Recent questions tagged sec-b

Solve:\[(x+y)^2\frac{dy}{dx}=a^2\]

asked Feb 4, 2013 by meena.p

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Form the differential equation of the family of parabolas having vertex at the origin and axis along positive y - axis.

asked Feb 4, 2013 by thanvigandhi_1

1 answer

Find a vector of magnitude 5 units, and parallel to the resultant of the vectors $ \overrightarrow a = 2\hat i + 3\hat j - \hat k \: and \: \overrightarrow b = \hat i - 2\hat j + \hat k$

asked Feb 4, 2013 by thanvigandhi_1

1 answer

Solve:\[(x+y+1)\frac{dy}{dx}=1\]

asked Feb 4, 2013 by meena.p

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If the function f(x) given by $ f(x) = \left\{ \begin{array}{l l}3ax+b, & \quad if { x > 0} \\ 11, & \quad if { x = 1} \\ 5ax-2b, & \quad if { x < 1 } \end{array} \right. $ is continuous at x = 1, find the values of a and b.

asked Feb 4, 2013 by thanvigandhi_1

1 answer

Show that $ Ax^2+By^2=1$ is a solution of the diff. equation. $ x\bigg[y\bigg(\Large\frac{d^2y}{dx^2}\bigg)+\bigg(\frac{dy}{dx}\bigg)^2\bigg]=y \frac{dy}{dx}$

asked Feb 4, 2013 by meena.p

0 answers

Form the differential equation of circles represented by \[(x-\alpha)^2+(y-\beta)^2=r^2\; by \;eliminating\;\alpha\;and\;\beta\]

asked Feb 4, 2013 by meena.p

0 answers

Using properties of determinants, prove the following : $ \begin{vmatrix} x & y & z \\ x^2 & y^2 & z^2 \\ x^3 & y^3 & z^3 \end{vmatrix} = xyz(x-y)(y-z)(z-x) $

asked Feb 4, 2013 by thanvigandhi_1

1 answer

Form the differential equation of the family of curves represented by the equation $ (x+a)^2-2y^2=a^2$

asked Feb 4, 2013 by meena.p

0 answers

Evaluate:$\int\limits_0^1 x\sqrt{\large\frac{1-x^2}{1+x^2}}$$dx$

asked Feb 4, 2013 by meena.p

1 answer

Prove the following : $ \cot^{-1} \bigg[ \large\frac{\sqrt{1+sinx}+\sqrt{1-sinx}}{\sqrt{1+sinx}-\sqrt{1-sinx}} \bigg] = \frac{x}{2}, x \in \bigg( 0, \frac{\pi}{4} \bigg). $

asked Feb 4, 2013 by thanvigandhi_1

1 answer

Evaluate: $\int\limits_0^ a \frac{dx}{x+\sqrt {a^2-x^2}}$

asked Feb 4, 2013 by meena.p

1 answer

Find the value of $ \tan{-1} \bigg(\large \frac{x}{y} \bigg)-\tan^{-1} \bigg(\large \frac{x-y}{x+y} \bigg). $

asked Feb 4, 2013 by thanvigandhi_1

1 answer

Using properties of determinants, prove that $\begin{vmatrix} -a^2 & ab & ac \\ ba & -b^2 & bc \\ ca & cb & -c^2 \end{vmatrix} = 4a^2b^2c^2 $

asked Feb 4, 2013 by thanvigandhi_1

0 answers

Find the value of 'a' for which the function f defined as $ f(x) = \left\{ \begin{array}{l l}asin\frac{\pi}{2}(x+1), & \quad { x \leq 0} \\ \large \frac{\tan\: x-\sin x}{x^3}, & \quad { x > 0} \end{array} \right. $ is continuous at x = 0.

asked Feb 4, 2013 by thanvigandhi_1

1 answer

Differentiate $ x^{\large xcos\: x}+\large\frac{x^2+1}{x^2-1} $ w.r.t. $ x $.

asked Feb 4, 2013 by thanvigandhi_1

0 answers

If $ x=a(\theta-\sin\theta),y=a(1+\cos\theta), $ find $ \large\frac{d^2y}{dx^2} $.

