Each of the integers from 1 to 16 are to be placed on the Venn diagram given below in the appropriate regions A to H. Take
S = {the set of Integers from 1 to 16}
I = {The set of odd integers from 1 to 16}
II = {The set of perfect square integers from 1 to 16}
III = {The set of prime integers from 1 to 16}
$$H = S - \left\{I \cup II \cup III \right\}$$
Answer the questions based on this data.
Which regions in the diagram are empty (notrepresented) ?
Which regions contain a single integer ?
Which regions contain five integers ?
Which regions contain two integers ?
The number of elements contained in the regions E and D puttogether is
In a code, the $$n^{th}$$ letter in English alphabet is coded to $$k^{th}$$ letter, where $$k \equiv 3n + 2$$(mod 26), $$1 \leq k \leq 26$$. For example, the $$5^{th}$$ letter E is coded as Q since $$3 \times 5 + 2 = 17 \equiv 17$$(mod 26) and Q is the $$17^{th}$$ letter. The reverse of this process is used for decoding. Based on this coding and decoding processes, answer the questions:
The code word for STATE is
The code word for MOUSE is
The code word for JOLLY is
The word coded as XEDI is
The number of letters that are invariant in this code is