answer

Integrate $\int \limits _0^1 \tan ^{-1}(x^2+1-x)dx$

asked Dec 30, 2013 by meena.p

1 answer

If $\lim\limits_{x\to k}\large\frac{x^k-5^k}{x-5}$ $=500$ then positive value of k is

asked Dec 30, 2013 by sreemathi.v

1 answer

$f(x)=\left\{\begin{array}{1 1}\large\frac{x^5-32}{x-2}&x\neq 2\\k&x=2\end{array}\right.$ is continuous at $x=2$ then $k=$

asked Dec 30, 2013 by sreemathi.v

1 answer

$\lim\limits_{x\to\large\frac{-\pi}{4}}\large\frac{1+\tan x}{\cos 2x}$ =

asked Dec 30, 2013 by sreemathi.v

1 answer

If $f$ is continuous on $[0,1]$ and $f\big(\large\frac{1}{3}\big)$ $=1$ then $\lim\limits_{n\to \infty}f(\large\frac{n}{\sqrt{9n^2+1}}\big)$ =

asked Dec 30, 2013 by sreemathi.v

1 answer

Integrate : $\int \limits_0^{\pi/2} \bigg( \large\frac{\theta}{ \sin \theta }\bigg)^2.$ $d \theta$

asked Dec 30, 2013 by meena.p

1 answer

If $x_1=1$ and $x_{n+1}=\large\frac{4+3x_n}{3+2x_n}\qquad$ $n \geq 1$ and if $\lim\limits_{n\to \infty}x_n=l$ then l is

asked Dec 30, 2013 by sreemathi.v

1 answer

If $\lim\limits_{x\to \infty}\big(\large\frac{x^3+1}{x^2+1}$ $-(ax+b)\big)=2$ then

asked Dec 30, 2013 by sreemathi.v

1 answer

Integrate : $\int \sqrt{\large\frac{x}{1+x}}$ $dx$

asked Dec 30, 2013 by meena.p

1 answer

If $\log (x+y)=2xy$ then $y'(0)=$

asked Dec 30, 2013 by sreemathi.v

1 answer

In a GP, the first term is $312\large\frac{1}{2}$ , the common ratio is $\large\frac{1}{2}$ . Find the sum of the series to $\infty$ terms.

asked Dec 30, 2013 by yamini.v

1 answer

$\lim\limits_{h\to 0}\large\frac{f(2h+2+h^2)-f(2)}{f(h-h^2+1)-f(1)}$ given that $f'(2)=6$ and $f'(1)=4$

asked Dec 30, 2013 by sreemathi.v

1 answer

Let $f:R\to R$ be such that $f(1)=3$ and $f'(1)=6$ .Then $\lim\limits_{x\to 0}\bigg[\large\frac{f(1+x)}{f(1)}\bigg]^{1/x}$ equals

asked Dec 30, 2013 by sreemathi.v

1 answer

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