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The integrating factor of the differential equation $\Large \frac{dy}{dx}\normalsize+y=\Large \frac{1+y}{x}$ is

asked Jan 18, 2013 by sreemathi.v

1 answer

The solution of the differential equation $\Large \frac{dy}{dx}=\frac{1-y^2}{1-x^2}$ is:\begin{array}{1 1}(A)\;y=\tan^{-1}x & (B)\;y-x=k(1+xy)\\(C)\;x=tan^{-1}y & (D)\;\tan (xy)=k\end{array}

asked Jan 18, 2013 by sreemathi.v

1 answer

Integrating factor of the differential equation $\large\frac{dy}{dx}$$+y\tan x-\sec x=0$ is \begin{array}{1 1}(A)\;\cos x & (B)\;sec x\\(C)\;e^{\cos x} & (D)\;e^{\sec x} \end{array}

asked Jan 18, 2013 by sreemathi.v

1 answer

The solution of $\Large \frac{dy}{dx}\normalsize +y=e^{-x},y(0)=0$ is:\begin{array}{1 1}(A)\;y=e^x(x-1) & (B)\;y=xe^{-x}\\(C)\;y=xe^{-x}+1 & (D)\;y=(x+1)e^{-x}\end{array}

asked Jan 18, 2013 by sreemathi.v

1 answer

The degree of the differential equation $\large\frac{d^2y}{dx^2}+\bigg(\frac{dy}{dx}\bigg)^3$$+6y^5=0$ is\[(A)\;1\quad(B)\;2\quad(C)\;3\quad(D)\;5\]

asked Jan 18, 2013 by sreemathi.v

1 answer

The general solution of $e^x\cos y\;dx-e^x\sin y\;dy=0$ is:\begin{array}{1 1}(A)\;e^x\cos y=c & (B)\;e^x\sin y=c\\(C)\;e^x=c\;\cos y & (D)\;e^x=c\;\sin y\end{array}

asked Jan 18, 2013 by sreemathi.v

1 answer

The differential equation $y\Large \frac{dy}{dx}\normalsize+x=c$ represents:\begin{array}{1 1}(A)\;family \;of \;hyperbolas & (B)\;family \;of \;parabolas \\(C)\;family \;of \;ellipses & (D)\;family\; of \;circles\end{array}

asked Jan 18, 2013 by sreemathi.v

1 answer

$\tan^{-1}x+\tan^{-1}y=c$ is the general solution of the differential equation:

asked Jan 18, 2013 by sreemathi.v

1 answer

Integrating factor of the differential equation $(1-x^2)\Large \frac{dy}{dx}\normalsize -xy=1$ is \[(A)\;-x\quad(B)\;\frac{x}{1-x^2}\quad(C)\;\sqrt {1-x^2}\quad(D)\;\frac{1}{2}log(1-x^2)\]

asked Jan 18, 2013 by sreemathi.v

1 answer

Which of the following is a second order differential equation\begin{array}{1 1}(A)\;(y')^2+x=y^2 & (B)\;y' y''+y=\sin x\\(C)\;y'''+(y'')^2+y=0 & (D)\;y'=y^2\end{array}

asked Jan 18, 2013 by sreemathi.v

1 answer

The number of solutions of$\Large\frac{dy}{dx}=\Large\frac{y+1}{x-1}$ when y(1)=2 is\[(A)\;none\quad(B)\;one\quad(C)\;two\quad(D)\;infinite\]

asked Jan 18, 2013 by sreemathi.v

1 answer

Solution of $\Large \frac{dy}{dx}$$-y=1,y(0)=1$ is given by \[(A)\;xy=-e^x\quad(B)\;xy=-e^{-x}\quad(C)\;xy=-1\quad(D)\;y=2e^x-1\]

asked Jan 18, 2013 by sreemathi.v

1 answer

Integrating factor of $x\Large \frac{dx}{dy}\normalsize-y=x^4-3x$ is \[(A)\;x\quad(B)\;log x\quad(C)\;\frac{1}{x}\quad(D)\;-x\]

