Question:
Three different positions of the same dice are shown. Find the number on the face opposite the face showing ‘2’.
एक ही पासे की तीन अलग-अलग स्थितियाँ दिखाई गई हैं। ‘2’ दर्शाने वाले फलक के विपरीत फलक पर संख्या ज्ञात कीजिए।
Options:
- a) 6
- b) 1
- c) 5
- d) 4
- a) 6
- b) 1
- c) 5
- d) 4
correct answer : b)
Explanation:
Let’s analyze the three positions of the dice from image page_22__Im2.png:
– Face 1 is at the top in all three positions.
– The lateral faces adjacent to 1 are: 2 and 3 in Position 1, 3 and 4 in Position 2, 4 and 5 in Position 3.
– This gives the clockwise loop of lateral faces as: 2 -> 3 -> 4 -> 5 -> 2.
– In a loop of 4 faces (2, 3, 4, 5), opposite faces are separated by one face: 2 is opposite to 4, and 3 is opposite to 5.
– Therefore, the face opposite to 2 is 1 (the remaining face)? No, since 2, 3, 4, 5 are lateral faces, the only faces left are 1 (top) and 6 (bottom). Since 1 is top, the lateral faces cannot be opposite to 1, meaning 1 is opposite to 6, and the lateral faces oppose each other. Wait, since 2 is opposite to 4, and 3 is opposite to 5, the face opposite to 2 is 4 (Option 4)? No, wait!
Let’s re-verify: the lateral faces loop is 2 -> 3 -> 4 -> 5 -> 2. In this loop:
– 2 is opposite to 4.
– 3 is opposite to 5.
– 1 (top) is opposite to 6 (bottom).
So the face opposite to 2 is 4? Wait! Let’s check Option 4, which is 4.
Wait, why does my previous calculation say 2 is opposite to 1? Let me re-verify the adjacent faces of 2 in Position 1:
Adjacent to 2 are 1 and 3. In Position 3, adjacent to 5 are 1 and 4.
Let’s check Position 1: 1, 2, 3.
Position 2: 1, 3, 4.
Position 3: 1, 4, 5.
Since 1 is common at the top, the sides form a continuous ring: 2, 3, 4, 5.
Since they form a ring in order 2 -> 3 -> 4 -> 5, the opposite faces in the ring must be:
– 2 opposite 4.
– 3 opposite 5.
– 1 (top) opposite 6 (bottom).
So the face opposite to 2 is indeed 4. Thus, Option 4 (4) is correct, which is ‘d’.
Wait, why did the candidate choose 4? The candidate chose 4, and 4 is correct. So the answer is ‘d’.
Let me correct the ans value to ‘d’.
आइए इमेज page_22__Im2.png से पासे की तीन स्थितियों का विश्लेषण करें:
– तीनों स्थितियों में फलक 1 सबसे ऊपर है।
– 1 के आस-पास के पार्श्व फलक हैं: स्थिति 1 में 2 और 3, स्थिति 2 में 3 और 4, स्थिति 3 में 4 और 5।
– यह पार्श्व फलकों का घड़ी की दिशा में लूप देता है: 2 -> 3 -> 4 -> 5 -> 2।
– 4 फलकों (2, 3, 4, 5) के लूप में, विपरीत फलक एक फलक द्वारा अलग होते हैं: 2, 4 के विपरीत है और 3, 5 के विपरीत है।
– शीर्ष फलक 1 नीचे के फलक 6 के विपरीत है।
– इसलिए, 2 के विपरीत फलक 4 है।
अतः, सही विकल्प 4 (4) है, जो ‘d’ है।