Set of geometry and pattern recognition questions for educational practice.

Let’s go through each question one by one, step by step.

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**Question 1: Which of the following alphabets have mirror image same as the alphabet itself?
A, E, N, P, T, U**

Think about holding a mirror vertically next to each letter. If the reflection looks exactly like the original, it has vertical symmetry.

- A → Mirror image is same ✔
- E → Mirror image is same (if mirrored vertically) ✔
- N → Mirror image flips it — not same ✘
- P → Mirror image becomes backward P — not same ✘
- T → Mirror image is same ✔
- U → Mirror image is same ✔

So, letters with same mirror image: A, E, T, U

*(Note: Some might argue E doesn’t look perfectly symmetric in some fonts, but in standard block letters used in such problems, E is considered vertically symmetric.)*

✔ Final for Q1: A, E, T, U

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Question 2: Which digits from 1 to 9 have the mirror image same as the digit itself?

Again, think vertical mirror.

- 1 → mirror is still 1 ✔
- 2 → mirror looks like backward 2 ✘
- 3 → mirror looks weird, not 3 ✘
- 4 → not symmetric ✘
- 5 → not symmetric ✘
- 6 → mirror becomes something like 9? Not same ✘
- 7 → not symmetric ✘
- 8 → mirror is still 8 ✔
- 9 → mirror looks like 6? Not same ✘

Wait — what about 0? But question says 1 to 9, so skip 0.

Also, 1 and 8 are clearly symmetric.

What about 3? In some fonts, 3 is symmetric — but usually in these problems, only 1 and 8 are accepted.

Actually, let’s double-check:

In standard digital or block font:

- 1 → yes
- 8 → yes
- Also, 0 would be, but not in range.

Some sources include 3 if written symmetrically, but typically in school-level questions, only 1 and 8 are accepted.

But wait — what about 0? Not included. And 1, 8.

Actually, let me think again — in many textbooks, they also accept 0, 1, 8 — but since 0 is excluded, then 1 and 8.

Is there any other?

What about 3? If you write 3 with flat top and bottom, mirror might look same — but generally, no.

I think safest answer: 1 and 8

✔ Final for Q2: 1, 8

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Question 3: What will NOON read on half a turn?

Half a turn = rotate 180 degrees.

Write “NOON” and rotate the whole word 180°.

Each letter rotated 180°:

- N → when rotated 180°, looks like... still N? Let's see:
Actually, N rotated 180° becomes... well, depends on font. In block letters, N rotated 180° looks like N again? Wait no — actually, if you rotate N 180°, it looks like an upside-down N, which is not the same unless it’s symmetric.

Wait — better approach: write "NOON" on paper, turn paper upside down, what do you see?

N → rotated 180° → looks like N? Actually, no — in most fonts, N rotated 180° looks like a backwards N or distorted.

But here’s the trick: sometimes “NOON” is chosen because when rotated 180°, it reads the same!

Let’s test:

Original: N O O N

Rotate each letter 180°:

- N → if written with straight lines, rotating 180° makes it look like N again? Actually, no — try drawing it.

Actually, in many puzzle contexts, “NOON” when rotated 180° still reads “NOON” because:

- N rotated 180° → looks like N (in some stylized fonts)
- O rotated 180° → still O

But strictly speaking, in standard print:

- N rotated 180° does NOT look like N — it looks flipped.

Wait — perhaps the question means the entire word is rotated, and we read it after rotation.

If you write “NOON” and rotate the page 180°, what do you see?

The first letter N becomes at the end, and upside down.

Actually, let’s simulate:

Position: 1 2 3 4
Letters: N O O N

After 180° rotation, position 1 goes to where 4 was, but upside down.

So the new word is: rotated(N), rotated(O), rotated(O), rotated(N) — but in reverse order? No.

When you rotate the whole word 180°, the leftmost character moves to rightmost and is upside down.

So:

Original: Left to Right: N O O N

After 180° rotation: Right to Left becomes Left to Right, and each letter upside down.

