Ch 14: Non-Verbal II — Dice, Cubes & Paper Folding

Badhai ho dosto — ye aakhri chapter hai! 🎉 Ismein teen mazedar topics hain:

1. Dice (paasa) — aamne-saamne kaunsa number. 2. Cube cutting — rangaa hua cube kaat do, kitne tukdon par kitne rang. 3. Paper folding — kagaz mod ke chhed karo, kholne par kitne chhed.

Teeno mein pakke formule hain — ratt lo aur sawal 20 second ka. CET Group D mein inse 1 question lagbhag pakka aata hai. Chalo course khatam karein! 💪

1. ⭐ DICE — "jod hamesha 7"

⭐ Standard dice: aamne-saamne ke chehron ka jod = 7 Jodiyan: 1↔6 · 2↔5 · 3↔4
Matlab agar upar 3 hai to neeche 4 hoga. Aur 1 aur 6 kabhi bagal-bagal (adjacent) nahi ho sakte — wo to aamne-saamne hain!

Ek hi baar mein sirf teen chehre dikhte hain — aur unme kabhi koi jodi (1-6, 2-5, 3-4) saath nahi hogi.

✏️ Solved Examples Q: Paase par upar 2 hai, neeche kya? → 7 − 2 = 5 ✓
Q: Kya 1 aur 6 bagal-bagal ho sakte hain? → Nahi, wo opposite hain ✓
Q: Ek paase par 2, 3, 5 dikh rahe hain — kya ye ho sakta hai? → Haan (2-5 jodi hai… ruko! 2 aur 5 to opposite hain → nahi ho sakta) ✓

2. ⭐ CUBE CUTTING — chaar formule

⭐ Bahar se ranga hua cube, n×n×n tukdon mein kaata gaya 3 face range (kone wale) = hamesha 8
2 face range (kinare wale) = 12 × (n − 2)
1 face ranga (beech wale) = 6 × (n − 2)²
0 face ranga (bilkul andar) = (n − 2)³
Kul tukde = n³ (chaaron ka jod isse match hona chahiye — ye aapka self-check hai!)

Chaaron ginti ka jod hamesha n³ aana chahiye — agar nahi aaya to kahin galti hai.

✏️ Solved Example — 4×4×4 (64 tukde) 3 face: hamesha 8 · 2 face: 12 × (4−2) = 24
1 face: 6 × (4−2)² = 6 × 4 = 24 · 0 face: (4−2)³ = 8
Check: 8 + 24 + 24 + 8 = 64 ✓

📌 Cube ke basic facts Cube mein 6 chehre (faces), 12 kinare (edges) aur 8 kone (corners/vertices) hote hain. Isiliye 3-face wale hamesha 8 (kone jitne) aur 2-face wale 12 ke guna mein hote hain!

3. ⭐ PAPER FOLDING & PUNCHING

⭐ Har fold se chhed DOUBLE ho jate hain 1 fold + 1 punch → 2 chhed · 2 fold → 4 chhed · 3 fold → 8 chhed
Formula: chhed = 2^folds × punch
Aur chhed hamesha fold ki line ke aamne-saamne barabar doori par bante hain (symmetric).

Ulta chalo — folded kagaz ko ek-ek fold khol ke socho, har baar chhed aaine ki tarah dobara ban jate hain.

4. Dice ke thode aage wale sawal

📌 Do tasveerein di hon to Kabhi ek hi paase ki do position di jati hain. Tarika: dono mein jo number common ho use pakdo — baaki numbers ke ghoomne se pata chalta hai kaunsa kiske saamne hai.
Sabse aasan check: jo do number ek saath dikh rahe hain wo kabhi opposite nahi ho sakte.

✏️ Type 1 — "Upar X hai to neeche kya?" Seedha 7 − X. Sabse aasan sawal — ye kabhi mat chhodo.

✏️ Type 2 — "Kaunse do number saath nahi aa sakte?" Jo jodi banate hain (1-6, 2-5, 3-4) wo kabhi saath nahi dikhenge.

✏️ Type 3 — Cube cutting ki ginti Chaar formule lagao aur jod = n³ se check karo. 3×3×3 → 8, 12, 6, 1. 4×4×4 → 8, 24, 24, 8.

✏️ Type 4 — Paper folding 2^folds chhed. Aur unki jagah fold-line se barabar doori par, aaine ki tarah.

