Numbers and Quantification — Flashcards
CBSE · Class 11 · Applied Mathematics
22 flashcards for Numbers and Quantification (CBSE Class 11 Applied Mathematics) to test yourself on key terms and facts.
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What is a prime number? Give three examples.
Answer
A prime number is a positive integer p > 1 that has exactly two positive divisors: 1 and p itself. Examples: 2, 3, 5, 7, 11, 13, 17, 19, 23. Note: 2 is the only even prime number.
State the Fundamental Theorem of Arithmetic.
Answer
Every positive integer n > 1 can be written as a product of primes, and this representation is unique up to the order of primes. Form: n = p₁^a₁ × p₂^a₂ × ... × pᵣ^aᵣ where p₁ < p₂ < ... < pᵣ are dist…
Why is 1 neither prime nor composite?
Answer
If 1 were considered prime, it would violate the uniqueness part of the Fundamental Theorem of Arithmetic. For example, 10 = 2 × 5 = 1 × 2 × 5 = 1² × 2 × 5, giving multiple factorizations. Since 1 has…
Describe the Sieve of Eratosthenes method.
Answer
A method to find all prime numbers up to n: 1) List all integers from 2 to n 2) Start with 2, mark it as prime and cross out all its multiples 3) Find next unmarked number, mark as prime and cross out…
What is RSA encryption and why are prime numbers important in it?
Answer
RSA is a cryptographic system that uses two large prime numbers p and q to create public key (n=pq, e) and private key (d). Security depends on the difficulty of factoring n into p and q. Large primes…
Convert the decimal number 23 to binary.
Answer
23 = 16 + 4 + 2 + 1 = 2⁴ + 2² + 2¹ + 2⁰. Therefore, 23 in binary is (10111)₂. Method: Divide by 2 repeatedly: 23÷2=11 R1, 11÷2=5 R1, 5÷2=2 R1, 2÷2=1 R0, 1÷2=0 R1. Read remainders from bottom: 10111.
Convert the binary number (1101)₂ to decimal.
Answer
(1101)₂ = 1×2³ + 1×2² + 0×2¹ + 1×2⁰ = 8 + 4 + 0 + 1 = 13. General method: Starting from rightmost digit, multiply each digit by corresponding power of 2 and sum all terms.
What is the imaginary unit i and what are its basic properties?
Answer
i is defined as √(-1), so i² = -1. Powers of i follow a cycle: i¹ = i, i² = -1, i³ = -i, i⁴ = 1, then the pattern repeats. General rule: i⁴ⁿ = 1, i⁴ⁿ⁺¹ = i, i⁴ⁿ⁺² = -1, i⁴ⁿ⁺³ = -i for any integer n ≥ …
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