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Recent questions tagged sec4

For each operation $\ast$ defined below, determine whether $\ast$ is binary, commutative or associative: On $Z$, define $a \ast b = a-b$

asked Mar 19, 2013 by balaji.thirumalai

1 answer

If a matrix has 13 elements.What are the possible orders it can have? (Note: This question has been split into 2 questions)

asked Mar 19, 2013 by sreemathi.v

1 answer

Let \(\ast\) be a binary operation on the set \(Q\) of rational numbers as follows: $(vi)\;\; a \ast b = {ab}^2$ Find which of the binary operations are commutative and which are associative.

asked Mar 13, 2013 by sreemathi.v

1 answer

Let \(\ast\) be a binary operation on the set \(Q\) of rational numbers as follows: $(v)\;\; a \ast b = \frac{ab}{4}$ Find which of the binary operations are commutative and which are associative.

asked Mar 13, 2013 by sreemathi.v

1 answer

Let \(\ast\) be a binary operation on the set \(Q\) of rational numbers as follows: $(iv)\;\; a \ast b = (a-b)^2$ Find which of the binary operations are commutative and which are associative.

asked Mar 13, 2013 by sreemathi.v

1 answer

Let \(\ast\) be a binary operation on the set \(Q\) of rational numbers as follows: $(iii)\;\; a \ast b = a+ab$ Find which of the binary operations are commutative and which are associative.

asked Mar 13, 2013 by sreemathi.v

1 answer

Let \(\ast\) be a binary operation on the set \(Q\) of rational numbers as follows: $(ii)\;\; a \ast b = a^2+b^2 $ Find which of the binary operations are commutative and which are associative.

asked Mar 13, 2013 by sreemathi.v

1 answer

Determine whether or not each of the definition of $\ast$ given below gives a binary operation. In the event that $\ast$ is not a binary operation, give justification for this: (v)On $Z^+,define \;\ast\;by\;a\;\ast\;b=a.$

asked Mar 13, 2013 by sreemathi.v

1 answer

In the event that $\ast$ is not a binary operation, give justification for this: On $Z^+,$ defined $\;\ast\;by\;a\;\ast\;b=|a-b|.$

asked Mar 13, 2013 by sreemathi.v

1 answer

Determine whether or not each of the definition of $\ast$ given below gives a binary operation. In the event that $\ast$ is not a binary operation, give justification for this: On $R$,defined $\ast\;by\;a\;\ast \;b=ab^2$

asked Mar 13, 2013 by sreemathi.v

1 answer

Determine whether or not each of the definition of $\ast$ given below gives a binary operation. In the event that $\ast$ is not a binary operation, give justification for this $on\; z^+,define\; \ast by \;a\;\ast\; b=ab.$

asked Mar 13, 2013 by sreemathi.v

1 answer

Write Minors and Cofactors of the elements of following determinants: $ (ii) \quad \begin{vmatrix} 1&0&4 \\ 3&5&-1 \\ 0&1&2 \end{vmatrix} $

asked Mar 6, 2013 by sreemathi.v

1 answer

Write Minors and Cofactors of the elements of following determinants: $ \quad \begin{vmatrix} a&c \\ b&d \end{vmatrix}$

asked Mar 6, 2013 by sreemathi.v

1 answer

Differentiate the following w.r.t $x$ :$\large \frac{8^x}{x^8}$

asked Dec 31, 2012 by sreemathi.v

1 answer

Differentiate the following w.r.t $x$: $2^{\large \cos^2x}$

asked Dec 31, 2012 by sreemathi.v

1 answer

Integrate the functions\[\frac{3x^2}{x^6+1}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions\[\frac{1}{\sqrt{1+4x^2}}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions\[\frac{1}{\sqrt{(2-x)^2+1}}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions $\frac{1}{\sqrt{9-25x^2}}$

