Recent questions in Mathematics

The solution of the differential equation $\large\frac{dy}{dx}=\frac{y}{x}+\frac{\phi (y/x)}{\phi ' (y/x)}$ is

asked Sep 20, 2013 by meena.p

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Let $f(0)=1,f(0.5)=\large\frac{5}{4}$$, f(1)=2,f(1.5)=\large\frac{13}{4}$ and $f(2)=5$. Using Simpson's rule, $\int \limits_0^{2} f(x) dx=$

asked Sep 20, 2013 by meena.p

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If $I_n=\int \limits _0^{\pi/4} \tan ^n \theta d \theta$ for $n=1,2,3........$ then $I_{n-1}+I_{n+1}=.............$

asked Sep 20, 2013 by meena.p

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The area (in square units) of the region bounded by the curves $x=y^2$ and $x=3-2y^2$ is

asked Sep 20, 2013 by meena.p

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$\int \large\frac{1+\cos 4x}{\cot x -\tan x}$$dx$=

asked Sep 20, 2013 by meena.p

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If $\int \large\frac{\sin ^8 x -\cos ^8 x}{1-2 \sin ^2 x \cos ^2 x}$$dx=A \sin 2x+B,$ then $A=$

asked Sep 20, 2013 by meena.p

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$\large\int \bigg(\sqrt {\large\frac{a+x}{a-x}}+\sqrt {\large\frac{a-x}{a+x}}\bigg)$$dx= $

asked Sep 20, 2013 by meena.p

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$u=u(x,y)=\sin (y+ax)-(y+ax)^2=>$

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The length of the sub tangent at any point $(x_1,y_1)$ on the curve$y=5^x$

asked Sep 20, 2013 by meena.p

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If the distance travelled by a particle in time $t$ is given by $s=t^2-2t+5$ then its acceleration is

asked Sep 20, 2013 by meena.p

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If $1^{\circ}=\alpha$ radians then the approximate value of $\cos(60^{\circ}1')$ is

asked Sep 20, 2013 by meena.p

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If $ y =\large\frac{\log_{\Large e}x}{x}$ and $z= \log_ ex,$ then $\large\frac{d^2y}{dz^2}+\frac{dy}{dx}=$

asked Sep 20, 2013 by meena.p

1 answer

If $f(x) =|x|+ | \sin x|$ for $x \in \bigg(-\large\frac{\pi}{2},\frac{\pi}{2}\bigg),$ then its left hand derivative at $x=0$ is

asked Sep 20, 2013 by meena.p

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If $\cos^{-1}\bigg(\large\frac{x^2-y^2}{x^2+y^2}\bigg)=k$ (a constant ), then $\large\frac{dy}{dx}=$

asked Sep 20, 2013 by meena.p

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If $y=(1+x)(1+x^2)(1+x^4)........(1+x^{2^{n}}),$ then $\bigg(\large\frac{dy}{dx}\bigg)_{x =0}=$

asked Sep 20, 2013 by meena.p

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If [x] denotes the greatest integer not exceeding x and if the function f defined by \[f(x) = \left\{ \begin{array}{l l} \frac{a+2 \cos x}{x^2} & \quad ( x < 0) \\ b\;\tan \frac{\pi}{[x+4]} & \quad (x \geq 0) \end{array} \right. \] is continuous at $x=0,$ then the ordered pair $(a,b)=$

asked Sep 20, 2013 by meena.p

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$\lim\limits_{x \to 8} \large\frac{\sqrt {1+\sqrt {1+x}}-2}{x-8}=$

asked Sep 19, 2013 by meena.p

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The solution of the differential equation $\large\frac{dy}{dx}$$-2y \tan 2x =e^x\;sec 2x$ is :

asked Sep 17, 2013 by meena.p

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An integrating factor of the equation $(1+y+x^2y) dx +(x+x^3)dy=0$ is

asked Sep 17, 2013 by meena.p

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The approximate value of $ \int \limits_1^3 \large\frac{dx}{2+3x}$ using Simpson's Rule and dividing the interval $[1,3]$ into two equal parts is

asked Sep 17, 2013 by meena.p

1 answer

The area (in square units) bounded by the curves $x=-2y^2$ and $x=1-3y^2$ is

asked Sep 17, 2013 by meena.p

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If $\int \limits_0^b \large\frac{dx}{1+x^2}$$=\int \limits_b^{\infty} \large \frac{dx}{1+x^2},$ then $b=$

asked Sep 17, 2013 by meena.p

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$\int \large\frac{dx}{x (\log x -2)(\log x-3)}$$=1+c=>1=$

asked Sep 17, 2013 by meena.p

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$\int \large \frac{x -\sin x}{1+ \cos x} $$ dx=x \tan \bigg(\large\frac{x}{2}\bigg)$$+p \log \bigg |\sec \bigg(\large\frac{x}{2}\bigg)\bigg |$$+c=>p=$

asked Sep 17, 2013 by meena.p

1 answer

$\int e^x \bigg(\large\frac{2+\sin 2x}{1+\cos 2x}\bigg)$$dx=$

asked Sep 17, 2013 by meena.p

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$u=\log(x^3+y^3+z^3-3xyz)=>(x+y+z)(u_x+u_y+u_z)=$