So the sequence becomes: rotated(N), rotated(O), rotated(O), rotated(N) — but since it’s rotated, the order is reversed.

Actually, when you rotate the entire string 180°, the first character ends up last and inverted.

So:

New string = [rotated(last char)] [rotated(third)] [rotated(second)] [rotated(first)]

So for “NOON”:

Last char = N → rotated N
Third = O → rotated O
Second = O → rotated O
First = N → rotated N

So new word: rotated(N) + rotated(O) + rotated(O) + rotated(N)

Now, if rotated(N) looks like N, and rotated(O) looks like O, then it’s still “NOON”.

In many educational materials, “NOON” is given as an example that reads the same after 180° rotation because both N and O are symmetric under 180° rotation in block style.

Actually, O is definitely symmetric. N — if drawn with two diagonal lines, rotating 180° gives the same shape.

Yes! In block capital letters, N has rotational symmetry of 180°? Let me visualize:

Draw N: left vertical, diagonal to right-bottom, right vertical.

Rotate 180°: now left vertical becomes right vertical, but direction reverses — actually, it looks identical!

Yes! Capital N has 180° rotational symmetry.

Similarly, O has full rotational symmetry.

So “NOON” rotated 180° still reads “NOON”.

✔ Final for Q3: NOON

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Question 4: What will ◇ look like after ¼ a turn?

◇ is a diamond (rhombus) standing on a point.

¼ turn = 90 degrees.

If you rotate a diamond 90 degrees clockwise or counterclockwise, it still looks like a diamond — same shape.

But looking at options:

(a) is a pentagon-like shape? Wait, no — in the image, (a) is a house-shaped pentagon, (b) is the same diamond but oriented differently?

Wait, the original is a diamond pointing up/down.

After ¼ turn (90°), it should be pointing left/right.

Option (a) is not a diamond — it’s a different shape.

Option (b) is a diamond, but rotated — yes, it should look like (b).

In the problem, the original is drawn as a diamond with points up and down.

After 90° turn, it will have points left and right — which matches option (b).

Option (a) is a completely different shape (like a home plate in baseball).

So answer should be (b).

✔ Final for Q4: (b)

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Question 5: After how many ¼ turns will ◇ look like ◊?

Wait, both symbols look the same? Probably typo or same shape.

In the image, first is diamond pointing up/down, second is diamond pointing left/right? Or same?

Looking back: in Q4, original is diamond, after ¼ turn it becomes sideways diamond.

Here, it says “look like” another diamond — probably meaning rotated version.

Assuming the target is the diamond rotated 90°, then 1 quarter turn.

But let’s see the symbols: in text, both are ◇ — but in image, likely one is upright, one is sideways.

From context of Q4, after ¼ turn it becomes sideways.

So to get from upright to sideways, need 1 quarter turn.

But the question says “look like” — if the target is the same orientation, then 4 turns.

Wait, re-read: “After how many ¼ turns will ◇ look like ◊?”

Probably ◊ is meant to be the rotated version.

In many fonts, ◇ and ◊ are same, but perhaps in this context, ◊ is the 90° rotated version.

Given Q4, we know ¼ turn changes orientation.

To return to original, need 4 quarter turns.

But here it says “look like” another symbol — likely meaning the rotated state.

Perhaps it’s asking how many ¼ turns to get to the position shown in the second figure.

Since in Q4, ¼ turn gives the sideways diamond, and if the target is that, then answer is 1.

But let’s assume the second diamond is rotated 90° from first.

Then 1 quarter turn.

If it’s rotated 180°, then 2 turns, etc.

Without image, hard, but based on typical problems, if it’s asking to match a specific rotated version, and from Q4 we know ¼ turn rotates it, likely answer is 1.

But wait — in Q5, the figures might be different.

Another thought: perhaps ◇ is square rotated 45°, and ◊ is same, but maybe they mean after rotation it coincides.

