Mathematics Test 295

Result

Mathematics Test 295

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Weekly Quiz Competition

Question 1
4 / -1

Let R be a relation on the set L of all lines in a plane defined by R = {(L₁, L₂) : L₁ is perpendicular to L₂}. Which properties does R satisfy?

A
Reflexive

B
Symmetric

C
Transitive

D
Equivalence relation

Solution

Given: A relation R defined on the set of lines where L₁ R L₂ if L₁ is perpendicular to L₂.

Solution:

R is not reflexive since no line is perpendicular to itself.

R is symmetric because if L₁ is perpendicular to L₂, then L₂ is perpendicular to L₁.

R is not transitive because if L₁ ⊥ L₂ and L₂ ⊥ L₃, then L₁ is parallel to L₃, not perpendicular.

Answer: Thus, only symmetry holds.
Question 2
4 / -1

Which law states that (A ∩ B)' = A' ∪ B'?

A
Complement law

B
Associative law

C
De Morgan's law

D
Distributive law

Solution

De Morgan's law states that the complement of the intersection of two sets is the union of their complements: (A ∩ B)' = A' ∪ B'.
Question 3
4 / -1

Which set-builder form represents the set {3, -3}?

A
{x : x is a positive integer}

B
{x : x² = 9}

C
{x : x is a prime factor of 9}

D
{x : x is an integer and x + 3 = 0}

Solution
Question 4
4 / -1

The sum of three numbers is 6 . If we multiply third number by 3 and add second number to it, we get 11 . By adding first and third numbers, we get double of the second number. Represent it algebraically and find the numbers using matrix method.

After solving AX = B using the inverse matrix method, what is the value of z?

A
1

B
2

C
3

D
4

Solution

Given:

Let first, second and third numbers be denoted by x,y and z, respectively. Then, according to given conditions, we have

Solution:
Question 5
4 / -1

If sin lies in the second quadrant, what is the value of tan ⁡2x ?

A

B

C

D

Solution
Question 6
4 / -1

A
1/2

B
3/10

C
1/4

D
1/3

Solution

Step-by-step Solution
Question 7
4 / -1

The total number of different combinations of one or more letters which can be made from the letters of the word ‘MISSISSIPPI’ is

A
150

B
148

C
149

D
None of these

Solution

The word 'MISSISSIPPI' contains the following letters with their respective frequencies:

• M : 1

• I : 4

• S : 4

• P : 2

Solution:

The total number of combinations of one or more letters that can be formed from a multiset of letters with frequencies n₁,n₂,…,n_k is given by the formula:

(n₁+ 1) (n₂+ 1)…(n_k+ 1) − 1

The minus one at the end excludes the case where no letters are selected (the empty set).
Question 8
4 / -1

A

B

C

D

Solution
Question 9
4 / -1

The points A(5,−1,1) ; B,(7,−4,7);C(1,−6,10) and D(−1,−3,4) are vertices of a

A
Square

B
Rhombus

C
Rectangle

D
None of these

Solution
Question 10
4 / -1

A

B

C

D

Solution