Recent questions tagged q3

If $ A' = \begin{bmatrix} 3 & 4 \\ -1 & 2 \\ 0 & 1 \end{bmatrix} \text{ and } B = \begin{bmatrix} -1 & 2 &1 \\ 1 & 2 & 3 \end{bmatrix}$, then verify that $ (ii) ( A - B )' = A' - B' $

asked Mar 5, 2013 by balaji.thirumalai

1 answer

Construct $a_{2\times 2}$ matrix where $a_{ij} =|2i+3j|$

asked Mar 4, 2013 by sreemathi.v

1 answer

Find values of $k$ if area of triangle is $4\; sq. units$ and vertices are $(-2, 0), (0, 4), (0, k)$

asked Feb 23, 2013 by pady_1

1 answer

Prove that \[cot(\frac{\pi}{4}-2cot^{-1}3)=7\]

asked Feb 19, 2013 by sreemathi.v

1 answer

Find the direction cosines of the line passing through the points $(-2,4,-5)$ and $(1,2,3)$

asked Feb 17, 2013 by thanvigandhi_1

1 answer

If $ \begin{bmatrix} x+3y & y \\ 7-x & 4 \end{bmatrix}=\begin{bmatrix} 4 & -1 \\ 0 & 4 \end{bmatrix} $, find the values of x and y.

asked Feb 15, 2013 by thanvigandhi_1

1 answer

Find the value of x and y if $ 2\begin{bmatrix} 1 & 3 \\ 0 & x \end{bmatrix} + \begin{bmatrix} y & 0 \\ 1 & 2 \end{bmatrix} =\begin{bmatrix} 5 & 6 \\ 1 & 8 \end{bmatrix} $

asked Feb 11, 2013 by thanvigandhi_1

1 answer

If $A = \begin{bmatrix} -1 \\ 2 \\ 3 \end{bmatrix} \: and \: B = \begin{bmatrix} -2 & -1 & -4 \end{bmatrix} $verify that $ (AB)^T=B^TA^T $

asked Feb 9, 2013 by thanvigandhi_1

1 answer

If $A = \begin{bmatrix} 2 & 3 \\ 5 & -2 \end{bmatrix} $ show that $A^{-1} = \frac{1}{19}A.$

asked Feb 8, 2013 by thanvigandhi_1

1 answer

If $ tan^{-1}x+tan^{-1}y=\frac{\pi}{4} $, then write the value of $ x+y+xy$.

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Construct a 2 x 2 matrix $ A = [ a_{ij} ]$, whose elements are given by $ a_{ij} $ is $ \large\frac{( \hat i + \hat j )^2}{2} $

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Write the values of $ x-y+z$ from the following equation : $ \begin{bmatrix} x+y+z \\ x+z \\ y+z \end{bmatrix} = \begin{bmatrix} 9 \\ 5 \\ 7 \end{bmatrix} $

asked Feb 6, 2013 by thanvigandhi_1

1 answer

Given P(A) = 0.3, P(B) = 0.2, Find P(B/A) if A and B are mutually exclusive events.

asked Feb 5, 2013 by meena.p

5 answers

Evaluate : $\begin{vmatrix} cos 15^{\circ} & sin 15^{\circ} \\ sin 75^{\circ} & cos 75^{\circ} \end{vmatrix} $

asked Feb 5, 2013 by thanvigandhi_1

1 answer

An oil company has tow depots A and B with capacities of 7000L and 4000L respectively. The company is to supply oil to three petrol pumps D, E and F whose requirements are 4500L, 3000L and 3500L respectively. The distances (in km) between the depots and the petrol pumps is given in the following table:

asked Feb 5, 2013 by meena.p

0 answers

What are the conditions that the planes $ a_1x+b_1y+c_1z=d_1\;and\; a_2x+b_2y+c_2z=d_2 $ are (i) parallel (ii) perpendicular to each other?

