In a school $70\%$ of the boys like cricket and $50\%$ like football. If $x\%$ like both Cricket and Football, then

In a class, 60% and 68% of students passed their Physics and Mathematics examinations respectively. Then at least ________ percentage of students passed both their Physics and Mathematics examinations.

Let the set $P= \{2,3,4,..., 25\}$. For each $k ∈ P$, define $Q(k)= \{x ∈ P$ such that $x > k$ and $k$ divides $x\}$. Then the number of elements in the set $P - U_{k=2}^{25} Q(k)$ is

In a class, 25% of all students read news from the Internet. Moreover, 45% of all students read news from printed newspaper. Further, 20% of all students read news from both the Internet and printed newspaper and they do not play video games. It is also known that 30% of the students who do not read news play video games. The minimum percentage of students who do not play video games is

Let $P(X)$ denote power set of a set $X$. If $A$ is the null set, then the number of elements in $P(P(P(P(A))))$ is _________.

English exam and Math exam were conducted separately for a class of 120 students. The number of students who did not appear for the English exam is twice the number of students who did not appear for the Math exam. The number of students who passed the Math exam is twice the number of students who appeared but failed the English exam. If the number of students who passed the English exam is twice the number of students who appeared but failed the Math exam, then the number of students who appeared but failed the English exam is ________

Let $A$ and $B$ be two sets such that the Cartesian product $A \times B$ consists of four elements. If two elements of $A \times B$ are $(1,4)$ and $(4,1)$, then