Recent questions tagged q8

Akhil and Vijay appear for an interview for two vacancies.The probability of Akhil's selection is $\large\frac{1}{4}$ and Vijay's selection is $\large\frac{2}{3}$.Find the probability that only one of them will be selected.

asked Apr 12, 2013 by sreemathi.v

1 answer

Aman and Bhavan throw a pair of dice alternately.In order to win,they have to get a sum of 8.Find their respective probabilities of winning if Aman starts the game.

asked Apr 11, 2013 by sreemathi.v

0 answers

A purse contains 4 silver and 5 copper coins.A second purse contains 3 silver and 7 copper coins.If a coin is taken out at random from one of the purses,what is the probability that it is a copper coin?

asked Apr 11, 2013 by sreemathi.v

0 answers

A satellite is travelling around the earth in an elliptical orbit having the earth heat a focus and of eccentricity $\large\frac{1}{2}.$ The shortest distance that the satellite get to the earth is $400kms.$ Find the longest distance that the satellite gets from the earth.

asked Apr 11, 2013 by poojasapani_1

1 answer

A box contains 30 bolts and 40 nuts .Half of the bolts and half of the nuts are rusted.If two items are drawn at random from the box,what is the probability that either both are rusted or both are bolts?

asked Apr 10, 2013 by sreemathi.v

0 answers

A bag contains 8 red and 5 white balls.Two successive draws of 3balls are made at random from the bag without replacements.Find the probability that the first draw yields 3 white balls and the second draw 3 red balls.

asked Apr 10, 2013 by sreemathi.v

0 answers

Find the vector and cartesian equations of the plane through the point $(1 , 3 , 2 ) $ and parallel to the lines $\large\frac{x+1}{2}=\frac{y+2}{-1}=\frac{z+3}{3}$ and parallel to the line $\large\frac{x-2}{1}=\frac{y+1}{2}=\frac{z+2}{2}$

asked Apr 7, 2013 by poojasapani_1

1 answer

Find the angle between the following lines. $\large\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-4}{6}$ and $ x+1=\large\frac{y+2}{2}=\frac{z-4}{2}$

asked Apr 6, 2013 by poojasapani_1

1 answer

Prove that $( \overrightarrow{a}\times \overrightarrow{b})\times \overrightarrow{c}= \overrightarrow{a}\times (\overrightarrow{b}\times \overrightarrow{c})$ if $ \overrightarrow{a}$ and $ \overrightarrow{c}$ are collinear. (Where vector triple product is non-zero).

asked Apr 5, 2013 by poojasapani_1

1 answer

Forces $\overrightarrow{2i}+\overrightarrow{7j}, \overrightarrow{2i}-\overrightarrow{5j}+\overrightarrow{6k}, \overrightarrow{-i}+\overrightarrow{2j}-\overrightarrow{k}$ act at a point $P$ Whose position vector is $\overrightarrow{4i}-\overrightarrow{3j}-\overrightarrow{2k}.$ Find the moment of the resultant of three forces acting at $P$ about the point $Q$ whose position vector is $\overrightarrow{6i}+\overrightarrow{j}-\overrightarrow{3k}.$

asked Apr 5, 2013 by poojasapani_1

1 answer

For any three vectors $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ show that $\overrightarrow{a}\times(\overrightarrow{b}+\overrightarrow{c})+\overrightarrow{b}\times(\overrightarrow{c}+\overrightarrow{a})+\overrightarrow{c}\times(\overrightarrow{a}+\overrightarrow{b})=\overrightarrow{0}$

asked Apr 4, 2013 by poojasapani_1

1 answer

Forces of magnitudes $3$ and $4$ units acting in the directions $\overrightarrow{6i}+ \overrightarrow{2j} +\overrightarrow{3k}$ and $\overrightarrow{3i}-\overrightarrow{2j}+\overrightarrow{6k}$ respectively act on a particle which is displaced from the point $(2,2,-1)$to$( 4,3,1)$. find the work done by the forces.

asked Apr 4, 2013 by poojasapani_1

1 answer

If the sum of two unit vectors is a unit vector prove that the magnitude of their difference is $\sqrt{3}$.

