A letter lock consists of three rings with 15 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The total number of possible combinations for the three rings is $15^3 = 3375$.There is only $1$ correct combination to open the lock.Therefore, t

Vedclass · Accepted Answer

$N$ is the product of three distinct prime numbers.

Vedclass · Answer

(C) The total number of possible combinations for the three rings is $15^3 = 3375$.There is only $1$ correct combination to open the lock.Therefore, the number of unsuccessful attempts $N$ is given by $N = 15^3 - 1$.Using the algebraic identity $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$, we have $N = (15 - 1)(15^2 + 15 	imes 1 + 1^2) = 14 	imes (225 + 15 + 1) = 14 	imes 241$.Since $14 = 2 	imes 7$, we get $N = 2 	imes 7 	imes 241$.Here, $2$, $7$, and $241$ are all prime numbers.Thus, $N$ is the product of three distinct prime numbers.

$A$ letter lock consists of three rings with $15$ different letters each. If $N$ denotes the number of ways in which it is possible to make unsuccessful attempts to open the lock, then:

Similar Questions

Let $A = \{(a, b, c) : a, b, c \text{ are non-negative integers and } a + b + 2c = 22\}$. Then $n(A)$ is equal to:

Let $x, y, z$ be three non-negative integers such that $x+y+z=10$. The maximum possible value of $xyz+xy+yz+zx$ is

If $^nP_3 + ^nC_{n-2} = 14n$,then $n = $

The digit in the unit place of the number $2009! + 3^{7886}$ is

The number of ways of selecting $15$ teams from $15$ men and $15$ women,such that each team consists of one man and one woman,is

Vedclass Test Series

Exam Paper Generator

Online Exam Module