Recent questions tagged p24

Let $\ast$ be the binary operation on $N$ given by $a \ast b =$ LCM of $a$ and $b$. $(v)$ Which elements of $N$ are invertible for the operation $\ast$ ?

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 $b$. $(iv)$ Find the identity of $\ast$ in $N$.

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 $b$. $(iii)$ Is $ \ast$ associative?

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 $b$. $(ii)$ Is $\ast$ commutative?

asked Mar 19, 2013 by balaji.thirumalai

1 answer

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

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

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

asked Jan 31, 2013 by meena.p

0 answers

$\int \sqrt {1+x^2} d(x^2)=$\[(a)\;\frac{2}{3x}(1+x^2)^{3/2}\qquad (b)\;\frac{2}{3}(1+x^2)^{3/2}\qquad(c)\;\frac{2x}{3}(1+x^2)^{3/2}\qquad(d)\;\frac{2x}{3}(1+x^2)\]

asked Jan 31, 2013 by meena.p

0 answers

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

asked Jan 31, 2013 by meena.p

0 answers

$\Large\int \frac {dx}{x\sqrt{1-x^3}} =$\[\begin {array} {1 1} (a)\;\frac{1}{3} log \bigg | \frac {\sqrt {1-x^2}+1}{\sqrt {1-x^2}-1}\bigg | & \quad (b)\;\frac{1}{3} log \bigg |\frac{\sqrt {1-x^2}-1}{\sqrt {1-x^2}+1}\bigg| & \quad \\(c)\;\frac{2}{3} log \bigg |\frac{1}{\sqrt {1-x^3}}\bigg| & \quad(d)\;\frac{1}{3} log | 1-x^3 | \end {array}\]

asked Jan 31, 2013 by meena.p

0 answers

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

asked Jan 31, 2013 by meena.p

0 answers

$\Large\int \frac {x+\sin x}{1+\cos x} \normalsize dx=$\[(a)\;\tan \frac{x}{2}\qquad (b)\;x\tan \frac{x}{2}\qquad(c)\;\cot \frac{x}{2}\qquad(d)\;x \cot \frac{x}{2}\]

asked Jan 31, 2013 by meena.p

0 answers

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

asked Jan 30, 2013 by meena.p

0 answers

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

asked Jan 30, 2013 by meena.p

0 answers

Consider the binary operation $ \wedge$ on the set $\{1, 2, 3, 4, 5\}$ defined by $a \wedge b = min \{a, b\}$. Write the multiplication table of the operation $ \wedge$ .

asked Nov 20, 2012 by vaishali.a

1 answer

For each operation $\ast$ defined below, determine whether $\ast$ is binary, commutative or associative. $\begin{array}{1 1}(i) \;\;\; On\, Z,\, define \,ab\, = a-b & \;\\(ii) \;\;\; On\, Q,\, define \,ab\, = ab+1 & \;\\(iii) \;\;\; On\, Q,\, define \,ab\, = \frac {ab} {2} & \;\\(iv) \;\;\; On\, Z^+, \, define\, ab= 2^{ab} & \;\\(v) \;\;\; On\, Z^+,\, define \,ab\, = a^b & \;\\(vi) \;\;\; On R - \{ -1\},\, define\, ab= \frac {a} {b+1} & \;\end{array}$

asked Nov 20, 2012 by vaishali.a

5 answers

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^+,\,$ defined $\,$ by$\; ab= a-b $

asked Nov 19, 2012 by vaishali.a

1 answer

Ask Questions, Get Answers

Let $\ast$ be the binary operation on $N$ given by $a \ast b =$ LCM of $a$ and $b$. $(v)$ Which elements of $N$ are invertible for the operation $\ast$ ?

Let $\ast$ be the binary operation on $N$ given by $a \ast b =$ LCM of $a$ and $b$. $(iv)$ Find the identity of $\ast$ in $N$.

Let $\ast$ be the binary operation on $N$ given by $a \ast b =$ LCM of $a$ and $b$. $(iii)$ Is $ \ast$ associative?

Let $\ast$ be the binary operation on $N$ given by $a \ast b =$ LCM of $a$ and $b$. $(ii)$ Is $\ast$ commutative?

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

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 $Z^+,define \;\ast\;by\;a\;\ast\;b=a.$

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

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 $\ast\;by\;a\;\ast \;b=ab^2$

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 $on\; z^+,define\; \ast by \;a\;\ast\; b=ab.$

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

$\int \sqrt {1+x^2} d(x^2)=$\[(a)\;\frac{2}{3x}(1+x^2)^{3/2}\qquad (b)\;\frac{2}{3}(1+x^2)^{3/2}\qquad(c)\;\frac{2x}{3}(1+x^2)^{3/2}\qquad(d)\;\frac{2x}{3}(1+x^2)\]

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

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

$\Large\int \frac {x+\sin x}{1+\cos x} \normalsize dx=$\[(a)\;\tan \frac{x}{2}\qquad (b)\;x\tan \frac{x}{2}\qquad(c)\;\cot \frac{x}{2}\qquad(d)\;x \cot \frac{x}{2}\]

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

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

Consider the binary operation \( \wedge\) on the set \(\{1, 2, 3, 4, 5\}\) defined by \(a \wedge b = min \{a, b\}\). Write the multiplication table of the operation \( \wedge\) .

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^+,\,$ defined $\,$ by$\; ab= a-b $