asked Jan 18, 2013 by sreemathi.v

1 answer

Family $y=Ax+A^3$ of curves is represented by the differential equation of degree\[(A)\;1\quad(B)\;2\quad(C)\;3\quad(D)\;4\]

asked Jan 18, 2013 by sreemathi.v

1 answer

Solution of the differential equation $\tan y\sec^2x dx+\tan x\sec^2y dy=0$ is \[(A)\;\tan x+\tan y=c \quad (B)\;\tan x-\tan y=c \quad(C)\;\frac{\tan x}{\tan y}=c \quad (D\;\tan x.tan y=c\]

asked Jan 18, 2013 by sreemathi.v

1 answer

Integrating factor of the differential equation $\cos x\large\frac{dy}{dx}$$+y\sin x=1$ is:\[(A)\;\cos x\quad(B)\;\tan x\quad(C)\;\sec x\quad(D)\;\sin x\]

asked Jan 18, 2013 by sreemathi.v

1 answer

Solution of differential equation $x dy-y dx=0$ represents:

asked Jan 18, 2013 by sreemathi.v

1 answer

The differential equation for $y=A\cos\alpha x+B\sin\alpha x,$where A and B are arbitrary constants is\begin{array}{1 1}(A)\;\frac{d^2y}{dx^2}+x^2y=0 & (B)\;\frac{d^2y}{dx^2}+\alpha^2y=0\\(C)\;\frac{d^2y}{dx^2}+y=0 & (D)\;\frac{d^2y}{dx^2}-y=0\end{array}

asked Jan 18, 2013 by sreemathi.v

1 answer

If $y=e^{-x}(A\cos x+B\sin x)$, then $y$ is a solution of

asked Jan 18, 2013 by sreemathi.v

1 answer

The order and degree of the differential equation $\large\frac{d^2y}{dx^2}+\bigg(\frac{dy}{dx}\bigg)^{\frac{1}{4}}+x^{\frac{1}{5}}=0$,respectively,are\[(A)\;2\;and\;not\;defined\quad(B)\;2\;and\;2\quad(C)\;2\;and\;3\quad(D)\;3\;and\;3\]

asked Jan 18, 2013 by sreemathi.v

1 answer

The degree of the differential equation $1+\bigg[\bigg(\large\frac{dy}{dx}\bigg)^2\bigg]^{\large\frac{3}{2}}=\frac{d^2y}{dx^2}$ is:\[(A)\;4\quad(B)\;\frac{3}{2}\quad(C)\;not\;defined\quad(D)\;2\]

asked Jan 18, 2013 by sreemathi.v

1 answer

The degree of the differential equation $\large\bigg(\frac{d^2y}{dx^2}\bigg)^2+\bigg(\frac{dy}{dx}\bigg)^2$$=x\sin \bigg(\large\frac{dy}{dx}\bigg)$ is:\[(A)\;1\quad(B)\;2\quad(C)\;3\quad(D)\;not\;defined\]

asked Jan 18, 2013 by sreemathi.v

1 answer

The area of the region bounded by the curve $x=2y+3$ and the y-lines $y=1$ and $y=-1$ is \[(A)\;4 sq.units\quad(B)\;\frac{3}{2} sq. units\quad(C)\;6 sq.units\quad(D)8 sq.units\]

asked Jan 16, 2013 by sreemathi.v

1 answer

The area of the region bounded by the curve $y=x+1$ and the lines $x=2$ and $x=3$ is \[(A)\frac{7}{2} sq.units\quad(B)\;\frac{9}{2}sq. units\quad(C)\frac{11} {2}sq.units\quad(D)\frac{13}{2} sq.units\]

asked Jan 16, 2013 by sreemathi.v

1 answer

The area of the region bounded by the circle $x^2+y^2=1$ is \[(A)\;2\pi sq.units\quad(B)\;\pi sq. units\quad(C)\;3\pi sq.units\quad(D)4\pi sq.units\]

asked Jan 16, 2013 by sreemathi.v

1 answer

The area of the region bounded by the ellipse $\large\frac{x^2}{25}+\frac{y^2}{16}=1$ is \begin{array}{1 1}(A)\;2 \pi sq.units & (B)\;20{\pi}^2 sq.units\\(C)\;16{\pi}^2 sq.units & (D)\;25\pi sq.units \end{array}

