Directions: Each question contains Statement-1 and...

Directions: Each question contains Statement-1 and Statement-2 and has the following choices (a), (b), (c) and (d), out of which ONLY ONE is correct. (a) Statement- 1 is True, Statement- 2 is True; Statement- 2 is a correct explanation for Statement-1 (b) Statement- 1 is True, Statement- 2 is True; Statement- 2 is NOT a correct explanation for Statement-1 (c) Statement- 1 is True, Statement- 2 is False (d) Statement- 1 is False, Statement- 2 is True Statement 1 2-digit numbers are formed by using the digits $1,2,3,5,7,9$ no digit being repeated in any number. Then, the probability that a number thus formed is a prime number $>50$ is $\frac{2}{5}$ and Statement 2 Number of 2 -digit odd numbers that can be formed using the digits $1,2,3,5,7,9$ without repetition is $25 .$

Directions: Each question contains Statement-1 and Statement-2 and has the following choices (a), (b), (c) and (d), out of which ONLY ONE is correct.
(a) Statement- 1 is True, Statement- 2 is True; Statement- 2 is a correct explanation for Statement-1
(b) Statement- 1 is True, Statement- 2 is True; Statement- 2 is NOT a correct explanation for Statement-1
(c) Statement- 1 is True, Statement- 2 is False
(d) Statement- 1 is False, Statement- 2 is True
Statement 1 2-digit numbers are formed by using the digits $1,2,3,5,7,9$ no digit being repeated in any number. Then, the probability that a number thus formed is a prime number $>50$ is $\frac{2}{5}$ and
Statement 2
Number of 2 -digit odd numbers that can be formed using the digits $1,2,3,5,7,9$ without repetition is $25 .$

Key Concepts

Permutations without Repetition

This concept deals with arranging a set of distinct items in order, where no item can be used more than once. In forming numbers from given digits without repetition, the arrangement of the digits matters, and each digit is used only once, which influences the total number of possible outcomes.

Counting Principles

Counting principles involve methods to determine the total number of possible outcomes in a situation. Using the fundamental counting principle, one multiplies the number of choices for each digit’s position to calculate the overall number of outcomes when constructing two-digit numbers.

Combinatorial Probability

Combinatorial probability is the technique of determining the likelihood of an event by calculating the ratio of favorable outcomes to the total number of outcomes. It requires careful enumeration of both the successful cases (such as numbers meeting a specific property) and the total cases available.

Prime Numbers

Prime numbers are natural numbers greater than 1 that have no divisors other than 1 and themselves. In problems where one must identify prime numbers from a set of formed numbers, understanding the definition and testing criteria of primes is crucial.

Parity and Formation of Odd Numbers

Parity refers to whether a number is odd or even. When forming numbers with restrictions, such as creating only odd numbers, it is important to consider the positions that determine a number’s parity, typically focusing on the units digit to ensure the number meets the odd criterion.

Transcript

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