Question

Identify the correct statement(s).

• A. Number of naughts standing at the end of $\boxed{125}$ is 30
• B. A telegraph has 10 arms an each arm is capable of 9 distinct positions excluding t number of signals that can be transmitted is $10^{10}-1$
• C. Number greater than 4 lacs which can be formed by using only the digits 0, 2, 2,
• D. In a table tennis tournament, each player plays with every other player. If the nu 5050 then the number of players in the tournament is 100

Answer 1

Answer: (B)

(B)

Answer 2

(A) The number of trailing zeros in 125! is given by

$\left\lfloor\frac{125}{5}\right\rfloor+\left\lfloor\frac{125}{25}\right\rfloor+\left\lfloor\frac{125}{125}\right\rfloor = 25+5+1 = 31$, not 30.

(B) A standard telegraph problem states that if there are 10 arms and each arm can take 10 positions, then excluding the “all-arms-down” (null) signal, the total number of signals is

$10^{10}-1$.

Here the statement (despite the wording “9 distinct positions” which likely represents the 10 positions with one being omitted for the null signal) matches the standard result.

(C) The statement is incomplete (or based on available digits 0,2,2 it is impossible to form a number greater than 4 lacs); hence it is incorrect.

(D) In a tournament with n players the number of matches is

$\frac{n(n-1)}{2}=5050$.

Solving, $n^2-n-10100=0$ gives

$n=\frac{1+ \sqrt{1+40400}}{2}=\frac{1+201}{2}=101$, not 100.

Thus, the only correct statement is option (B).