Mathematics Test 91

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Mathematics Test 91

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Weekly Quiz Competition

Question 1
4 / -1

The variance of first five prime numbers is

A
10

B
3.2

C
10.24

D
None of these
Question 2
4 / -1

If P → (q v r) is false then the true value of p, q, r respectively are

A
F, T, T

B
T, T, F

C
T, F, F

D
F, F, F
Question 3
4 / -1

If n(A) = 3, n(B) = 6 and A ⊆ B then the number of elements in A ∪ B is equal to :-

A
3

B
9

C
6

D
12

Solution

Since A ⊆ B ∴ A ∪ B = B

so, n(A ∪ B) = n(B)= 6
Question 4
4 / -1

The negation of p → (~ p ∨ q) is –

A
p ∨ (p ~ q)

B
p → ~ (p ∨ q)

C
p → q

D
p ∨ ~ q

Solution

p → (~ p ∨ q) ≡ (~ p) ∨ ((~ p) ∨ q)

≡ ((~ p) ∨ (~ p)) ∨ q ≡ (~ p) ∨ q

Now, the negation of the given expression

≡ ~((~ p) ∨ q) ≡ (~(~ p)) ∨ (~ q) ≡ p ∨ (~ q)
Question 5
4 / -1

Two finite sets have m and n elements. The total number of subsets of the first set is 56 more than the total number of subsets of second set. The value of m and n are :-

A
7, 6

B
6, 3

C
5, 1

D
8, 7

Solution

since 2^m – 2ⁿ = 56

⇒ 2n (2^{m – n} – 1) = 2³ × 7

⇒ 2ⁿ = 2³, 2^{m – n} – 1 = 7

⇒ n = 3, 2^{m – n} = 8

⇒ m – n = 3 ⇒ m = 6
Question 6
4 / -1

If p : 4 is an even prime number

q : 6 is a divisor of 12 and

r : the HCF of 4 and 6 is 2, then which one of the following is true ?

A
(p ∧ q)

B
(p ∨ q) ∧ ~r

C
~(q ∧ r) ∨ p

D
~p ∨ (q ∧ r)

Solution

After seeing the given statements we can say that p is false and q and r are true.

Only option (d) is true

~p ∨ (q ∧ r) ≡ ~ (F) ∨ (T ∧ T) ≡ T ∨ T ≡ T
Question 7
4 / -1

If p : 5 is not greater than 2 and q : Jaipur is capital of Rajasthan, are two statements. Then negation of statement p ⇒ q is the statement

A
5 is not greater than 2 or Jaipur is not capitalof Rajasthan

B
5 is not greater than 2 and Jaipur is not capital of Rajasthan

C
5 is greater than 2 and Jaipur is capital of Rajasthan

D
5 is greater than 2 and Jaipur is not capital of Rajasthan

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Mathematics Test 91

Result

Mathematics Test 91

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SHARING IS CARING

Question 1

10

3.2

10.24

None of these

Question 2

F, T, T

T, T, F

T, F, F

F, F, F

Question 3

3

9

6

12

Solution

Question 4

p ∨ (p ~ q)

p → ~ (p ∨ q)

p → q

p ∨ ~ q

Solution

Question 5

7, 6

6, 3

5, 1

8, 7

Solution

Question 6

(p ∧ q)

(p ∨ q) ∧ ~r

~(q ∧ r) ∨ p

~p ∨ (q ∧ r)

Solution

Question 7

5 is not greater than 2 or Jaipur is not capitalof Rajasthan

5 is not greater than 2 and Jaipur is not capital of Rajasthan

5 is greater than 2 and Jaipur is capital of Rajasthan

5 is greater than 2 and Jaipur is not capital of Rajasthan

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