asked Feb 4, 2013 by thanvigandhi_1

0 answers

Sand is pouring from a pipe at the rate of $ 12 cm^3/s.$ The falling sand forms a cone on the ground in such a way that the height of the cone is always one-sixth of the radius of the base. How fast is the height of the sand cone increasing when the height is 4 cm?

asked Feb 4, 2013 by thanvigandhi_1

0 answers

Find the points on the curve $ x^2+y^2-2x-3=0$ at which the tangents are parallel to x - axis.

asked Feb 4, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int \large\frac{5x+3}{\sqrt{x^2+4x+10}}$$dx $

asked Feb 4, 2013 by thanvigandhi_1

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Evaluate : $\int \large\frac{2x}{(x^2+1)(x^2+3)}$$dx $

asked Feb 4, 2013 by thanvigandhi_1

0 answers

Solve the following differential equation: $e^x\tan\: y\: dx+(1-e^x)\sec^2ydy=0$

asked Feb 4, 2013 by thanvigandhi_1

0 answers

Solve the following differential equation : $ \cos^2x\frac{dy}{dx}+y=\tan \: x$

asked Feb 4, 2013 by thanvigandhi_1

0 answers

Find a unit vector perpendicular to each of the vectors $ \overrightarrow a+\overrightarrow b \: and \: \overrightarrow a-\overrightarrow b$, where $ \overrightarrow a=3\hat i+2\hat j +2 \hat k $ and $ \overrightarrow b = \hat i + 2\hat j -2\hat k.$

asked Feb 4, 2013 by thanvigandhi_1

0 answers

Find the angle between the following pair of lines : $\large\frac{-x+2}{-2}=\frac{y-1}{7}=\frac{z+3}{-3}$ and $\large\frac{x+2}{-1}=\frac{2y-8}{4}=\frac{z-5}{4} $ and check whether the lines are parallel or perpendicular.

asked Feb 4, 2013 by thanvigandhi_1

0 answers

Probabilities of solving a specific problem independently by A and B are $ \frac{1}{2} \: and \frac{1}{3} $ respectively. If both try to solve the problem independently, find the probability that (i) the problem is solved (ii) exactly one of them solves the problem.

asked Feb 4, 2013 by thanvigandhi_1

1 answer

Solve $ \tan^{-1}(x+1)+tan^{-1}(x-1)=tan^{-1}\large\frac{8}{31} $.

asked Feb 4, 2013 by thanvigandhi_1

1 answer

Let * be binary operation on Q defined by $ ab=\large\frac{3ab}{5} $ show that is commutative as well as associative. Also find its identity element if it exists.

asked Feb 4, 2013 by thanvigandhi_1

0 answers

using properties of determinants, prove that $ \begin{vmatrix} -bc & b^2+bc & c^2+bc \\ a^2+ac & -ac & c^2+ac \\ a^2+ab & b^2+ab & -ab \end{vmatrix} = (ab+bc+ca)^2 $

asked Feb 4, 2013 by thanvigandhi_1

0 answers

Using elements transformation find the inverse of $ \begin{bmatrix} 2 & -6 \\ 1 & -2 \end{bmatrix} $

asked Feb 4, 2013 by thanvigandhi_1

1 answer

Show that the function f defined as follows, is continuous at x = 2 but not differentiable $f(x) = \left\{ \begin{array}{l l}3x-2, & \quad { 0 < x \leq 1} \\ 2x^2-x, & \quad { 1 < x \leq 2} \\ 5x-4, & \quad { x > 2 } \end{array} \right. $

asked Feb 4, 2013 by thanvigandhi_1

0 answers

Find $ \large\frac{dy}{dx},$$ if \: y=\sin^{-1} \bigg[ x \sqrt{1-x}-\sqrt x \sqrt{1-x^2} \bigg] $.

asked Feb 4, 2013 by thanvigandhi_1

0 answers

If $ y=\sqrt{x^2-1}-\log \bigg( \large\frac{1}{x}+\sqrt{1+\frac{1}{x^2}} \bigg) $ find $\large\frac{dy}{dx} $.

asked Feb 4, 2013 by thanvigandhi_1

0 answers

A water tank has the shape of an inverted right circular cone with its axis vertical and vertex lower most. Its semi-vertical angle is $ \tan^{-1} \bigg(\large\frac{1}{2} \bigg) $. Water is poured into it at a constant rate of 5 cubic meter per minute. Find the rate at which the level of the water is rising at the instant when the depth of water in the tank is 10 m.