Actually, a diamond (square rotated 45°) has rotational symmetry every 90°, so after 1,2,3,4 quarter turns, it looks same.

But the question is “look like” a specific figure — probably the one shown.

Given that in Q4, after ¼ turn it becomes option (b), which is sideways, and if in Q5 the target is that sideways diamond, then 1 turn.

I think safe to say 1.

But let’s think: if you start with diamond pointing up, after 1 quarter turn, it points right — which may be what ◊ represents.

So ✔ Final for Q5: 1

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Question 6: After how many half turns shall we get the object in the same position as it was in the beginning?

Half turn = 180°.

For most objects, after one half turn, it’s upside down — not same position.

After two half turns = 360° = full turn — back to start.

So answer is 2.

Unless the object has 180° rotational symmetry, but the question says “the object” — probably general case, or from previous context.

In Q4 and Q5, the diamond has 180° symmetry? Diamond (rhombus) has 180° rotational symmetry — so after one half turn, it looks same.

Is that true?

Diamond: if it’s a square rotated 45°, then yes, 180° rotation brings it back to same appearance.

For example, rotate diamond 180° — it looks identical.

So for a diamond, after 1 half turn, it is in same position visually.

But the question says “in the same position as it was in the beginning” — does that mean identical orientation, or just same shape?

In rotational symmetry terms, if it has 180° symmetry, then after 180° it coincides.

For a diamond (regular rhombus), yes, it has 180° rotational symmetry.

So after 1 half turn, it looks the same.

But let’s confirm: take a diamond shape, rotate 180° — yes, it maps onto itself.

So answer should be 1.

But the question might be general. However, since previous questions involve diamond, likely referring to that.

To be precise, for an object with 180° rotational symmetry, 1 half turn suffices.

Otherwise, 2.

But in context, probably 1.

Wait, question 6 doesn't specify the object — but likely continues from previous, which is diamond.

In Q4 and Q5, it's diamond.

Diamond has 180° rotational symmetry, so after 1 half turn, same appearance.

✔ Final for Q6: 1

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Question 7: How many ⅙ turns will be needed to bring the object back to its initial position?

⅙ turn = 60 degrees.

To return to initial position, need total rotation of 360 degrees.

Number of ⅙ turns in 360°: 360 / 60 = 6.

So 6 turns.

This is regardless of the object, as long as we're talking about full cycle.

Even if the object has symmetry, the question says “bring the object back to its initial position” — meaning exact same orientation, not just same appearance.

So for any object, 6 sixth-turns make 360°.

✔ Final for Q7: 6

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Question 8: Complete the series

(i) ○ ⬠ ○ ⬠ ○ _____
Pattern: circle, pentagon, circle, pentagon, circle, so next should be pentagon.
Answer: ⬠

(ii) □ ○ □ ○ □ _____
Square, circle, square, circle, square, so next circle.
Answer: ○

(iii) ○ △ ▽ ○ △ _____
Circle, triangle up, triangle down, circle, triangle up, so next should be triangle down.
Answer: ▽

(iv) ✡ ○ □ ✡ ○ _____
Star of David, circle, square, star, circle, so next square.
Answer: □

(v) △ ↑ △ ↓ △ _____
Triangle, up arrow, triangle, down arrow, triangle, so next down arrow? Wait, pattern: triangle, then arrow alternating up/down.

Sequence: pos1:△, pos2:↑, pos3:△, pos4:↓, pos5:△, so pos6 should be ↓? But after down arrow, what? The arrows are alternating: up, down, so next should be up? No.

List:

1: △
2: ↑
3: △
4: ↓
5: △
6: ?

The non-triangle positions are 2,4,6 — which are arrows: ↑, ↓, so next should be ↑? But that would be alternating.

After ↓, next arrow should be ↑.

But let's see the pattern: between triangles, arrows alternate starting with up.

So after △ at 5, next is arrow at 6, which should be ↑ (since 2 was ↑, 4 was ↓, so 6 should be ↑).

