Recent questions tagged 2012

Find the equation of the line through the point ( 3, 4 ) which cuts from the first quadrant a triangle of minimum area.

asked Jan 7, 2013 by thanvigandhi_1

0 answers

Show that the maximum volume of the cylinder which can be inscribed in a sphere of radius $ 5\sqrt 3$ cm is $ 500\pi \: cm^3$

asked Jan 7, 2013 by thanvigandhi_1

0 answers

Using integration, find the area of the circle $ x^2+y^2=16$ which is exterior to the parabola $ y^2=6x$.

asked Jan 7, 2013 by thanvigandhi_1

0 answers

Prove that $ \int_0^a f(x)dx = \int_0^a f(a-x)dx. $ Using it, evaluate $ \int_0^2 x\sqrt {2-x} dx.$

asked Jan 7, 2013 by thanvigandhi_1

0 answers

Find the equation of the plane which contains the line of intersection of the planes $ \overrightarrow r. (\hat i + 2\hat j + 3\hat k ) -4 = 0 \overrightarrow r. (2\hat i + \hat j - \hat k ) + 5 = 0$ and which is perpendicular to the plane $\overrightarrow r. (5\hat i + 3\hat j - 6\hat k ) + 8 = 0 $ .

asked Jan 7, 2013 by thanvigandhi_1

1 answer

Solve the following linear programming problem graphically Minimize $ Z = x-5y+20$. Subject of the constraints : $ \begin{array} xx-y \geq 0 \\ -x+2y \geq 2 \\ x \geq 3 \\ y \leq 4 \\ x,y \geq 0. \end{array} $

asked Jan 7, 2013 by thanvigandhi_1

0 answers

Bag I contains 3 red and 4 black balls and bag II contains 4 red and 5 black. One ball is transferred from Bag I to II, then a ball is drawn from Bag II, the ball so drawn is found to be red in colour. Find the probability that the transferred ball is black.

asked Jan 6, 2013 by thanvigandhi_1

0 answers

Let * be a binary operation defined by ab = 2a+b-3, find 34.

asked Jan 6, 2013 by thanvigandhi_1

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Write the principal value of : $ \cos^{-1}\bigg( \cos\large\frac{7\pi}{6} \bigg). $

asked Jan 6, 2013 by thanvigandhi_1

1 answer

Compute the following : $\begin{bmatrix} a^2+b^2 & b^2+c^2 \\ a^2+c^2 & a^2+b^2 \end{bmatrix} + \begin{bmatrix} 2ab & 2bc \\ -2ac & -2ab \end{bmatrix} $

asked Jan 6, 2013 by thanvigandhi_1

0 answers

Find the transpose of each of the following matrices : $ (i)\begin{bmatrix} 5 \\ \frac{1}{2} \\ -2 \end{bmatrix} $.

asked Jan 6, 2013 by thanvigandhi_1

1 answer

Find the co-factor of $ a_{12}$ in the following $ \begin{bmatrix} 2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7 \end{bmatrix} $.

asked Jan 6, 2013 by thanvigandhi_1

0 answers

$\int \: \bigg[ \sqrt x - \large\frac{1}{\sqrt x}\bigg]^2$$dx. $

asked Jan 6, 2013 by thanvigandhi_1

0 answers

$ \int\: \frac{\large x^3+3x+4}{\large \sqrt x}dx.$

asked Jan 6, 2013 by thanvigandhi_1

0 answers

If $ \overrightarrow a = \hat i + 2\hat j - \hat k\: and \: \overrightarrow b =( 3\hat i + \hat j - 5\hat k)$, find a unit vector in the direction of $ \overrightarrow a - \overrightarrow b.$

asked Jan 6, 2013 by thanvigandhi_1

0 answers

Find the angle between the vectors $ \overrightarrow a = \hat i - \hat j + 4\hat k \: and \: \overrightarrow b = \hat i + \hat j - \hat k $

asked Jan 6, 2013 by thanvigandhi_1

0 answers

If $ \overrightarrow a = \hat i - 2\hat j + 3\hat k \: and \: \overrightarrow b = -2\hat i + 3\hat j - 4\hat k \: and \: \overrightarrow c = \hat i - 3\hat j - \lambda \hat k $ are coplanar if $ \lambda = 5.$

asked Jan 6, 2013 by thanvigandhi_1

0 answers

Prove that the relation R in the set A = {1, 2, 3, 4, 5}given by R = {(a, b):|a-b) is even }, is an equivalence relation.

asked Jan 6, 2013 by thanvigandhi_1

0 answers

Prove that :$ \sin^{-1}\bigg(\large\frac{ 4}{ 5} \bigg) $$+ \sin^{-1}\bigg(\large\frac{ 5}{ 13} \bigg)$$+ \sin^{-1}\bigg(\frac{\large 16}{\large 65}\bigg) = \frac{\large \pi}{\large 2}.$

asked Jan 6, 2013 by thanvigandhi_1

0 answers

Solve for : $ x : tan^{-1}3x+tan^{-1}2x=\frac{\large \pi}{\large 4}. $

asked Jan 6, 2013 by thanvigandhi_1

0 answers

Using properties of determinants, prove the following : $ \begin{bmatrix} (b+c)^2 & a^2 & a^2 \\ b^2 & (c+a)^2 & b^2 \\ c^2 & c^2 & (a+b)^2 \end{bmatrix} = 2abc(a+b+c)^33 - 3abc. $

asked Jan 6, 2013 by thanvigandhi_1

0 answers

Using properties of determinants, prove the following : $ \begin{bmatrix} (b+c)^2 & a^2 & a^2 \\ b^2 & (c+a)^2 & b^2 \\ c^2 & c^2 & (a+b)^2 \end{bmatrix} = 2abc(a+b+c)^3. $

asked Jan 6, 2013 by thanvigandhi_1

0 answers

If $ y=3 \cos (log\: x) + 4\sin (\log x)$ then show that $ x^2\frac{\large d^2y}{\large dx^2}+x\frac{\large dy}{\large dx}+y=0. $

asked Jan 6, 2013 by thanvigandhi_1

0 answers

Find $\large \frac{dy}{dx}$ if $ (x^2+y^2)^2=xy$

asked Jan 6, 2013 by thanvigandhi_1

0 answers