The number of elements in the set $\{ (a, b) : 2a^2 + 3b^2 = 35, a, b \in \mathbb{Z} \}$,where $\mathbb{Z}$ is the set of all integers,is

If $A = \{ 1, 2, 3, 4 \}$ and $B = \{ a, b \}$,and $f$ is a mapping such that $f: A \to B$,then the Cartesian product $A \times B$ is:

Suppose $A_1, A_2, A_3, \dots, A_{30}$ are $30$ sets each having $5$ elements and $B_1, B_2, \dots, B_n$ are $n$ sets each with $3$ elements. Let $\bigcup_{i=1}^{30} A_i = \bigcup_{j=1}^n B_j = S$ and each element of $S$ belongs to exactly $10$ of the $A_i$'s and exactly $9$ of the $B_j$'s. Then $n$ is equal to:

The equivalent function of $\log {x^2}$ is

If $X$ and $Y$ are two sets such that $X \cup Y$ has $18$ elements,$X$ has $8$ elements,and $Y$ has $15$ elements,how many elements does $X \cap Y$ have?

In an examination,$40 \%$ students failed in Hindi,$50 \%$ students failed in English. If $21 \%$ students failed in both the subjects,find the percentage of those who passed in Hindi.