✏️ Type 5 — Cube ke basic facts 6 faces, 12 edges, 8 corners — seedha bhi poocha jata hai aur cube-cutting samajhne mein bhi kaam aata hai.

Trick 1: Dice ka sirf ek number — 7
Neeche = 7 − upar
Poore dice topic ka 70% isi ek line se ban jata hai.

Trick 2: 3-face wale hamesha 8
Kyunki cube ke 8 kone hote hain
Cube chahe 3×3×3 ho ya 10×10×10 — kone hamesha 8 hi rahenge. Ye ratne ki cheez nahi, samajh ki hai.

Trick 3: Jod se self-check
8 + 12(n−2) + 6(n−2)² + (n−2)³ = n³
Chaaron ginti ka jod n³ na aaye to kahin galti hai — 5 second mein khud pakad lo.

Trick 4: Paper folding ulta socho
Fold kholte jao, chhed dugne karte jao
1 punch, 2 fold → khola to 2, phir 4. Har fold khulne par chhed aaine ki tarah dobara bante hain.

Trick 5: (n−2) hi asli number hai
Bahar ki layer hata do
Cube cutting ke teeno formule mein (n−2) aata hai — matlab "bahar wali layer chhod ke andar kitna bacha".

❌ Galti 1: Dice mein jod 6 ya 8 maan lena Standard paase mein aamne-saamne ka jod hamesha 7 hota hai (1-6, 2-5, 3-4).

❌ Galti 2: Cube cutting mein (n−2) ki jagah n lagana 2-face wale 12(n−2) hote hain, 12n nahi. 3×3×3 mein 12 × 1 = 12 (12 × 3 = 36 galat).

❌ Galti 3: 1-face wale mein square bhoolna Formula 6(n−2)² hai — square lagana zaroori hai. 4×4×4 mein 6 × 2² = 24 (6 × 2 = 12 galat).

❌ Galti 4: Paper folding mein fold ginna bhool jana "Do baar moda" = 2 folds = 4 chhed (2 nahi). Sawal mein kitni baar moda, wo dhyan se gino.

❌ Galti 5: Jod se check na karna Cube cutting mein chaaron ginti ka jod n³ aana chahiye. Ye check na karne se galti pakdi nahi jati.

Dice mein aamne-saamne ka jod?tap 👆

7 (1-6, 2-5, 3-4)

Upar 3 hai to neeche?tap 👆

4

Kya 2 aur 5 saath dikh sakte hain?tap 👆

Nahi — wo opposite hain

Ek baar mein kitne chehre dikhte hain?tap 👆

Teen

Cube mein faces / edges / corners?tap 👆

6 / 12 / 8

3 face range wale cube?tap 👆

Hamesha 8 (kone jitne)

2 face range wale?tap 👆

12 × (n − 2)

1 face ranga wale?tap 👆

6 × (n − 2)²

0 face wale (andar wale)?tap 👆

(n − 2)³

3×3×3 ka poora hisab?tap 👆

8, 12, 6, 1 (jod 27)

4×4×4 ka poora hisab?tap 👆

8, 24, 24, 8 (jod 64)

Cube cutting ka self-check?tap 👆

Chaaron ka jod = n³

1 fold + 1 punch → kitne chhed?tap 👆

2

2 fold + 1 punch → ?tap 👆

4 chhed

3 fold + 1 punch → ?tap 👆

8 chhed (2^folds)

Chhed kahan bante hain?tap 👆

Fold line se barabar doori par (aaine jaisa)

Cube formulon mein (n−2) ka matlab?tap 👆

Bahar wali layer hata ke andar bacha hissa

Do dice tasveerein di hon to?tap 👆

Common number pakdo

Ch	Topic	Sabse zaroori baat
1	Number Series	4-step: antar → ×/÷ → square/cube → alternate
2	Letter Series	EJOTY (5,10,15,20,25) · right = 27 − left
3	Analogy & Classification	Rishta vakya mein likho · "teen mein common" dhundo
4	Coding-Decoding	Pehle letter se shift · alphabet gol chakkar hai
5	Alphabet Test	Left jaana = −, right = + · beech = (bada−chhota)−1
6	Direction Sense	Naksha banao · right: N→E→S→W · √(a²+b²)
7	Blood Relations	Family tree · "pita ka iklauta beta = main khud"
8	Ranking	Total = L + R − 1
9	Seating (Linear)	Left-right baithne wale ka · south = ulta
10	Seating (Circular)	Andar mukh → left clockwise; bahar → ulta
11	Syllogism	Venn banao · har tasveer mein sach ho tabhi "follows"
12	Clock & Calendar	\|30H − 5.5M\| · odd days · leap = ÷4 (century ÷400)
13	Non-Verbal I	Mirror = left-right · Water = upar-neeche · ghadi 11:60 −
14	Non-Verbal II	Dice jod 7 · cube: 8, 12(n−2), 6(n−2)², (n−2)³ · fold = 2ⁿ