asked Feb 5, 2013 by meena.p

0 answers

If $ \overrightarrow {a}+ \overrightarrow {b}+ \overrightarrow {c}=\overrightarrow 0$ show that $ \overrightarrow {a} \times \overrightarrow {b}=\overrightarrow {b} \times \overrightarrow {c}=\overrightarrow {c} \times \overrightarrow {a}$

asked Feb 4, 2013 by meena.p

1 answer

Write the order and degree of the diff. equation $ \bigg(\large\frac{d^2y}{dx^2}\bigg)^{2/3}=\bigg(y+\frac{dy}{dx}\bigg)^{1/2}$

asked Feb 4, 2013 by meena.p

0 answers

Find the area included between the parabolas $ y^2=4ax\;and\;x^2=4ay$

asked Feb 4, 2013 by meena.p

2 answers

For a 2 x 2 matrix, A = $ [a_{ij} ], $ whose elements are given by $ a_{ij}=\large\frac{i}{j},$ write the value of $ a_{12}.$

asked Feb 4, 2013 by thanvigandhi_1

1 answer

Find the value of y, if $\begin{bmatrix} x-y & 2 \\ x & 5 \end{bmatrix} = \begin{bmatrix} 2 & 2 \\ 3 & 5 \end{bmatrix} $

asked Feb 4, 2013 by thanvigandhi_1

1 answer

Find x if $ \begin{bmatrix} 3 & 4 \\ -5 & 2 \end{bmatrix} = \begin{bmatrix} 2x & 4 \\ -5 & 3 \end{bmatrix} $

asked Feb 3, 2013 by thanvigandhi_1

1 answer

Find the value of x, if : $ \begin{bmatrix} 1 & x & 1 \end{bmatrix} \; \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 3 & 2 & 5 \end{bmatrix} \; \begin{bmatrix} 1 \\ -2 \\ 3 \end{bmatrix} = 0 $

asked Feb 3, 2013 by thanvigandhi_1

1 answer

Differentiate $ \cos^{-1}x^4$ w.r.t. $ x.$

asked Feb 2, 2013 by thanvigandhi_1

1 answer

If $ A = \begin{bmatrix} cos\: \alpha & sin\: \alpha \\ -sin\: \alpha & cos\: \alpha \end{bmatrix} $, then show that AA' = I.

asked Jan 31, 2013 by thanvigandhi_1

1 answer

$\Large\int \frac {\sqrt {\tan x}}{\sin x \cos x} \normalsize dx=$\[(a)\;2\sqrt {\tan x} \qquad (b)\;2\sqrt {\cot x} \qquad(c)\;\sqrt {\cot x} \qquad(d)\;\sqrt {\tan x}\]

asked Jan 30, 2013 by meena.p

0 answers

A matrix A of order 3 x 3 has determinant 4. What is the value of |4A|?

asked Jan 30, 2013 by thanvigandhi_1

0 answers

If $ A = \begin{bmatrix} \cos\theta & -\sin\theta \\ \sin\theta &\cos\theta \end{bmatrix} $ and $A + A'= I$, then find the value of $ \theta $.

asked Jan 29, 2013 by thanvigandhi_1

1 answer

Find the values of x,y and z, if $ \begin{bmatrix} x+y+z \\ x+z \\ y+z \end{bmatrix} = \begin{bmatrix} 9 \\ 5 \\ 7 \end{bmatrix} $

asked Jan 28, 2013 by thanvigandhi_1

1 answer

If $ A = \begin{bmatrix} 6 & -5 \\ 2 & 3 \end{bmatrix} $, then show that A-A' is skew matrix.

asked Jan 27, 2013 by thanvigandhi_1

1 answer

What is the value of $ |4I_3|,$ where $ I_3$ is the identity matrix of order 3?

asked Jan 25, 2013 by thanvigandhi_1

0 answers

If $ \begin{bmatrix} 2x+5 & 3 \\ 5x+2 & 9 \end{bmatrix} = 0$, find x.

