List of top Mathematics Questions on Binary operations

The mean of coefficients of x, x2, ....., x7 in the binomial expansion of (2 + x)9 is?

The number of rational terms in the expansion of (33/4 + 53/2)60?

Let ⊙ be a binary operation on Q - {0} defined by a⊙b=\(\frac{a}{b}\). Then 1⊙(2⊙(3⊙4)) is equal to
For any two positive rational numbers m and n, a binary operation * is defined by \(m*n=\frac{m+n}{3}\), then \(\frac{7}{2}*\frac{5}{2}\) is equal to
If $*$ is a binary operation defined by $a*b=\frac{a}{b}+\frac{b}{a}+\frac{1}{ab}$ for positive integers $a$ and $b$, then $2*5$ is equal to
If A = {a, b, c}, then the number of binary operations on A is
If $A = \{a,b,c\}$, then the number of binary operations on $A$ is
If $*$ is the operation defined by $a * b = a^b$ for $a, b \in \mathbb{N}$, then $(2 * 3) * 2$ is equal to:
The number of values of $r$ satisfying the equation $^{39}C_{3r-1} - ^{39}C_{r^{2}} = ^{39}C_{r^{2}-1} - ^{39}C_{3r} $ is
An integrating factor of the differential equation \( \sin x \frac{dy}{dx} + 2y \cos x = 1 \) is:
An integrating factor of the differential equation \( \sin x \frac{dy}{dx} + 2y \cos x = 1 \) is:
An integrating factor of the differential equation \( \sin x \frac{dy}{dx} + 2y \cos x = 1 \) is:
Let $R$ be the relation on the set $R$ of all real numbers, defined by $aRb$ If $|a - b| \le 1$. Then, $R$ is
The Boolean expression for the $XOR$ gate is
A binary sequence is an array of $0's$ and $1's$. The number of $n$ -digit binary sequences which contain even number of $0's$ is
On the set $Q$ of all rational numbers the operation $\star$ which is both associative and commutative is given by $a \star b$, is:
In the group $G = \{1,5,7,11\}$ under multiplication modulo $12$, the solution of $ 7^{-1} \; \otimes_{12} (x \otimes_{12} 11) = 5$ is $x$ =
$(10101101)_2 = (................)_{10}$
In the group $ (Q^+ ,\star )$ of positive rational numbers w.r.t. the binary operation $\star$ defined by $a^{\star} b=\frac {ab}{3} , \forall a,b \in Q^{+}$ the solution of the equation $5 ^{\star} x=4^{-1}$ in $Q^+$ is
In the group $G. = \{1, 3,7,9 \}$ under multiplication modulo $10$, the inverse of $3$ is
The image of the interval [-1, 3] under the mapping $f : R\rightarrow R$ given by $f \left(x\right)=4x^{3}-12x$ is
The number of bijective function from a set A to itself when A contains 106 elements is
On $Q - \{1\}$ such that $a * b = a + b-ab$. Find the identity element.
Suppose that the number of elements in set $A$ is $p$, the number of elements in set $B$ is $q$ and the number of elements in $A \times B$ is $7$. Then $p^2 +q^2 =$
The inverse of the function $ y = \frac{10^x - 10^{-x}}{10^x + 10^{-x}}$ is equal to :