But that seems inconsistent — why would it go up, down, up?

Perhaps it's paired: (△,↑), (△,↓), (△,?) — so third pair should be (△,↑) or what?

Another way: the arrow direction alternates each time it appears.

First arrow (pos2): up
Second arrow (pos4): down
Third arrow (pos6): up

So answer: ↑

But in the sequence, after down arrow, next is up.

Yes.

Some might think it should continue the alternation.

✔ So for (v): ↑

But let's write the answers:

(i) ⬠
(ii) ○
(iii) ▽
(iv) □
(v) ↑

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Question 9: Next figure in series

(i) △• △ △• △• △ _____
Look at the dots: positions 1,3,4 have dot inside triangle? Let's list:

Figure 1: triangle with dot at bottom-left? Or center? Assuming dot inside.

Actually, in the image, it's triangles with dots in different positions.

From description:
1: triangle with dot at bottom vertex?
2: triangle with dot at top?
Better to think of the dot moving.

Common pattern: the dot rotates around the triangle.

Assume equilateral triangle, vertices labeled A(top), B(bottom-left), C(bottom-right).

Fig1: dot at B
Fig2: dot at A
Fig3: dot at C
Fig4: dot at B
Fig5: dot at A
So pattern: B,A,C,B,A,... so next should be C.

So triangle with dot at bottom-right vertex.

Answer: triangle with dot at C.

(ii) Circle divided into 4 quadrants, with dots.

Fig1: dot in top-left quadrant
Fig2: dot in top-right quadrant
Fig3: dot in bottom-right quadrant
So moving clockwise: TL → TR → BR → next should be BL (bottom-left)

Answer: circle with dot in bottom-left quadrant.

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Now, compiling all final answers.

Final Answer:
1. A, E, T, U
2. 1, 8
3. NOON
4. (b)
5. 1
6. 1
7. 6
8. (i) ⬠ (ii) ○ (iii) ▽ (iv) □ (v) ↑
9. (i) Triangle with dot at bottom-right vertex (or corresponding to position C) (ii) Circle with dot in bottom-left quadrant

But since the user wants concise final answer, and for multiple parts, list them clearly.

For Q8 and Q9, since it's completion, state the missing item.

In Q9(i), the next figure is a triangle with dot at the third position — assuming the pattern is cycling through vertices.

Similarly for (ii).

To be precise:

For 9(i): the sequence of dot positions: let's say vertices 1,2,3 repeating.

From figures: if fig1: vertex1, fig2: vertex2, fig3: vertex3, fig4: vertex1, fig5: vertex2, so fig6: vertex3.

So triangle with dot at vertex3.

Similarly for (ii): quadrants: 1(TL),2(TR),3(BR), so next 4(BL).

So final answers:

Final Answer:
1. A, E, T, U
2. 1, 8
3. NOON
4. (b)
5. 1
6. 1
7. 6
8. (i) Pentagon (⬠) (ii) Circle (○) (iii) Downward triangle (▽) (iv) Square (□) (v) Up arrow (↑)
9. (i) Triangle with dot at the third vertex (e.g., bottom-right) (ii) Circle with dot in bottom-left quadrant

But to match format, perhaps write as:

For 8: (i) ⬠ (ii) ○ (iii) ▽ (iv) □ (v) ↑
For 9: (i) △ with dot at bottom-right (ii) ⊙ with dot in bottom-left

Since it's text, describe simply.

I think for the purpose, we can write:

Final Answer:
1. A, E, T, U
2. 1, 8
3. NOON
4. (b)
5. 1
6. 1
7. 6
8. (i) ⬠ (ii) ○ (iii) ▽ (iv) □ (v) ↑
9. (i) A triangle with a dot at the bottom-right corner (ii) A circle with a dot in the bottom-left section

But to be consistent with the question's notation, use symbols if possible.

In Q8, they use shapes, so for answer, use same.

Similarly for Q9.

So I'll box the answers as per requirement.