Video summary

Rajasthan Computer Anudeshak Bharti 2026 | Maths Class – संख्या पद्धति (Number System) Part 05

Main summary

Key takeaways

Educational

Main Ideas / Concepts Taught

1) Number system basics (prime vs. composite; divisibility rules)

  • The topics in “Number System” include: divisible, prime, rational, and irrational.
  • Emphasis: learn rules of divisibility first; then primes/composites become easier to identify.

Key contrast

  • Prime number: divisible only by 1 and itself.
  • Composite number: divisible by some number other than 1 and itself.

2) Twin primes and consecutive primes

Twin primes

  • A prime pair that differs by 2.
  • Examples discussed:
    • (59, 61) and (29, 31) are twin primes (difference = 2).
  • Clarification:
    • (2, 3) are consecutive primes, but are not treated as “twin primes” here since the discussion frames twin primes specifically as prime pairs differing by 2.

Consecutive primes

  • The instructor notes there is only one example of consecutive primes in their framing: (2, 3).

Twin prime validity test (pair must both be prime)

  • If either number in a supposed twin prime pair is composite, the pair cannot be twin primes.
  • Example logic:
    • (131, 133): difference is 2, but 133 is composite (divisible by 19) → not twin primes.

3) Counting primes using known results

Pre-stated counts used:

  • From 1 to 100: 25 primes
  • From 1 to 200: 46 primes
  • From 1 to 1000: 68 primes

Question example: “How many odd primes between 1 and 200?”

  • Total primes (1 to 200) = 46
  • The only even prime is 2
  • So, odd primes = 46 − 1 = 45

4) Coprime (co-prime) concept using HCF

Definition

  • Two numbers are coprime if their HCF (GCD) = 1.

Shortcuts discussed

  • If both numbers are prime, they are automatically coprime (primes only have factors 1 and themselves).
  • If one number is prime and the other is composite, they can still be coprime if gcd is 1.
  • The instructor stresses: compute/verify HCF, not guess based on options.

5) Solving prime-related MCQs via quick checks

Common patterns:

  • Apart from 2, any even number cannot be prime.
  • Use divisibility tests for candidate numbers.

Example approach:

  • To find the prime between 110 and 120:
    • Eliminate evens
    • Consider odds only: 111, 113, 115, 117, 119
    • Then apply divisibility checks by small primes to determine which is not divisible.

6) Sum/difference properties of primes

Question idea

  • “If sum of all odd primes is subtracted from sum of all even primes, result is?”

Core reasoning

  • The only even prime is 2.
  • Subtracting odd primes from the “even primes total” leaves the effective difference: 2.

7) Prime numbers in equations (maximum value reasoning)

Question

  • “x, y, z are prime numbers and x + y + z = 38; find maximum value of x.”

Logic used

  • Since 38 is even, the primes must include 2 (the only even prime).
  • Set z = 2 → then x + y = 36.
  • To maximize x, choose the largest prime ≤ 36 such that y = 36 − x is also prime.
  • Conclusion: x = 31 (with y = 5).

8) Rational numbers and “infinite” between two rationals

Core fact

  • Between any two rational numbers, there are infinitely many rational numbers.

For MCQs, a “fixed” method is used to pick one rational number between them.

Method 1: midpoint [ \frac{x+y}{2} ]

Example:

  • Between 3/4 and 3/8: [ \frac{\frac{3}{4}+\frac{3}{8}}{2}=\frac{9}{16} ] (Used to match an option.)

Method 2: denominator manipulation (alternate option-based approach)

  • Convert fractions into comparable forms using numerator/denominator manipulation.
  • Choose the option that lies strictly between the given two rationals.

9) Irrational numbers (perfect surds vs. incomplete radicals)

Criteria

  • An expression with roots is rational only if the radical simplifies to a perfect power (a “complete surd”).
  • If it doesn’t simplify to a perfect power, it is irrational.

Examples

  • Cube root / square root expressions are simplified by rewriting as powers (e.g., cube root of 64 → 4).
  • An irrational example:
    • A cube root term is irrational if it does not become an integer power.

10) Real vs. imaginary classification (for irrational numbers)

Question framing

  • “Are all irrational numbers integers/imaginary/whole/real?”

Instructor conclusion

  • Irrational numbers are real numbers (not imaginary).

11) “Karni” / root power notation explanation

  • The root symbol is referred to as “karni”.
  • Power interpretation:
    • Square root corresponds to power 1/2
    • Cube root corresponds to power 1/3
  • General rule:
    • With root index n, interpret the power as 1/n.

Methodologies / Instruction-like Steps

A) Determining prime vs. composite (quick approach used)

  • Check divisibility:
    • If divisible by some number other than 1 and itself → composite
    • If divisible only by 1 and itself → prime
  • Shortcut elimination:
    • If the number is even and not equal to 2 → not prime
  • Efficient testing:
    • Try divisibility by small primes (e.g., 2, 3, 5, 7, 11, 13, …) up to a relevant limit.

B) Twin prime identification (as applied)

  1. Look for prime pairs that differ by exactly 2.
  2. Verify both numbers in the pair are prime.
  3. If either is composite, reject the pair.

C) Coprime (co-prime) checking (as applied)

  1. Compute whether HCF/GCD = 1.
  2. Shortcut:
    • If both numbers are prime, gcd is 1 → coprime
  3. Otherwise:
    • Compute/argue the gcd; if any common factor > 1 exists → not coprime.

D) Counting “number of odd primes” in a range (used for 1 to 200)

  1. Start from total primes in the range (given: 46 for 1–200).
  2. Subtract 1 for the only even prime (2).
  3. Odd primes = total primes − 1.

E) Finding a rational number between two rationals (MCQ “fixed answer”)

Method 1: midpoint [ \frac{x+y}{2} ] Then simplify and match to the options.

Method 2: alternate comparison

  • Manipulate denominators/numerators into comparable values.
  • Select the option strictly between the two rationals.

F) Max value of a prime in x + y + z = 38 (prime constraint method)

  1. Note 38 is even; only 2 is an even prime.
  2. Include 2 among x, y, z.
  3. Set one variable (e.g., z = 2) → then x + y = 36.
  4. Pick the largest prime x such that y = 36 − x is also prime.

G) Irrational vs. rational using radicals (“complete surd” idea)

  1. Simplify the radical to see whether it becomes an integer.
  2. If it simplifies perfectly to a perfect power (square root of a perfect square, cube root of a perfect cube, etc.) → rational.
  3. If it remains an incomplete radical → irrational.

Speakers / Sources Featured

  • Main instructor (speaking throughout; referred to as “Master ji” / sometimes “Sir”)
  • Alok ji (mentioned about recruitment forms)
  • Dhurandhar sir (named acknowledgment/invitation; students referenced)
  • Chaudhary saheb / Chaudhary ji
  • Sunny (student/participant)
  • Piyush ji / Piyush (student/participant)
  • Rihanna ji / Rihanna (student/participant)
  • Ramesh ji (student/participant)
  • Ankit Sir (mentioned regarding motivation/T-shirts)
  • Other students (e.g., “weak students”, “students”, “all of you” collectively)

Original video