🎯 Exam ki raat ka plan Ye table + har chapter ke flip-cards ek baar dekh lo. Naya topic mat padho. CET mein Reasoning ke 15 sawal hain aur negative marking nahi — isliye har sawal attempt karo. Aur diagram wale topics (direction, seating, blood relation) mein hamesha kagaz par banao — yahi sabse zyada marks dilata hai! 💪

🎯 Score: 0 / 0 Total questions: 14

Practice (exam-style)

Q1. On a standard dice, the sum of the numbers on opposite faces is always:

💡 Jodiyan: 1-6, 2-5, 3-4 — sabka jod 7.

Practice (exam-style)

Q2. If 3 is on the top face of a dice, what is on the bottom face?

💡 7 − 3 = 4.

Practice (exam-style)

Q3. Which pair of numbers can NEVER appear together on the visible faces of a dice?

💡 1 aur 6 opposite hain → kabhi saath nahi dikhenge.

Practice (exam-style)

Q4. A cube painted on all faces is cut into 27 equal smaller cubes. How many small cubes have exactly 3 faces painted?

💡 Kone wale hamesha 8 (cube ke 8 corners).

Practice (exam-style)

Q5. In the same 3 × 3 × 3 cube, how many small cubes have exactly 2 faces painted?

💡 12 × (n−2) = 12 × 1 = 12 (kinare wale).

Practice (exam-style)

Q6. In the same 3 × 3 × 3 cube, how many small cubes have exactly 1 face painted?

💡 6 × (n−2)² = 6 × 1 = 6 (har chehre ka beech wala).

Practice (exam-style)

Q7. In the same 3 × 3 × 3 cube, how many small cubes have NO face painted?

💡 (n−2)³ = 1³ = 1 (bilkul beech wala). Check: 8+12+6+1 = 27 ✓

Practice (exam-style)

Q8. A painted cube is cut into 64 equal smaller cubes. How many have exactly 3 faces painted?

💡 Kone hamesha 8 — cube kitna bhi bada ho.

Practice (exam-style)

Q9. In a 4 × 4 × 4 painted cube, how many small cubes have exactly 1 face painted?

💡 6 × (4−2)² = 6 × 4 = 24 (square lagana mat bhoolo).

Practice (exam-style)

Q10. In a 4 × 4 × 4 painted cube, how many small cubes have no face painted?

💡 (4−2)³ = 2³ = 8. Check: 8 + 24 + 24 + 8 = 64 ✓

Practice (exam-style)

Q11. A sheet of paper is folded once and a single hole is punched. On unfolding, how many holes are there?

💡 Har fold se chhed double → 2¹ = 2.

Practice (exam-style)

Q12. A sheet is folded twice and a single hole is punched. On unfolding, how many holes are there?

💡 2² = 4 chhed.

Practice (exam-style)

Q13. How many edges does a cube have?

💡 Cube: 6 faces, 12 edges, 8 corners.

Practice (exam-style)

Q14. In a cube-cutting question, the four counts (3-face, 2-face, 1-face, 0-face) should always add up to:

💡 Kul chhote cube n³ hote hain — yahi aapka self-check hai.

Dice: aamne-saamne ka jod hamesha 7 (1-6, 2-5, 3-4) — aur jodi wale number kabhi saath nahi dikhte. Cube cutting: 3-face wale hamesha 8 (kone), 2-face 12(n−2), 1-face 6(n−2)², 0-face (n−2)³ — aur chaaron ka jod n³ aana chahiye (self-check!). Paper folding: har fold se chhed dugne — 2^folds, aur chhed fold-line se barabar doori par bante hain.

🎉 Aur yahin Reasoning course poora hua — 14 chapters, 196 MCQs! Upar wala "Poore Course ka Revision" table apna final-day notes bana lo. CET mein Reasoning ke 15 sawal hain aur negative marking nahi — har sawal attempt karo. All the best! 🏆