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions\[\frac{3x}{1+2x^4}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions\[\frac{x^2}{1-x^6}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions\[\frac{x-1}{\sqrt{x^2-1}}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions\[\frac{x^2}{\sqrt{x^6+a^6}}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions\[\frac{\sec^2x}{\sqrt{\tan^2x+4}}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions\[\frac{1}{\sqrt{x^2+2x+2}}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions\[\frac{1}{9x^2+6x+5}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions\[\frac{1}{\sqrt{7-6x-x^2}}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions\[\frac{1}{\sqrt{(x-1)(x-2)}}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions\[\frac{1}{\sqrt{8+3x-x^2}}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions $\frac{1}{\sqrt{(x-a)(x-b)}}$

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions\[\frac{4x+1}{\sqrt{2x^2+x-3}}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions\[\frac{x+2}{\sqrt{x^2-1}}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions\[\frac{5x-2}{1+2x+3x^2}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions\[\frac{6x+7}{\sqrt{(x-5)(x-4)}}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions\[\frac{x+2}{\sqrt{4x-x^2}}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions\[\frac{x+2}{\sqrt{x^2+2x+3}}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions\[\frac{x+3}{x^2-2x-5}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions\[\frac{5x+3}{\sqrt{x^2+4x+10}}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Choose the correct answer in $\Large \int \normalsize\frac{\large dx}{\large x^2+2x+2}$ equals

asked Dec 5, 2012 by sreemathi.v

1 answer

$\Large \int \normalsize\frac{dx}{\sqrt{9x-4x^2}}$ equals

asked Dec 5, 2012 by sreemathi.v

1 answer

Find $| a × b |$, if $a = \hat i - 7\hat j + 7\hat k$ and $b = 3\hat i - 2\hat j + 2\hat k$

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Find a unit vector perpendicular to each of the vector \( \overrightarrow a + \overrightarrow b\) 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 Dec 5, 2012 by thanvigandhi_1

1 answer

If a unit vector \(\overrightarrow a\) makes angles \( \frac{\large \pi}{\large 3} \) with \( \hat i, \frac{\large \pi}{\large 3} \) with \( \hat j\) and an acute angle \(θ\) with \( \hat k\) , then find \( θ \) and hence, the components of \( \overrightarrow a \) .

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Show that $ ( \overrightarrow a - \overrightarrow b) \times ( \overrightarrow a + \overrightarrow b) = 2 ( \overrightarrow a \times \overrightarrow b) $

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Find $λ$ and $μ$ if $ ( 2\hat i + 6\hat j + 27\hat k)\times (\hat i + λ\hat j + μ\hat k) = \overrightarrow 0$

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Given that $\overrightarrow a . \overrightarrow b = 0$ and $ \overrightarrow a$ x $\overrightarrow b = \overrightarrow 0$ What can you conclude about the vectors $\overrightarrow a$ and $ \overrightarrow b$?

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Let the vectors \( \overrightarrow a, \overrightarrow b, \overrightarrow c\) be given as \(a_1\hat i + a_2\hat j + a_3\hat k, \: b_1\hat i + b_2\hat j + b_3\hat k, \: c_1\hat i + c_2\hat j + c_3\hat k \). Then show that \( \overrightarrow a × (\overrightarrow b + \overrightarrow c) = \overrightarrow a × \overrightarrow b + \overrightarrow a × \overrightarrow c\)

asked Dec 5, 2012 by thanvigandhi_1

1 answer

If either $ \overrightarrow a = \overrightarrow 0 $ or $ \overrightarrow b = \overrightarrow 0 $ then $ \overrightarrow a × \overrightarrow b = \overrightarrow 0$. Is the converse true? Justify your answer with an example.

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Find the area of the triangle with vertices $A(1, 1, 2), B(2, 3, 5)$ and $C(1, 5, 5)$.

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Find the area of the parallelogram whose adjacent sides are determined by the vectors $ \overrightarrow a = \hat i - \hat j + 3\hat k$ and $\overrightarrow b = 2\hat i - 7 \hat j + \hat k$

asked Dec 5, 2012 by thanvigandhi_1

1 answer

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