asked Jan 16, 2013 by sreemathi.v

1 answer

The area of the region bounded by the curve $y=sin x$ between the ordinates $x=0$ and $x=\large\frac{\pi}{2}$ and the x-axis is

asked Jan 16, 2013 by sreemathi.v

1 answer

The area of the region bounded by parabola $y^2=x$ and the straight line $2y=x$ is \begin{array}{1 1}(A)\;\frac{4}{3} sq.units & (B)\;1 sq.units\\(C)\;\frac{2}{3} sq.units & (D)\;\frac{1}{3}sq.units \end{array}

asked Jan 16, 2013 by sreemathi.v

1 answer

The area of the region bounded by the curve $y=\cos x$ between $x=0$ and $x=\pi$ is \begin{array}{1 1}(A)\;2 sq.units & (B)\;4 sq.units\\(C)\;3 sq.units & (D)\;1sq.units \end{array}

asked Jan 16, 2013 by sreemathi.v

1 answer

The area of the region in the first quadrant enclosed by the x-axis,the line y=x and the circle $x^2+y^2=32$ is \begin{array}{1 1}(A)\;16\pi\; sq.units & (B)\;4\pi \;sq.units\\(C)\;32\pi\; sq.units & (D)\;24\pi\;sq.units \end{array}

asked Jan 16, 2013 by sreemathi.v

2 answers

The area of the region bounded by the curve $y=\sqrt {16-x^2}$ and x-axis is \begin{array}{1 1}(A)\;8\pi \;sq.units & (B)\;20\pi\; sq.units\\(C)\;16\pi\; sq.units & (D)\;256\pi\; sq.units \end{array}

asked Jan 16, 2013 by sreemathi.v

1 answer

The area of the region bounded by the curve $x^2=4y$ and the straight line $x=4y-2$ is \begin{array}{1 1}(A)\;\frac{3}{8}sq.units & (B)\;\frac{5}{8}sq.units\\(C)\;\frac{7}{8}sq.units & (D)\;\frac{9}{8} sq.units \end{array}

asked Jan 16, 2013 by sreemathi.v

1 answer

The area of the region bounded by the y-axis ,$y=\cos x$ and $y=\sin x,0\leq x\leq \large\frac{\pi}{2}$ is\begin{array}{1 1}(A)\;1\sqrt 2sq.units & (B)\;(\sqrt 2+1)sq.units\\(C)\;(\sqrt 2-1)sq.units & (D)\;(2\sqrt 2-1)sq.units \end{array}

asked Jan 16, 2013 by sreemathi.v

1 answer

$\Large \int\limits_0^\frac{\pi}{2}\normalsize \sqrt {1-\sin2x}\;dx$ is equal to $(A)\;0\quad(B)\;2\quad(C)\;1\quad(D)\;-1$

asked Jan 15, 2013 by sreemathi.v

1 answer

$\Large \int\limits_\frac{-\pi}{4}^\frac{\pi}{4}\frac{dx}{1+\cos2x}$ is equal to $(A)\;1\quad(B)\;2\quad(C)\;3\quad(D)\;4$

asked Jan 15, 2013 by sreemathi.v

1 answer

If $\large \frac{x^3dx}{\sqrt{1-x^2}}=\normalsize a(1-x^2)^{\Large\frac{3}{2}}+b\sqrt{1-x^2}+C$,then

asked Jan 15, 2013 by sreemathi.v

1 answer

$\Large \int\frac{x+\sin x}{1+\cos x}\normalsize dx$ is equal to\begin{array}{1 1}(A)\;\log\mid1+\cos x\mid+C & (B)\;\log\mid x+\sin x\mid+C\\(C)\;x-\tan\frac{x}{2}+C & (D)\;x\;\tan\frac{x}{2}+C \end{array}

