Binary Operations

The binary operation $*R\times R\to R,$ is defined as  $a*b=2a+b.$ From the given options choose the value of  $\left(2*3\right)*4$ is equal to

Let $A$ be set of all real numbers except $-1$ and operation $*$ be defined on $A$ as $a*b=a+b+ab$ for all $a,b\in A.$ 

The value of $x$ in the equation $1*x*3=5$ is

Consider a binary operation $*$ on $N$ defined as $a*b=1,$ for all $a,b\in N.$ Choose the correct answer.

Consider a binary operation $*$ on $N$ defined as $a*b=a^3+b^3$. Choose the correct answer

Let $*$ be a binary operation on $A=Q\times Q,$ where $Q$ is the set of rational numbers, defined by $\left(a,b\right)*\left(c,d\right)=\left(ac,b+ad\right)$ for $\left(a,b\right),\left(c,d\right)\in Q\times Q,$, then the identity element in $A$, is

Let $*$ be a binary operation on $A=N\times N,$ where $N$ is the set of natural numbers, defined by $\left(a,b\right)*\left(c,d\right)=\left(a+c,b+d\right)$ for all $\left(a,b,c,d\right)\in N$, then the identity element , if any in $A$, is

If $*$ be a binary operation on the set $R-\left\{-1\right\}$ defined by $a*b=a+b+ab$, then the inverse of element $a\in R-\left\{-1\right\}$ is

If  $*$ is a binary operation on $Z$ defined by $a*b=a+3b^2,$ then $2*4$ is

Let $*$ be a binary operation on the set of non zero rational numbers $\left\{0\right\}$ defined by

$a*b=\frac{ab}{4},a,b\in Q,$ then inverse of an element $a\in Q^{\text{'}}$ is

Let $*$ be a binary operation on set $Q_0$ (set of non zero rational numbers) defined by $a*b=\frac{ab}{4},a,b\in Q_0,$ then the identity element in $Q_0$ is 

Let $*$ be a binary operation on set $R-\left\{-1\right\}$ defined by $a*b=a+b-ab.$ Then the identity element for $*$ is 

If $A=\left\{1,2\right\}$, the number of binary operations on $A$ having $1$ as identity element and $2$ as inverse of $2$ is

If $*$ be a binary operation on $R-\left\{-1\right\}$ defined by $a*b=\frac{a}{b+1},$ then the value of $3*2$ is

If $*$ be a binary operation on $N$ defined by $a*b=2^{ab},$ then the value of $1*3$ is

If $*$ be a binary operation on $N$ defined by $a*b=a^b,$ then the value of $2*3$ is

If $*$ be a binary operation defined by $a*b=3a+2b-2,$ then the value of $3*5$ is

If a binary operation $*$ is defined on the set $Q$ of rational numbers as $a*b=\frac{ab}{3},$ then the value of $\left(2*3\right)*4$ is

If a binary operation $*$ is defined on the set of integers $Z$ as $a*b=2a^2+b,$ then the value of $1*\left(2*3\right)$ is

Let $\odot$ be a binary opertation on $\mathrm{\mathbb{Q}}-\left\{0\right\}$ defined by a $\odot b=\frac{a}{b}$. Then $1\odot \left(2\odot \left(3\odot 4\right)\right)$ is equal to