Recent questions in Mathematics

Integrate : $\int \cos^{-1} \sqrt {\large\frac{x}{a+x}}$ $dx$

asked Jan 2, 2014 by meena.p

1 answer

$f(x)=\sin^{-1}\big(\large\frac{2x}{1+x^2}\big)$ is differentiable on

asked Jan 2, 2014 by sreemathi.v

1 answer

If $a, b, c$ are in $AP$ and $a^2,b^2,c^2$ are in $HP$ , how are $a, b$ and $\large\frac{-c}{2}$ related?

asked Jan 2, 2014 by yamini.v

1 answer

If $\big(\large\frac{2+\sin x}{1+y}\big)\frac{dy}{dx}$ $=-\cos x,y(0)=1$ then $y\big(\large\frac{\pi}{2}\big)=$

asked Jan 2, 2014 by sreemathi.v

1 answer

If $\lim\limits_{x\to 0}\large\frac{((a-n)nx-\tan x)\sin nx}{x^2}$ $=0$ where $n$ is a non zero real number, then $a$ is equal to

asked Jan 2, 2014 by sreemathi.v

1 answer

Which of the following function is differentiable at $x=0$ ?

asked Jan 2, 2014 by sreemathi.v

1 answer

Let $f:(0,\infty)\rightarrow R$ and $f(x)=\int_0^xf(t) dt$ if $f(x^2)=x^2(1+x)$ then f(4) equals

asked Jan 2, 2014 by sreemathi.v

1 answer

If the $i^{th},j^{th}\; and\; k^{th}$ term of an AP and a GP are equal and are $x,y,z$ find the value of $x^{(y-z)}\;.y^{(z-x)}\;.z^{(x-y)}$

asked Jan 2, 2014 by yamini.v

1 answer

Suppose $f:R\rightarrow R$ is a differentiable function and $f(1)=4$ .Then value of $\lim\limits_{x\to 1}\int\limits_4^{f(x)}\large\frac{2t}{x-1}$ $dt$ is

asked Jan 2, 2014 by sreemathi.v

1 answer

$\lim\limits_{x\to 0}\big(\large\frac{x^2+5x+3}{x^2+x+2}\big)^x$ =

asked Jan 2, 2014 by sreemathi.v

1 answer

If a $\xi\;b$ are two positive integers,x is their AM and $y\;\xi\;z$ are two GMs then calculate the value of $\frac{y^3+z^3}{xyz}$

asked Jan 2, 2014 by yamini.v

1 answer

$\lim\limits_{n\to \infty}\bigg[\large\frac{1}{1-n^2}+\frac{2}{1-n^2}+..........+\frac{n}{1-n^2}\bigg]$ is

asked Jan 2, 2014 by sreemathi.v

1 answer

If the harmonic mean H and geometric mean G of two positive numbers a and b are in ratio 3:5, then a and b are in the ratio

asked Jan 2, 2014 by yamini.v

1 answer

$\lim\limits_{x\to 0}\large\frac{2^x-1}{\sqrt{1+x}-1}$ =

asked Jan 2, 2014 by sreemathi.v

1 answer

In a triangle $\bigtriangleup ABC$ ,a,b,c are its sides ,A,B $\xi\;$ C are its angles, if $\cot A,\cot B\;\xi\;\cot C$ are in AP , the a,b, and c are in which progression?

asked Jan 2, 2014 by yamini.v

1 answer

In order that the function $f(x)=(x+1)^{\large\cot x}$ is continuous at $x=0$ . f(0) must be defined as

asked Jan 2, 2014 by sreemathi.v

1 answer

$\lim\limits_{x\to 1}\big[\sec\big(\large\frac{\pi x}{2}\big)$ $\log x\bigg]$ is

asked Jan 2, 2014 by sreemathi.v

1 answer

An infinite GP has its first term as x and sum is 6 , then which of the following is true?

asked Jan 2, 2014 by yamini.v

1 answer

If $f$ is twice differentiable and $f''(0)=2$ then $\lim\limits_{x\to 0}\large\frac{2f(x)-3f(2x)+f(4x)}{x^2}$ =

asked Jan 2, 2014 by sreemathi.v

1 answer

If 5, x, y, z, 1280 are in GP, what are the values of x, y, z.

asked Jan 2, 2014 by yamini.v

1 answer

If the $4^{th}$ term of a GP is the square of its second term and the first term is -2. Find the $7^{th}$ term of the GP.

asked Jan 2, 2014 by yamini.v

1 answer

$\lim\limits_{x\to 0}\large\frac{(1+x)^{1/x}-e}{x}$ is

asked Jan 2, 2014 by sreemathi.v

1 answer

Given that a,b $\xi$ c are in AP,which of the following is true?