asked Jan 15, 2013 by sreemathi.v

1 answer

$\Large \int\frac{x^3}{x+1}$ is equal to\begin{array}{1 1}(A)\;x+\frac{x^2}{2}+\frac{x^3}{3}-log\mid1-x\mid+C & (B)\;x+\frac{x^2}{2}-\frac{x^3}{3}-log\mid1-x\mid+C\\(C)\;x-\frac{x^2}{2}-\frac{x^3}{3}-log\mid1+x \mid+C & (D)\;x-\frac{x^2}{2}+\frac{x^3}{3}-log\mid1+x \mid+C\end{array}

asked Jan 15, 2013 by sreemathi.v

1 answer

If $\Large \int\frac{dx}{(x+2)(x^2+1)}=\normalsize a\log\mid 1+x^2\mid+b\tan^{-1}x+\frac{1}{5}\log\mid x+2\mid+C$,then\begin{array}{1 1}(A)\;a=\frac{-1}{10},b=\frac{-2}{5} & (B)\;a=\frac{1}{10},b=\frac{-2}{5}\\(C)\;a=\frac{-1}{10},b=\frac{2}{5} & (D)\;a=\frac{1}{10},b=\frac{2}{5}\end{array}

asked Jan 15, 2013 by sreemathi.v

1 answer

$\Large \int\frac{x^9}{(4x^2+1)^6}\normalsize dx $ is equal to\begin{array}{1 1}(A)\;\frac{1}{5x}\bigg(4+\frac{1}{x^2}\bigg)^{-5}+C & (B)\;\frac{1}{5}\bigg(4+\frac{1}{x^2}\bigg)^{-5}+C\\(C)\;\frac{1}{10x}(1+4)^{-5}+C & (D)\;\frac{1}{10}\bigg(\frac{1}{x^2}+4\bigg)^{-5}+C\end{array}

asked Jan 15, 2013 by sreemathi.v

1 answer

$\Large \int e^x\bigg(\frac{1-x}{1+x^2}\bigg)^2 \normalsize dx$ is equal to

asked Jan 15, 2013 by sreemathi.v

1 answer

$ \int\tan^{-1}\sqrt x$ is equal to which of the following options:

asked Jan 15, 2013 by sreemathi.v

1 answer

$\Large \int\frac{dx}{\sin(x-a)\sin(x-b)}$ is equal to\begin{array}{1 1}(A)\;\sin(b-a)\log\begin{vmatrix}\frac{\sin(x-b)}{\sin(x-a)}\end{vmatrix}+C & (B)\;cosec(b-a)\log\begin{vmatrix}\frac{\sin(x-a)}{\sin(x-b)}\end{vmatrix}+C \\(C)\;cosec(b-a)\log\begin{vmatrix}\frac{\sin(x-b)}{\sin(x-a)}\end{vmatrix}+C &(D)\;\sin(b-a)\log\begin{vmatrix}\frac{\sin(x-a)}{\sin(x-b)}\end{vmatrix}+C \end{array}

asked Jan 15, 2013 by sreemathi.v

1 answer

$\Large \int\frac{\cos 2x-\cos 2\theta}{\cos x-\cos\theta}\normalsize dx$ is equal to\begin{array}{1 1}(A)\;2(\sin x+x\cos\theta)+C & (B)\;2(\sin x-x\cos\theta)+C\\(C)\;2(\sin x+2x\cos\theta)+C & (D)\;2(\sin x-2x\cos\theta)+C\end{array}

asked Jan 15, 2013 by sreemathi.v

1 answer

The maximum value of $\Large\frac{1}{x}$ is:

asked Jan 12, 2013 by sreemathi.v

1 answer

$f(x)=x^x$ has a stationary point at

asked Jan 12, 2013 by sreemathi.v

1 answer

Maximum slope of the curve $y=x^3+3x^2+9x-27$ is

asked Jan 12, 2013 by sreemathi.v

1 answer

At $x=\Large\frac{5}{6}$$,f(x)=2\sin 3x+3\cos 3x$ is:

asked Jan 12, 2013 by sreemathi.v

1 answer

The maximum value of sin x,cos x is

asked Jan 12, 2013 by sreemathi.v

1 answer

The function $f(x)=2x^3-3x^2-12x+4$,has

asked Jan 12, 2013 by sreemathi.v

1 answer

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