Recent questions tagged p25

Consider a binary operation $\ast$ on the set $\{1, 2, 3, 4, 5\}$ given by the following multiplication table (Table 1.2). \begin{matrix} *&1&2&3&4&5 \\ 1&1&1&1&1&1 \\ 2&1&2&1&2&1 \\ 3&1&1&3&1&1 \\ 4&1&2&1&4&1 \\ 5&1&1&1&1&5 \end{matrix} (iii) Compute $(2 \ast 3) \ast (4 \ast 5)$

asked Mar 20, 2013 by balaji.thirumalai

1 answer

Consider a binary operation $\ast$ on the set $\{1, 2, 3, 4, 5\}$ given by the following multiplication table (Table 1.2). \begin{matrix} *&1&2&3&4&5 \\ 1&1&1&1&1&1 \\ 2&1&2&1&2&1 \\ 3&1&1&3&1&1 \\ 4&1&2&1&4&1 \\ 5&1&1&1&1&5 \end{matrix} (ii) is $\ast$ commutative?

asked Mar 20, 2013 by balaji.thirumalai

1 answer

Consider a binary operation $\ast$ on the set $\{1, 2, 3, 4, 5\}$ given by the following multiplication table (Table 1.2). \begin{matrix} &1&2&3&4&5 \\ 1&1&1&1&1&1 \\ 2&1&2&1&2&1 \\ 3&1&1&3&1&1 \\ 4&1&2&1&4&1 \\ 5&1&1&1&1&5 \end{matrix} (i) Compute $(23)4$ and $2(3*4)$

asked Mar 20, 2013 by balaji.thirumalai

1 answer

State whether the following statement is true or false. Justify. ii) If $\ast$ is a commutative binary operation on N, then $a \ast (b \ast c) = (c \ast b) \ast a$.

asked Mar 20, 2013 by balaji.thirumalai

1 answer

Find which of the operations given below has identity:$(vi)\;\; a \ast b = ab^2$

asked Mar 19, 2013 by meena.p

1 answer

Find which of the operations given below has identity:$(v)\;\; a \ast b = \large\frac {ab} {4}$

asked Mar 19, 2013 by meena.p

1 answer

Find which of the operations given below has identity: $(iv)\;\; a \ast b = (a-b)^2$

asked Mar 19, 2013 by meena.p

1 answer

Find which of the operations given below has identity: $(iii)\;\; a \ast b = a+ab$

asked Mar 19, 2013 by meena.p

1 answer

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

asked Mar 19, 2013 by balaji.thirumalai

1 answer

Let $\ast$ be the binary operation on $N$ given by $a \ast b = $ LCM of $a$ and $b$. $(i)$ Find $5 \ast 7, \; 20 \ast 16$.

asked Mar 19, 2013 by balaji.thirumalai

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

$\large \int \frac {\cos x}{\cos(x-a)} \normalsize dx=A\;x+B\;log \cos(x-\alpha),then $\[(a)\;A=\cos \alpha \qquad (b)\;B=\sin \alpha \qquad(c)\;A=\sin \alpha \qquad(d)\;B=\cos \alpha\]

asked Feb 1, 2013 by meena.p

0 answers

If $\Large \int \normalsize \tan^4 xdx = a\tan^3x+b\tan x+cx,then $\[(a)\;a=\frac{1}{3} \qquad (b)\;b=-1 \qquad(c)a=1\qquad(d)\;c=1\]

asked Feb 1, 2013 by meena.p

0 answers

If $\Large \int \frac {dx}{(x+1)(x-2)} \normalsize = A\; log(x+1)+B\; log(x-2)+c,then $\[(a)\;A+B=0 \qquad (b)\;AB=- \qquad(c)AB=\frac{1}{9}\qquad(d)\;AB=-9\]

asked Feb 1, 2013 by meena.p

0 answers

$S\sin 2x\;log\;\cos x\;dx=$\[(a)\;\frac{1}{2}\cos^2x-cos^2x log\cos x \qquad (b)\;\frac{1}{2}\cos^2x+\cos^2log\cos x \qquad(c)\;\cos^2x.log\cos x \qquad(d)\;\cos^2x (1-log\cos x)\]

asked Feb 1, 2013 by meena.p

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$\Large \int \frac {dx}{x+\sqrt x}=$\[(a)\;\log (1+\sqrt x) \qquad (b)\;\frac{1}{2}\log (1+\sqrt x) \qquad(c)\;2\log (1+\sqrt x) \qquad(d)\;\log (x+\sqrt x)\]

asked Feb 1, 2013 by meena.p

0 answers

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

asked Feb 1, 2013 by meena.p

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

asked Jan 31, 2013 by meena.p

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$\Large \frac {1}{x(x^4-1)^4}=$\[(a)\;\log \bigg[\frac{x^4}{x^4-1}\bigg]\qquad (b)\;\frac{1}{2}\log \bigg[\frac{x^2+1}{x^2+1}\bigg]\qquad(c)\;\frac{1}{4} log \bigg[\frac{x^4-1}{x^4}\bigg]\qquad(d)\;\log \frac{x(x^2-1}{x^2+1}\bigg]\]

asked Jan 31, 2013 by meena.p

0 answers