Chapter No 1 :Ring Theory (40 MCQ`S)

  1. Which of the following is not a ring?
    1. `(ZZ_(n ),+_n ,._n)`
    2. `(nZ_,+,.)`
    3. `M_(2X2)(RR)`
    4. `N`
    5. Show Answer
      Answer: D
      Explanation:
      • N/A
  2. Which of the following hold in a ring R?
    1. `0.a=a.0=0 ∀a∈R`
    2. ` a(-b)=(-a)b=-(ab)∀a,b∈R`
    3. `(-a)(-b)=ab∀ab∈R`
    4. All of These
    5. Show Answer
      Answer: D
      Explanation:
      • N/A
  3. The number of units in `ZZ_5`?
    1. 4
    2. 2
    3. 4
    4. 5
    5. Show Answer
      Answer: A
      Explanation:
      • N/A
  4. Which statement is true?
    1. Every ring is also a field.
    2. Every ring is a ring with unity.
    3. The units of `Z_n` form a group under multiplication.
    4. The distributive laws in the ring are not so important.
    5. Show Answer
      Answer: C
      Explanation:
      • N/A
  5. Which of the following is an integral domain?

    1. `ZZ_n, n ` is composite

    2. `ZZ_p` p is composite

    3. `ZZ_12`

    4. `M_(2×2)(RR)`

    5. Show Answer
      Answer: C
      Explanation:
      • N/A
  6. A division ring contains exactly ____ idempotent element?
    1. 1
    2. 2
    3. 3
    4. Only identity element is idempotent
    5. Show Answer
      Answer: B
      Explanation:
      • N/A
  7. Which is the commutative ring without unity?
    1. `M_(2×2) (ZZ)`
    2. `ZZ_n`
    3. 2Z
    4. `ZZ[x]`
    5. Show Answer
      Answer: C
      Explanation:
      • N/A
  8. Which of the following is an infinite non-commutative ring without unity?
    1. `2ZZ`
    2. `M_(2×2) (2ZZ)`
    3. `M_(2×2) (ZZ_n)`
    4. `ZZ[x]`
    5. Show Answer
      Answer: B
      Explanation:
      • N/A
  9. The ring in which ab = 0 but ba ≠ 0 ?
    1. Z
    2. `Q`
    3. `2ZZ`
    4. `M_(2×2) (ZZ)`
    5. Show Answer
      Answer: D
      Explanation:
      • N/A
  10. Infinite Boolean ring is?

    1. `Q`

    2. `M_(2×2) (ZZ_n)`

    3. `M_(2×2) (ZZ)`

    4. `Z_2⊕Z_2⊕Z_2 ⊕Z_2 ⊕….`

    5. Show Answer
      Answer: D
      Explanation:
      • N/A

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