asked Sep 17, 2013 by meena.p

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The focal length of a mirror is given by $\large\frac{2}{f}=\frac{1}{v}-\frac{1}{u}.$ In finding the values of $u$ and $v$, the error are equal and equal to 'p'. Then, the relative error in f is

asked Sep 17, 2013 by meena.p

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If the curves $x^2+py^2=1$ and $qx^2+y^2=1$ are orthogonal to each other, then

asked Sep 17, 2013 by meena.p

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The relation between pressure $p$ and volume $v$ is given by $pv^{\large\frac{1}{4}}$=Constant. If the percentage decrease in volume is $\large\frac{1}{2}$, then the percentage increase in pressure is

asked Sep 17, 2013 by meena.p

1 answer

$\cos ^{-1} \bigg(\large\frac{y}{b} \bigg)$$=2 \log \bigg(\large\frac{x}{2}\bigg),$$ x > 0=>x^2 \large\frac{d^2y}{dx^2}$$+x \large\frac{dy}{dx}=$

asked Sep 17, 2013 by meena.p

1 answer

$\large\frac{d}{dx}$$ [(x+1)(x^2+1)(x^4+1)(x^8+1)]=(15x^p-16x^q+1)(x-1)^{-2}=>(p,q)=$

asked Sep 17, 2013 by meena.p

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$\sqrt {\large\frac{y}{x}}+\sqrt {\large\frac{x}{y}}$$=2=>\large\frac{dy}{dx}=$

asked Sep 16, 2013 by meena.p

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$\lim \limits_{x \to 0} \large\frac{\tan ^3 x -\sin ^3 x}{x^5}=$

asked Sep 16, 2013 by meena.p

1 answer

$f(x)=\large\frac{1}{1+\Large\frac{1}{x}};$$g(x)=\large\frac{1}{1+\Large\frac{1}{f(x)}}$$=>g'(2)=$

asked Sep 16, 2013 by meena.p

1 answer

Let $f$ be a non-zero real valued continuous function satisfying $f(x+y)=f(x).f(y)$ for all $x,y \in R.$ If $f(2)=9,$ then $f(6)=$

asked Sep 16, 2013 by meena.p

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A variable plane passes through a fixed point $(1,2,3)$. Then the foot of the perpendicular from the origin to the plane lies on

asked Sep 16, 2013 by meena.p

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A plane passing through $(-1,2,3)$ and whose normal makes equal angles with the coordinate axes is

asked Sep 16, 2013 by meena.p

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The direction ratio's of two lines $AB,AC$ are $1,-1,-1$ and $2,-1,1.$ The direction ratios of the normal to the plane $ABC$ are

asked Sep 16, 2013 by meena.p

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$D(2,1,0),E(2,0,0),F(0,1,0)$ are mid-points of the sides $BC,CA,AB$ of $\Delta ABC$ respectively. Then, the centroid of $\Delta ABC$ is

asked Sep 16, 2013 by meena.p

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The perpendicular distance from the point $(1,\pi)$ to the line joining $(1,0^{\circ})$ and $(1, \large\frac{\pi}{2}),$ (in polar coordinates) is

asked Sep 16, 2013 by meena.p

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If $x=9$ is a chord of contact of the hyperbola $x^2-y^2=9,$ then the equation of the tangent at one of the points of contact is

asked Sep 16, 2013 by meena.p

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If the foci of the ellipse $\large\frac{x^2}{25}+\frac{y^2}{16}=1$ and the hyperbola $\large\frac{x^2}{4}-\frac{y^2}{b^2}=1$ coincide, then $b^2=$

asked Sep 16, 2013 by meena.p

1 answer

The midpoint of a chord of the ellipse $x^2+4y^2-2x+20 y=0$ is $(2,-4)$. The equation of the chord is?

asked Sep 16, 2013 by meena.p

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A circle of radius 4, drawn on a chord of the parabola $y^2=8x$ as diameter, touches the axis of the parabola. Then the slope of the chord is

asked Sep 16, 2013 by meena.p

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If the circle $x^2+y^2+4x-6y+c=0$ bisects the circumference of the circle $x^2+y^2-6x+4y-12=0,$ then $c=$

asked Sep 16, 2013 by meena.p

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$(a,0)$ and $(b,0)$ are center of two circles belonging to a co-axial system of which y-axis is the radical axis. If radius of one of the circles is 'r', then the radius of the other circle is

asked Sep 16, 2013 by meena.p

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If the length of the tangent from $(h,k)$ to the circle $x^2+y^2=16$ is twice the length of the tangent from the same point to the circle $x^2+y^2+2x+2y=0,$ then

asked Sep 16, 2013 by meena.p

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For the given circle $C$ with the equation $x^2+y^2-16x -12y +64=0$ match the list -I with the list II given below:

asked Sep 16, 2013 by meena.p

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The circle $4x^2+4y^2-12 x-12y+9=0$

asked Sep 16, 2013 by meena.p

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If the equation $ax^2+2hxy+by^2+2gx+2fy+c=0$ represents a pair of straight lines, then the square of the distance of their point of intersection from the origin is

asked Sep 16, 2013 by meena.p

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