asked Jan 25, 2013 by thanvigandhi_1

0 answers

Find $ \frac{dy}{dx}\;when\;y=\Large x^{x^{x^{x.....}}}$

asked Jan 24, 2013 by meena.p

1 answer

If $ |\overrightarrow a | = 3, |\overrightarrow b | = \large\frac{\sqrt 2}{3}$$ \: and \; \overrightarrow a \times \overrightarrow b$ is a unit vector, then find angle between $ \overrightarrow a \: and \overrightarrow b $.

asked Jan 24, 2013 by thanvigandhi_1

0 answers

If $ A=\begin{bmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{bmatrix}\;and\;A+A^T=1.$Find the possible values of $\theta=\large\pi/3.$

asked Jan 24, 2013 by meena.p

0 answers

Solve for $x$: $\sin\bigg[\sin^{-1}\frac{1}{3}+\cos^{-1}x\bigg]=1$

asked Jan 23, 2013 by meena.p

1 answer

Evaluate the determinant : $ \begin{bmatrix} log_ba & 1 \\ 1 & log_ab \end{bmatrix} .$

asked Jan 23, 2013 by thanvigandhi_1

0 answers

Let * be a binary operation on the set of real numbers. If a * b = a+b-ab, 2 * ( 3 * x ) = -7, find the value of x.

asked Jan 22, 2013 by meena.p

1 answer

Evaluate : $ \begin{bmatrix} a+ib & c+id \\ -c+id & a-ib \end{bmatrix} $

asked Jan 22, 2013 by thanvigandhi_1

1 answer

Given that $\large \frac{dy}{dx} = e^{-2y}$ and $y=0$ when $x=5$. Find the value of $x$ when $y=3$.

asked Jan 17, 2013 by sreemathi.v

1 answer

If $ \begin{bmatrix} x & 2 \\ 18 & x \end{bmatrix} = \begin{bmatrix} 6 & 2 \\ 18 & 6 \end{bmatrix} $, then find x?

asked Jan 17, 2013 by thanvigandhi_1

1 answer

Find a unit vector in the direction of $\overrightarrow{PQ},$where $P$ and $Q$ have co-ordinates $(5,0,8)$ and $(3,3,2)$,respectively.

asked Jan 17, 2013 by sreemathi.v

1 answer

Evaluate [ 1 2 1 ] $ \begin{bmatrix} 2 \\ 4 \\ 2 \end{bmatrix}$

asked Jan 16, 2013 by thanvigandhi_1

1 answer

Find the area of the region bounded by the curve $y=x^3$ and $y=x+6$ and $x=0$.

asked Jan 16, 2013 by sreemathi.v

1 answer

If $ \begin{bmatrix} 3a-b & -2b \\ 3 & 7 \end{bmatrix} = \begin{bmatrix} 5 & 3 \\ 3 & 7 \end{bmatrix}$ then find a.

asked Jan 15, 2013 by thanvigandhi_1

1 answer

Evaluate the following $ \displaystyle\int\frac{(x^2+2)}{x+1}dx$

asked Jan 14, 2013 by sreemathi.v

1 answer

Let A be a square matrix of order 3 x 3, then what is the value of | KA |.

asked Jan 11, 2013 by thanvigandhi_1

0 answers

A kite is moving horizontally at a height of 151.5 meters If the speed of kite is 10m/s,how fast is the string being let out,when the kite is 250m away from the boy who is flying the kite?The height of boy is 1.5m

asked Jan 10, 2013 by sreemathi.v

1 answer

Compute the following $ \begin{bmatrix} a & b \\ -b & a \end{bmatrix} + \begin{bmatrix} a & b \\ b & a \end{bmatrix} $

asked Jan 10, 2013 by thanvigandhi_1

1 answer

Find the values of x and y make the following pairs of matrices equal : $\begin{bmatrix} 3x+6 & 5 \\ y+1 & 2-x \end{bmatrix} = \begin{bmatrix} 0 & y-2 \\ 8 & 4 \end{bmatrix} $

asked Jan 10, 2013 by thanvigandhi_1

1 answer

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