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Recent questions tagged p197

Find the rate of change of the area of a circle with respect to its radius r when $(b)\; r = 4 cm$

asked Jul 5, 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

A stone is dropped into a quiet lake and waves move in circles at the speed of $5 \;cm/s$. At the instant when the radius of the circular wave is $8 \;cm$, how fast is the enclosed area increasing?

asked Nov 22, 2012 by thanvigandhi_1

1 answer

An edge of a variable cube is increasing at the rate of $3\; cm/s$. How fast is the volume of the cube increasing when the edge is $10\; cm$ long?

asked Nov 22, 2012 by thanvigandhi_1

1 answer

The radius of a circle is increasing uniformly at the rate of $3\; cm/s.$ Find the rate at which the area of the circle is increasing when the radius is $10\; cm$.

asked Nov 22, 2012 by thanvigandhi_1

1 answer

The volume of a cube is increasing at the rate of $ 8\;cm^ 3/s$ . How fast is the volume of a cube is increasing at the rate of $8\;cm^ 3 /s$ . How fast is the surface area increasing when the length of an edge is $12 cm$?

asked Nov 16, 2012 by kasturi.c

1 answer

Find the rate of change of the area of a circle with respect to its radius r when $(a)\; r = 3 cm$

asked Nov 16, 2012 by kasturi.c

1 answer

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