Generate Quiz 6A40D30484B10 - PLS Academy

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Generate Quiz 6A40D30484B10

1 / 10

The set {1, 1} is closed w. r. t. (which operation)

Addition

Multiplication

Subtraction

None

In mathematics, a set is closed under a specific operation if performing that operation on elements within the set always results in another element that is also in the set. As we saw, neither addition nor subtraction results in an element within the set {1, 1}. Multiplication works, but closure requires all applicable operations to work. Therefore, none of the provided operations make the set closed.

2 / 10

The number ‘0’ is

a rational number

an integer

even number

All of these

(d) all of these is the right choice.

Any number that can be represented as a fraction with an integer denominator (q) and numerator (p) and a non-zero denominator (q ≠ 0) is considered a rational number. Zero satisfies the criteria for being a rational number since it can be written as 0/1, 0/2, and so forth.
A whole number, including zero, that can be either positive, negative, or zero is called an integer. This includes zero.

An integer that is precisely divisible by two is called an even number. Zero is an even number since it is equal to 0 divided by 2.

(d) all of these is the right choice.

An integer that is precisely divisible by two is called an even number. Zero is an even number since it is equal to 0 divided by 2.

3 / 10

The numbers which can be put in the form of (p/q) where 𝑝,𝑞 ∈ 𝑍, and q ≠ 0 are:

Rational numbers

Irrational numbers

Natural numbers

Integers

Any number that can be represented as a fraction with an integer denominator (q) and numerator (p) and a non-zero denominator (q ≠ 0) is considered rational. This definition is exactly captured by the expression qp.

4 / 10

If R is the set of all real numbers, then the Cartesian product R x R represents

Cartesian plane

Argand diagram

Ordered pair

Real line

The collection of ordered pairs (x, y) where x ∈ X and y ∈ Y is the Cartesian product of two sets X and Y, represented by X x Y. R is the set of all real numbers in this instance. Therefore, the collection of ordered pairs with a real number as the first element and another as the second is represented by R x R. The points on the Cartesian plane are represented by this set of ordered pairs.

5 / 10

What is the golden rule of fraction in k ≠ 0 a/b =

(ka/kh)

(kb/ka)

(ab/k)

(kb/b)

The golden rule of fractions states that multiplying or dividing the numerator and denominator of a fraction by the same non-zero number keeps the value of the fraction the same. Option (C) is the correct answer. Dividing both the numerator and denominator by k leaves us with ba, which is the original fraction. Therefore, the golden rule of fractions in that form is ab/k.

6 / 10

Q35. The polar coordinates of a point are (2, 319) then the Cartesian coordinates of the point are.

(1.509, -1.312)

(-1.509, -1.312)

(1.509, 1.312)

(-1.509, 1.312)

(1.509, 1.312) c) d) (-1.509, 1.312)

The response is a (1.509, -1.312).

Polar coordinates r, θ are the solution.

r= 2 θ=3190 convert into radians.

θ = 319×180

Coordinates in Cartesian form x, y

For example, x=rcos θ and y=rsin θ

x=2 cos 319 π180 y =2sin319 π180

x=1.509 y= -1.312

(1.509, 1.312) c) d) (-1.509, 1.312)

The response is a (1.509, -1.312).

Polar coordinates r, θ are the solution.

r= 2 θ=3190 convert into radians.

θ = 319×180

Coordinates in Cartesian form x, y

For example, x=rcos θ and y=rsin θ

x=2 cos 319 π180 y =2sin319 π180

x=1.509 y= -1.312

7 / 10

If n is a negative number, then yn is

a rational number

an irrational number

only negative integer

a pure imaginary

Yn is an irrational number when n is a negative integer and y is any real number, including zero, positive, and negative.

Any number that cannot be represented as a straightforward fraction is considered irrational.

Positive integers are even powers of negative numbers, such as -2² = 4.

Negative numbers are odd powers of negative numbers (e.g., -2³ = -8).

Yn cannot be reliably categorized as either irrational (odd power) or rational (even power) since raising a negative number to any power produces either of these two outcomes. As a result, it is an illogical number.

Yn is an irrational number when n is a negative integer and y is any real number, including zero, positive, and negative.

Any number that cannot be represented as a straightforward fraction is considered irrational.

Positive integers are even powers of negative numbers, such as -2² = 4.

Negative numbers are odd powers of negative numbers (e.g., -2³ = -8).

8 / 10

The real part of (x+iy)ⁿ is

cos nθ

sin nθ

rn cos nθ

rn sin nθ

9 / 10

If z = x + ίy lies in the III quadrant then z̄ / z also lies in the III quadrant if:

x > y > 0

x < y < 0

y < x < 0

y > x > 0

10 / 10

(-1+-3 )4 + (-1–3 )4 =?

-2

-16

C (singleton) is the response.

a) Finite set is the set having countable elements.

b) Someone empty set is devoid of elements.

c) Singleton has only one element.

d) Infinite set had uncountable number of elements.

The set is a singleton since there is only one even prime natural number, which is 2.

C (singleton) is the response.

a) Finite set is the set having countable elements.

b) Someone empty set is devoid of elements.

c) Singleton has only one element.

d) Infinite set had uncountable number of elements.

The set is a singleton since there is only one even prime natural number, which is 2.

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