asked Apr 3, 2013 by poojasapani_1

1 answer

Solve the following non-homogeneous system of linear equation by determinant method : $ 2x-y+z=2\;,6x-3y+3z=6\;,4x-2y+2z=4$

asked Mar 29, 2013 by poojasapani_1

1 answer

Show that the adjoint of $A=\begin{bmatrix} -4 & -3 & -3 \\1 & 0 & 1 \\4 & 4 & 3 \end{bmatrix}$ is$\;A\;$ it self

asked Mar 28, 2013 by poojasapani_1

1 answer

Find the length of the perpendicular drawn from the origin to the plane 2X-3Y+6Z+21=0.

asked Mar 20, 2013 by sreemathi.v

1 answer

Find $\mid\overrightarrow{x}\mid$,if for a unit vector $\overrightarrow{a},(\overrightarrow{x}-\overrightarrow{a}).(\overrightarrow{x}+\overrightarrow{a})=15.$

asked Mar 20, 2013 by sreemathi.v

1 answer

By using the properties of determinants show that $ (ii) \quad \begin{vmatrix} 1&1&1 \\ a&b&c \\ a^3&b^3&c^3 \end{vmatrix} = (a-b)(b-c)(c-a)(a+b+c) $

asked Mar 6, 2013 by sreemathi.v

1 answer

For the matrix $ A = \begin{bmatrix} 1 & 5 \\ 6 & 7 \end{bmatrix} $ , verify that $(ii) (A - A') $ is a skew symmetric matrix.

asked Mar 5, 2013 by balaji.thirumalai

1 answer

Are the following set of ordered pairs function? If so,examine whether the mapping is injective or subjective $\;\{(a,b)\;:\;a\;$ is a person,$b\;$ is an ancestor of $a\}$

asked Mar 1, 2013 by meena.p

1 answer

Let A = $\begin{bmatrix} 1 & -2 & 1\\ -2 & 3 & 1\\ 1 & 1 & 5 \end{bmatrix}$. Verify that \[\] $(ii)\big(A^{-1}\big)^{-1}$

asked Mar 1, 2013 by sreemathi.v

1 answer

If $ \int_0^1 (3x^2+2x+k)dx=0,$ find the value of k

asked Feb 17, 2013 by thanvigandhi_1

1 answer

Find a vector in the direction of vector $ \overrightarrow a = \hat i - 2\hat j$, whose magnitude is 7.

asked Feb 15, 2013 by thanvigandhi_1

1 answer

Find a unit vector in the direction of $ \overrightarrow a = 3\hat i - 2\hat j + 6\hat k $

asked Feb 11, 2013 by thanvigandhi_1

1 answer

Find the projection of $ \overrightarrow a = 2\hat i +3\hat j + 2\hat k\: on \: \overrightarrow b = \hat i + 2\hat i - \hat j + \hat k$

asked Feb 9, 2013 by thanvigandhi_1

1 answer

Find a unit vector in the direction of the vector $ \overrightarrow a = -2\hat i + \hat j + 2\hat k$

asked Feb 9, 2013 by thanvigandhi_1

1 answer

Find the value of $ \lambda $ for which the vectors $ \overrightarrow \alpha = 3\hat i + \hat j - 2\hat k \: and \: \overrightarrow b = \hat i + \lambda\hat j - 3\hat k $ are perpendicular to each other.

asked Feb 8, 2013 by thanvigandhi_1

1 answer

Find the projection of $ \overrightarrow a = 2\hat i - \hat j + \hat k\: on \: \overrightarrow b = \hat i - 2\hat j + \hat k. $

asked Feb 7, 2013 by thanvigandhi_1

1 answer

For two non zero vectors $ \overrightarrow a \: and \: \overrightarrow b$ write when $ |\overrightarrow a+\overrightarrow b | = | \overrightarrow a | + | \overrightarrow b | $

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Write the position vector of the mid-point of the vector joining the points P(2,3,4) and Q(4,1,-2).

asked Feb 6, 2013 by thanvigandhi_1

1 answer

4 persons are chosen at random from a group of 3 men, 2 women, 3 children. Find the probability that out of 4 choice, exactly 2 are children.

asked Feb 5, 2013 by meena.p

0 answers

Write the direction - cosines of the line joining the points (1,0,0) and (0,1,1).

