Recent questions tagged q10

Find which of the operations given below has identity: (i) $a \ast b = a - b$.

asked Mar 19, 2013 by balaji.thirumalai

1 answer

Consider a binary operation * on the set ${1,2,3,4,5}$ given by the following multiplication table:

asked Mar 19, 2013 by balaji.thirumalai

0 answers

If A+B+C=0,then prove that $\begin{vmatrix}1& cosC &cos B\\cos C& 1 &cos A\\cos B & cos A &1\end{vmatrix}=0.$

asked Mar 15, 2013 by sreemathi.v

1 answer

By using the properties of determinants show that $ (ii) \begin{vmatrix} y+k&y&y \\ y&y+k&y \\ y&y&y+k \end{vmatrix} = k^2 (3y+k)$

asked Mar 11, 2013 by sreemathi.v

1 answer

Give an example of a relation which is (v) Symmetric and transitive but not reflexive.

asked Mar 8, 2013 by balaji.thirumalai

1 answer

Give an example of a relation which is (iv) Reflexive and transitive but not symmetric.

asked Mar 8, 2013 by balaji.thirumalai

1 answer

Give an example of a relation which is (iii) Reflexive and symmetric but not transitive.

asked Mar 8, 2013 by balaji.thirumalai

1 answer

Give an example of a relation which is (ii) Transitive but neither reflexive nor symmetric.

asked Mar 8, 2013 by balaji.thirumalai

1 answer

Give an example of a relation which is (i) Symmetric but neither reflexive nor transitive.

asked Mar 7, 2013 by balaji.thirumalai

1 answer

A manufacturer produces three products $( x, y, z )$ which he sells in two markets. Annual sales are indicated below: \[ \begin{array} { c c } \textbf{Market} & \textbf{Products} \\ I & 10,000 \quad 2,000 \quad 18,000 \\ II & 6,000 \quad 20,000 \quad 8,000 \end{array} \] If the unit costs of the above three commodities are Rs 2.00, Rs 1.00 and 50 paise respectively. Find the gross profit.

asked Mar 5, 2013 by balaji.thirumalai

1 answer

Express the following matrices as the sum of a symmetric and a skew symmetric matrix: $(iv) \begin{bmatrix} 1 & 5 \\ -1 & 2 \end{bmatrix} $

asked Mar 5, 2013 by balaji.thirumalai

1 answer

Express the following matrices as the sum of a symmetric and a skew symmetric matrix: $(iii) \begin{bmatrix} 3 & 3 & -1 \\ -2 & -2 & 1 \\ -4 & -5 & 2 \end{bmatrix} $

asked Mar 5, 2013 by balaji.thirumalai

1 answer

Express the following matrices as the sum of a symmetric and a skew symmetric matrix: $ (ii) \begin{bmatrix} 6 & -2 & 2 \\ -2 & 3 & -1 \\ 2 & -1 & 3 \end{bmatrix} $

asked Mar 5, 2013 by balaji.thirumalai

1 answer

if A is an invertible matrix of order 3 and |A|=5, then find |adj.A|.

asked Feb 17, 2013 by thanvigandhi_1

1 answer

if $ \begin{bmatrix} x+2 & 3 \\ x+5 & 4 \end{bmatrix}=3,$ find the value of x.

asked Feb 15, 2013 by thanvigandhi_1

1 answer

For what value of $ \lambda $ are the vectors $ \overrightarrow a = 2\hat i - \lambda \hat j + \hat k\: and \: \overrightarrow b = \hat i - 2\hat j + 3\hat k$ perpendicular to each other?

asked Feb 11, 2013 by thanvigandhi_1

1 answer

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

asked Feb 9, 2013 by thanvigandhi_1

1 answer

Write the direction cosines of a line parallel to the line $ \large\frac{3-x}{3} = \frac{y+2}{-2} = \frac{z+2}{6}.$

asked Feb 9, 2013 by thanvigandhi_1

1 answer

Compute the magnitude of the following vector $\large\frac{1}{\sqrt 3}\hat i + \frac{1}{\sqrt 3}\hat j - \frac{1}{\sqrt 3}\hat k. $

asked Feb 8, 2013 by thanvigandhi_1

1 answer

If $ | \overrightarrow a | = 2, | \overrightarrow b | = 7 \: and \: \overrightarrow a $ x $ \overrightarrow b=3\hat i + 2\hat j + 6\hat k$, find the angle between $ \overrightarrow a \: and \: \overrightarrow b.$

asked Feb 7, 2013 by thanvigandhi_1

1 answer

The cartesian equation of a line is $ \large\frac{x+3}{2} = \large\frac{y-5}{4}=\large\frac{z+6}{2} $ Find vector equation of line.

