R D Sharma Solutions for Chapter: Binary Operations, Exercise 1: MULTIPLE CHOICE QUESTIONS (MCQs)

Write the total number of binary operations on a set consisting of two elements.

Let $*$ be a binary operation, on the set of all non-zero real numbers, given by $a*b=\frac{ab}{5}$ for all $a,b\in R-\left|0\right|$
Write the value of $x$ given by $2*(x* 5)=10$.

Let $*$be a binary operation defined by $a*b= 3a+ 4b- 2$. Find $4 * 5.$

If the binary operation $*$on the set $Z$ of integers is defined by $a*b=a+3b^2$, find the value of $2*4$.

Let $*$ be a binary operation on N given by $a*b=$HCF $(a, b), a, b\in N$. Write the value of $22*4$.

Let $*$ be a binary operation on set of integers$I$, defined by $a*b=2a+b-3$. Find the value of  $3*4$..

If $a * b$ denotes the larger of ' $\text{'}a\text{'}$ and ${}^{\text{'}}b^{\text{'}}$ and if $a\circ b=(a·b)+3$, then write the value of $\left(5\right)\circ \left(10\right)$ where $*$ and $\circ$ are binary operations.

Let $*$ be a binary operation defined on $Q^{+}$ by the rule $a*b=\frac{ab}{3}$ for all $a,b\in Q^{+}.$ The inverse of $4 * 6$ is