9. If [tex]\( x \)[/tex] is a positive real number and [tex]\( x^2 = 3 \)[/tex], then [tex]\( x^4 \)[/tex] is:

(a) 9
(b) 3
(c) [tex]\( 3\sqrt{3} \)[/tex]
(d) [tex]\( \sqrt{3} \)[/tex]

10. The ordinate of all points on the [tex]\( y \)[/tex]-axis is:

(a) 9
(b) 3
(c) [tex]\( 3\sqrt{3} \)[/tex]
(d) [tex]\( \sqrt{3} \)[/tex]



Answer :

Sure, let's solve this step by step.

### Question 9: If [tex]\( x \)[/tex] is a positive real number and [tex]\( x^2 - 3 = 3 \)[/tex], then [tex]\( x^4 = \)[/tex] ?

1. Given Equation:
[tex]\[ x^2 - 3 = 3 \][/tex]

2. Solve for [tex]\( x^2 \)[/tex]:
[tex]\[ x^2 - 3 = 3 \][/tex]
[tex]\[ x^2 = 3 + 3 \][/tex]
[tex]\[ x^2 = 6 \][/tex]

3. Calculate [tex]\( x^4 \)[/tex]:
[tex]\[ x^4 = (x^2)^2 \][/tex]
[tex]\[ x^2 = 6 \][/tex]
[tex]\[ (x^2)^2 = 6^2 \][/tex]
[tex]\[ x^4 = 36 \][/tex]

Thus,:
[tex]\(_x^4 = 36_\)[/tex].

### Question 10: Ordinate of all points on [tex]\( y \)[/tex]-axis is:

The ordinate of a point is the y-coordinate of the point. For points on the y-axis, the x-coordinate is zero, but the y-coordinate can be any real number. We are given specific values to consider, and we need to determine if they fit the criteria of being y-coordinates of points that lie on the y-axis:

Given ordinate points:
- [tex]\( 9 \)[/tex]
- [tex]\( 3 \)[/tex]
- [tex]\( 3 \sqrt{3} \)[/tex]
- [tex]\( \sqrt{3} \)[/tex]

We observe that for all the listed values, they all represent valid ordinates, as they are real numbers and can each serve as a y-coordinate (ordinate) of a point on the y-axis.

Therefore, the ordinate points can be:
- [tex]\( 9 \)[/tex]
- [tex]\( 3 \)[/tex]
- [tex]\( 3 \sqrt{3} \)[/tex]
- [tex]\( \sqrt{3} \)[/tex]

Thus, all the provided coordinate points are valid as ordinates on the y-axis.

### Final Answers:

1. [tex]\( x^4 = 36 \)[/tex]
- (b) is the correct option.
2. Ordinate of all points on [tex]\( y \)[/tex] axis include:
- (a) [tex]\( 9 \)[/tex]
- (b) [tex]\( 3 \)[/tex]
- (c) [tex]\( 3 \sqrt{3} \)[/tex]
- (d) [tex]\( \sqrt{3} \)[/tex]