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Evaluate : $ \int\large \frac{e^{2x}-e^{-2x}}{e^{2x}+e^{-2x}}$$dx$

asked Feb 6, 2013 by thanvigandhi_1

1 answer

In a binomial distribution, the sum of mean and variance is 42. Product is 360. FInd the distribution.

asked Feb 5, 2013 by meena.p

0 answers

Find the maximum and minimum values of 5x+2y subject to constraints \[-2x-3y\leq-6\]\[x-2y\leq2\]\[6x+4y\leq24\]\[-3x+2y\leq3\]\[x\geq0\;and\;y\geq0\]

asked Feb 5, 2013 by meena.p

0 answers

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

asked Feb 5, 2013 by thanvigandhi_1

1 answer

Find the equation of the plane passing through the points (1,-1,2) and (2,-2,2) and perpendicular to the plane 6x-2y+2z = 9.

asked Feb 5, 2013 by meena.p

1 answer

Write the vector equation of the line given by $\large \frac{x-5}{3} = \frac{y+4}{7}=\frac{z-6}{2} $

asked Feb 5, 2013 by thanvigandhi_1

1 answer

What is the area of the parallelogram having diagonals $ 3\bar{i}+\bar{j}-2\bar{k}\;and\;\bar{i}-3\bar{j}+4\bar{k}$?

asked Feb 4, 2013 by meena.p

1 answer

Solve:\[\bigg[x\sqrt {x^2+y^2}-y^2\bigg]dx+xydy=0\]

asked Feb 4, 2013 by meena.p

0 answers

Find the area of the smaller region bounded by the curve $ \large\frac{x^2}{16}+\frac{y^2}{9}=1$ and the straight line $ \large\frac{x}{4}+\frac{y}{3}=1$

asked Feb 4, 2013 by meena.p

0 answers

Write the intercept cut off by the plane $ 2x+y-z=5$ on x - axis.

asked Feb 4, 2013 by thanvigandhi_1

1 answer

If a line makes an angle of $ 30^{\circ}, 60^{\circ}, 90^{\circ}$ with the positive direction of x,y,z axes, respectively, then find its direction cosines.

asked Feb 4, 2013 by thanvigandhi_1

0 answers

Find the direction cosines of a line, passing through origin and lying in the first octant, making equal angles with the three coordinates axes.

asked Feb 3, 2013 by thanvigandhi_1

1 answer

Find the distance between the parallel planes $ x+y-z=-4$ and $ 2x+2y-2z+10=0$

asked Feb 3, 2013 by thanvigandhi_1

0 answers

If A and B are independent events such that $ P(A) = 0.2, P(A \cup B)=0.5, \: find \: P(B).$

asked Feb 2, 2013 by thanvigandhi_1

1 answer

A line makes an angles $ 30^{\circ}, 90^{\circ}, 60^{\circ}$ with co-ordinate axes. Find its direction cosines.

asked Jan 31, 2013 by thanvigandhi_1

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$\int x\tan^{-1}x dx=$ \[(a)\;\bigg(\frac{x^2+1}{2}\bigg) \tan^{-1}x- \frac{x}{2} \qquad (b)\;\bigg(\frac{x^2+1}{2}\bigg)+\tan^{-1}x-x \qquad(c)\;(x^2+1)\tan^{-1}x-x \qquad(d)\;(x^2+1) \tan^{-1}x+x \]

asked Jan 30, 2013 by meena.p

0 answers

If A and B are skew-symmetric matrices, then prove that ABA is skew-symmetric.

asked Jan 30, 2013 by thanvigandhi_1

0 answers

Evaluate: $\lim\limits_{y \to 0}\large\frac{(x+y)\sec(x+y)-x\sec{x}}{y}$

asked Jan 30, 2013 by fingeazy

0 answers

Find the distance of the point (2, -1,-4) from the plane $ 3x-4y+12z=9.$

asked Jan 29, 2013 by thanvigandhi_1

0 answers

Find the area of a parallelogram whose adjacent sides are given by $ \overrightarrow a = 3\hat i + \hat j + 4\hat k \: and \: \overrightarrow b = \hat i - \hat j + \hat k$

asked Jan 28, 2013 by thanvigandhi_1

0 answers

Find the value of x, such that $ A = \begin{bmatrix} x & 5 \\ 4 & 2x \end{bmatrix} = \begin{bmatrix} 2 & 5 \\ 16 & 4 \end{bmatrix} $

asked Jan 27, 2013 by thanvigandhi_1

1 answer

Find the value of p, such that the line $ \large\frac{x-3}{12}=\frac{y+1}{p}=\frac{z-3}{17} $ is perpendicular to 4x+y-3z=5.

asked Jan 25, 2013 by thanvigandhi_1

0 answers

Find $\Large \frac{dy}{dx}$ when $y=\tan^{-1}\Large\frac{1+x^2}{1-x^2}$

asked Jan 25, 2013 by meena.p

1 answer

If matrix $ P = [ a_{ij}]_{m*m} $ is a diagonal matrix, then P is expressed as P = diagonal $ [ a_{11}, a_{22}, a_{33},....a_{mm} ].$ If A = diagonal [ 1, 4, -1 ]and B = diagonal [ 3, 2, 6], then write A+B.

asked Jan 25, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int \sec^2(5-7x)dx .$

asked Jan 24, 2013 by thanvigandhi_1

0 answers

The total number of elements in a matrix represents a prime number. How many possible orders a matrix can have.

asked Jan 24, 2013 by meena.p

0 answers

Prove that $\cos\bigg\{2\cot^{-1}\sqrt{\large\frac{1-x}{1+x}}\bigg\}+x=0$

asked Jan 23, 2013 by meena.p

1 answer

Find the vector equation of the line through the points $ 2\hat i - \hat j + \hat k $ and $ \hat i + 2\hat j - 3\hat k $.

asked Jan 23, 2013 by thanvigandhi_1

0 answers

Show that $\frac{1}{\sin^3x}+\cot x+\frac{1}{x^5}+x^3 $ is an odd function.

asked Jan 23, 2013 by meena.p

0 answers

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