asked Feb 5, 2013 by thanvigandhi_1

1 answer

Solve the following LPP graphically. Minimize Z = 3x+5y subject to \[-2x+y\leq4\]\[x+y\geq3\]\[x-2y\leq2\]\[x,y\geq0\]

asked Feb 5, 2013 by meena.p

0 answers

Show that the lines $ \Large\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ and $ \Large\frac{x-4}{5}=\frac{y-1}{2}=2$ intersect. Also find the point of intersection.

asked Feb 5, 2013 by meena.p

0 answers

If $ \hat{a}\;and\;\hat{b}$ are unit vectors inclined at an angle $\theta$,then prove that\[(a)\;\cos \frac{\theta}{2}=\frac{1}{2}|\hat{a}+\hat{b}|\qquad(b)\;\tan \frac{\theta}{2}=\frac {|\hat{a}-\hat{b}|}{|\hat{a}+\hat{b}|}\]

asked Feb 4, 2013 by meena.p

1 answer

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

asked Feb 4, 2013 by meena.p

0 answers

Find the area of the region lying above x-axis and included between the curves $ x^2+y^2=2ax\;and\;y^2=ax$

asked Feb 4, 2013 by meena.p

0 answers

For what value of 'a' the vectors $ 2\hat i - 3\hat j + 4\hat k $ and $ a\hat i + 6\hat j - 8\hat k $ are collinear?

asked Feb 4, 2013 by thanvigandhi_1

1 answer

Find the angle between $ \overrightarrow a \: and \: \overrightarrow b$ with magnitude 1 and 2 respectively and when $ |\overrightarrow a$ x $ \overrightarrow b | = \sqrt 3 $

asked Feb 4, 2013 by thanvigandhi_1

0 answers

If $\overrightarrow a$ and $\overrightarrow b $ represent the two adjacent sides of a parallelogram, then write the area of parallelogram in terms of $ \overrightarrow a \: and \: \overrightarrow b$

asked Feb 3, 2013 by thanvigandhi_1

0 answers

Find the magnitude of two vectors $ \overrightarrow a \: and \: \overrightarrow b$ having the same magnitude and such that angle between them is $ 30^{\circ} $ and their scalar product is 3.

asked Feb 3, 2013 by thanvigandhi_1

0 answers

For what values of p, $ \overrightarrow a = (2\hat i + 6\hat j + 3\hat k)$ p is a unit vector.

asked Feb 2, 2013 by thanvigandhi_1

1 answer

Show that the vectors $ \hat i + \hat j + \hat k $ is equally inclined to the axes.

asked Jan 31, 2013 by thanvigandhi_1

0 answers

$\Large\int x^3 e^{x^2} dx=$ \[(a)\;x^2(e^{x^2}-1) \qquad (b)\;\frac{1}{2}x^2(e^{x^2}-1)\qquad(c)\;\frac{1}{2}e^{x^2}(x^2-1) \qquad(d)\;\frac{1}{2}(e^x-1)\]

asked Jan 30, 2013 by meena.p

0 answers

Evaluate : $ \int \large\frac{dx}{5+9x^2} $

asked Jan 30, 2013 by thanvigandhi_1

0 answers

Find a unit vector perpendicular to the vectors $ \hat i + \hat j - \hat k $ and $ \hat i - 2\hat j + \hat k.$

asked Jan 29, 2013 by thanvigandhi_1

0 answers

If $\theta$ is the semivertical angle of a cone of maximum volume and given slant height, then $\tan \theta$ is given by \[(a)\;2\qquad(b)\;1\qquad(c)\;\sqrt 2\qquad(d)\;\sqrt 3\]

asked Jan 28, 2013 by meena.p

0 answers

Find a unit vector parallel to the sum of the vectors $ \overrightarrow a = 2\hat i + 4\hat j - 5\hat k \: and \: \overrightarrow b = \hat i + 2\hat j - 3\hat k $

asked Jan 28, 2013 by thanvigandhi_1

0 answers

Find a vector in the direction of $ -\hat i + \sqrt3 \hat k,$ whose magnitude is 3.

asked Jan 27, 2013 by thanvigandhi_1

0 answers

For what value of k, the vectors $ 2\hat i - \hat j + \hat k$ and $ \hat i+\hat kj - 5\hat k $ are perpendicular to each other.

asked Jan 25, 2013 by thanvigandhi_1

0 answers

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