asked Jan 2, 2014 by yamini.v

1 answer

$\lim\limits_{x\to 0^+}x^m(\log x)^n,(m,n\in N)$ is

asked Jan 2, 2014 by sreemathi.v

1 answer

The value of $\lim\limits_{n\to \infty}x\bigg[\tan^{-1}\large\frac{x+1}{x+2}$ $-\cot^{-1}\large\frac{x+2}{x}\bigg]$ is

asked Jan 2, 2014 by sreemathi.v

1 answer

If $f(x)=\left\{\begin{array}{1 1}\large\frac{1-\cos\lambda x}{x\sin x}&x\neq 0\\\large\frac{1}{2}&x=0\end{array}\right.$ is continuous at $x=0$ then $\lambda$ is

asked Jan 2, 2014 by sreemathi.v

1 answer

The equation of the plane whose foot of $\perp$ drawn from origin is $(1,2,1)$ . is?

asked Jan 1, 2014 by rvidyagovindarajan_1

1 answer

The equation of the plane that meets the coordinated axis at the points $A,B,C$ respectively so that the centroid of the $\Delta ABC$ is $(\alpha,\beta,\gamma)$ is ?

asked Jan 1, 2014 by rvidyagovindarajan_1

1 answer

The direction ratio of the line $3x+1=6y-2,\:z=1$ is ?

asked Jan 1, 2014 by rvidyagovindarajan_1

1 answer

Find 3 numbers in AP whose sum is 18 and the sum of its cube is 972.

asked Jan 1, 2014 by yamini.v

1 answer

The point on the line $\overrightarrow r=(-2\hat i-\hat j+3\hat k)+\lambda(3\hat i+2\hat j+2\hat k)$ which is at a distance of $3\sqrt 2$ units from the point $(1,2,3)$ is ?

asked Jan 1, 2014 by rvidyagovindarajan_1

1 answer

Find n such that is $\large\frac{512}{729}\;$ is the nth term of the GP 18,-12,8,-----------------

asked Jan 1, 2014 by yamini.v

1 answer

The equation of a line that are equally inclined with the coordinate axis and and which passes through $(-1,2,3)$ is?

asked Jan 1, 2014 by rvidyagovindarajan_1

1 answer

The angle between the lines whose $d.c.$ are given by the equations $3l+m+5n=0$ and $6mn-2nl+5lm=0$ is?

asked Jan 1, 2014 by rvidyagovindarajan_1

1 answer

Find n where 1536 is the nth term of the series 3,6,12---------------

asked Jan 1, 2014 by yamini.v

1 answer

What are next two terms of the GP $\sqrt{2},\;1/\sqrt{2},\;1/2\sqrt{2}$

asked Jan 1, 2014 by yamini.v

1 answer

The equation of the line through the point $(1,2,3)$ and $\perp$ to the plane $\overrightarrow r.(\hat i+2\hat j-5\hat k)+9=0$ is ?

asked Dec 31, 2013 by rvidyagovindarajan_1

1 answer

The equation of the line through the point $(1,1,3)$ and parallel to the planes $\overrightarrow r.(\hat i-\hat j+2\hat k)=5$ and $\overrightarrow r.(3\hat i+\hat j+\hat k)=6$ is ?

asked Dec 31, 2013 by rvidyagovindarajan_1

1 answer

The line $\large\frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{5}$ is parallel to the which of the following?

asked Dec 31, 2013 by rvidyagovindarajan_1

1 answer

Integrate: $\int \cos^{-1} (-3x +4x^3)dx$

asked Dec 31, 2013 by meena.p

1 answer

Integrate : $\int x\bigg( \large\frac{\sec 2x -1}{\sec 2x+1}\bigg) dx$

asked Dec 31, 2013 by meena.p

1 answer

If a line makes angle $\alpha,\:\beta,\:\gamma$ with $x-axis,\:y-axis\:and\:\:z-axis$ respectively, then $sin^2\alpha+sin^2\beta+sin^2\gamma=?$

asked Dec 31, 2013 by rvidyagovindarajan_1

1 answer

Integrate : $\int \log _a x dx$

asked Dec 31, 2013 by meena.p

1 answer

Integrate : $\int \large\frac{1}{5-4 \sin x}$ $dx$

asked Dec 31, 2013 by meena.p

1 answer

The angle between the planes $3x+4y+5z=3$ and $4x-3y+5z=2$ is ?

asked Dec 31, 2013 by rvidyagovindarajan_1

1 answer

The angle between the lines $\large\frac{2-x}{1}=\frac{y}{2}=\frac{z+3}{1}\:\:and\:\:\large\frac{x-4}{4}=\frac{y-1}{1}=\frac{z-5}{2}$ is?

asked Dec 31, 2013 by rvidyagovindarajan_1

1 answer

If the planes $x=cy+bz,\:\:y=az+cx,\:z=bx+ay$ pass through a line then $a^2+b^2+c^2+2abc=?$

asked Dec 31, 2013 by rvidyagovindarajan_1

1 answer

Integrate : $\int \large\frac{1}{\Large\frac{\sqrt 3}{2} \sin x + \cos x }$ $dx$

asked Dec 31, 2013 by meena.p

1 answer

Integrate : $\int \large\frac{\sin 4x}{\sqrt {8+\sin ^4 2x}}$ $dx$

asked Dec 31, 2013 by meena.p

1 answer

If both the roots of the quadratic equation $(b-c)x^2+(c-a)x+(a-b)=0$ are equal. Then $a, b, c$ are in

asked Dec 31, 2013 by yamini.v

1 answer

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