asked Feb 4, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int_0^{\pi}\large\frac{x\: dx}{a^2\cos^2x+b^2\sin^2x}$$a,b>0 $

asked Feb 4, 2013 by thanvigandhi_1

0 answers

Show that the differential equation $ 2y.e^{\large\frac{x}{y}}dx+(y-2xe^{\large\frac{x}{y}})dy=0. $ is homogeneous and find its particular solution given that x = 0 when y = 1.

asked Feb 4, 2013 by thanvigandhi_1

0 answers

Find the particular solution of the differential equation : $ \large\frac{dy}{dx}+y\cot x=2x+x^2\cot x, x \neq 0$ given that y = 0 when $ x=\large\frac{\pi}{2}.$

asked Feb 4, 2013 by thanvigandhi_1

0 answers

Form a differential equation of the family of ellipse having foci on y - axis and centre at origin.

asked Feb 4, 2013 by thanvigandhi_1

0 answers

The scalar product of the vector $ \hat i + 2\hat j + 4\hat k $ with a unit vector along the sum of vectors $ \hat i + 2\hat j + 3\hat k $ and $ \lambda \hat i + 4\hat j - 5\hat k $ is equal to one. Find the value of $ \lambda $.

asked Feb 4, 2013 by thanvigandhi_1

0 answers

Find a vector in the direction of vectors $ 5\hat i - \hat j + 2\hat k$ which has magnitude 8 units.

asked Feb 4, 2013 by thanvigandhi_1

0 answers

Find the value of p so that the lines $ \large\frac{1-x}{3}=\frac{7y-14}{2p}=\frac{z-3}{2}$ and $\large\frac{7-7x}{3p}=\frac{y-5}{1}=\frac{6-z}{5} $ are right angles.

asked Feb 4, 2013 by thanvigandhi_1

0 answers

A foot ball match may be either won, drawn or lost by the host country's team. So there are three ways of forecasting the result of any one match. One correct and two incorrect. Find the probability of forecasting at least three correct result for four matches.

asked Feb 4, 2013 by thanvigandhi_1

0 answers

Evaluate: $ \int \limits _0 ^{\pi} log(1+\cos x)dx$

asked Feb 3, 2013 by meena.p

1 answer

Evaluate:$\int _0 ^{\pi/2} \frac {1}{2 \cos x+4 \sin x}dx$

asked Feb 3, 2013 by meena.p

0 answers

Show that the relation R in the set $ A = ( x ; x \in Z, 0 \leq x \leq 12)$ given by $ R = \{(a,b) : |a-b| $ is divisible by 4} is an equivalence relation. Find the set of all elements related to 1.

asked Feb 3, 2013 by thanvigandhi_1

0 answers

Solve for x : $ 2\tan^{-1}(\sin x)=\tan^{-1} (2\sec x),0 < x < \large\frac{\pi}{2} $

asked Feb 3, 2013 by thanvigandhi_1

1 answer

Show that : $ \tan\large\frac{1}{2} \bigg[ \sin^{-1}\frac{2x}{1+x^2} + \cos^{-1}\large\frac{1-y^2}{1+y^2} \bigg] =\large \frac{x+y}{1-xy}$$, |x| < 1, y > 0 \: xy < 1 $

asked Feb 3, 2013 by thanvigandhi_1

1 answer

If none of a,b and c is zero, using properties of determinants, prove that $ \begin{vmatrix} -bc & b^2+bc & c^2+bc \\ a^2+ac & -ac & c^2+ac \\ a^2+ab & b^2+ab & -ab \end{vmatrix} = (bc=ca+ab)^3 $

asked Feb 3, 2013 by thanvigandhi_1

0 answers

If $ \sqrt{1-x^2}+\sqrt{1-y^2}=a(x-y),$ prove that $ \large\frac{dy}{dx}=\sqrt{\frac{1-y^2}{1-x^2}} $.

asked Feb 3, 2013 by thanvigandhi_1

0 answers

If $ y= \bigg( x+\sqrt{x^2-1} \bigg)^m,$ then show that $(x^2+1)\large\frac{d^2y}{dx^2}$$+x\large\frac{dy}{dx}$$-m^2y=0 $

asked Feb 3, 2013 by thanvigandhi_1

0 answers

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