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12th Standard Maths Discrete Mathematics English Medium Free Online Test One Mark Questions 2020 - 2021

12th Standard

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Maths

Time : 00:10:00 Hrs
Total Marks : 10

    Answer all the questions

    10 x 1 = 10
  1. A binary operation on a set S is a function from

    (a)

    S ⟶ S

    (b)

    (SxS) ⟶ S

    (c)

    S⟶ (SxS)

    (d)

    (SxS) ⟶ (SxS)

  2. The operation * defined by a*b =\(\frac{ab}{7}\) is not a binary operation on

    (a)

    Q+

    (b)

    Z

    (c)

    R

    (d)

    C

  3. If a*b=\(\sqrt { { a }^{ 2 }+{ b }^{ 2 } } \) on the real numbers then * is

    (a)

    commutative but not associative

    (b)

    associative but not commutative

    (c)

    both commutative and associative

    (d)

    neither commutative nor associative

  4. Which one is the inverse of the statement (PVq)➝(pΛq)?

    (a)

    (p∧q)➝(pVq)

    (b)

    ᄀ(pvq)➝(p∧q)

    (c)

    (ᄀpvᄀq)➝(ᄀp∧ᄀq)

    (d)

    (ᄀp∧ᄀq)➝(ᄀpVᄀq)

  5. Which one of the following is incorrect? For any two propositions p and q, we have

    (a)

    ¬ (p∨q) ≡ ¬ p ∧ ¬q

    (b)

    ¬ ( p∧ q)≡¬p ∨ ¬q

    (c)

    ¬ (p ∨ q)≡¬p∨¬q

    (d)

    ¬(¬p)≡ p

  6. The dual of ᄀ(p V q) V [p V (p ∧ ᄀr)] is

    (a)

    ᄀ(p ∧ q) ∧ [p V (p ∧ ᄀr)]

    (b)

    (p ∧ q) ∧ [p ∧ (p V ᄀr)]

    (c)

    ᄀ(p ∧ q) ∧ [p ∧ (p ∧ r)]

    (d)

    ᄀ(p ∧ q) ∧ [p ∧ (pV ᄀr)]

  7. The binary operation * defined on a set s is said to be commutative if

    (a)

    a*b \(\in \) S ∀ a, b \(\in \) S

    (b)

    a*b = b*a ∀ a, b \(\in \) S

    (c)

    (a*b) * c = a*(b*c) ∀ a, b \(\in \) S

    (d)

    a*b = e ∀ a, b \(\in \) S

  8. The number of binary operations that can be defined on a set of 3 elements is

    (a)

    32

    (b)

    33

    (c)

    39

    (d)

    31

  9. Which of the following is a contradiction?

    (a)

    p v q

    (b)

    p ∧ q

    (c)

    q v ~ q

    (d)

    q ∧ ~ q

  10. Let p: Kamala is going to school
    q: There are 20 students in the class. Then Kamala is not going to school or there are 20 students in the class is represented by

    (a)

    p v q

    (b)

    p ∧ q

    (c)

    ~ p

    (d)

    ~ p v q

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