Class 6 Maths Chapter 1 NCERT Solutions Hinglish mein: Patterns in Mathematics

Ganita Prakash (Reprint 2026-27) ke Chapter 1, Patterns in Mathematics, ke har Figure it Out sawal ke jawab, text ke sawalon ke saath. Page numbers book se match karte hain, aur jawab chapter PDF ke aakhir mein di NCERT ki answer key se mila liye gaye hain. Short notes: Chapter 1 notes.

Figure it Out: maths kya hai? (page 2)

1. Roz ki zindagi mein maths ki madad ke aur udaharan: phal aur kiraane ka hisaab aur bacha paisa ginna; khaana banaate hue cheezein naapna; cheezein barabar baantna; ghadi, calendar aur timetable padhna; khel ke score rakhna; kamre ya plot ka area nikaalna; doori aur speed se safar plan karna; imaaraton, rangoli aur kapdon ke design aur patterns.

2. Maths ne insaaniyat ko aage kaise badhaaya:

• Science: prayog numbers se naape, likhe aur parkhe jaate hain; grahon ki chaal ke patterns se gravitation ka siddhaant aur satellites aur rockets mile.
• Arthvyavastha aur loktantra: banking, budget aur daam; voton ki ginti; janganana.
• Nirmaan: pul, ghar aur oonchi imaaratein naap, angles aur majbooti ke hisaab maangti hain.
• Technology: TV, mobile aur computer numbers aur codes se chalte hain; cycle, train, car aur plane mein speed, doori aur bal ke hisaab lagte hain.
• Samay: calendar aur ghadi sooraj, chaand aur taaron ki chaal ke patterns se bane hain.

Figure it Out: number sequences (page 3)

1 aur 2. Table 1 ke har sequence ka pattern, agle teen numbers aur niyam:

Sequence	Agle teen	Apne shabdon mein niyam
All 1’s	1, 1, 1	har number 1
Counting numbers	8, 9, 10	har baar 1 jodo
Odd numbers	15, 17, 19	1 se shuru, 2 jodo
Even numbers	16, 18, 20	2 se shuru, 2 jodo
Triangular numbers	36, 45, 55	2, phir 3, phir 4, … jodo; 1 + 2 + … + n
Squares	64, 81, 100	1 × 1, 2 × 2, 3 × 3, …
Cubes	343, 512, 729	1 × 1 × 1, 2 × 2 × 2, …
Virahānka numbers	34, 55, 89	har number pichhle do ka jod
2 ki powers	128, 256, 512	har baar 2 se guna
3 ki powers	2187, 6561, 19683	har baar 3 se guna

Figure it Out: sequences ko dekhna (page 5)

1. Table 2 ke har sequence ki agli tasveer: all 1’s: ek bindu; counting numbers: 6 binduon ki row; odd numbers: 11 bindu do rows mein, upar 5 aur neeche 6; even numbers: 6-6 ki do rows (12 bindu); triangular numbers: 1 se 6 binduon ki rows waala triangle (21); squares: 6 by 6 grid (36); cubes: 6 × 6 × 6 ka dher (216).

2. Ye naam kyun? 1, 3, 6, 10, 15, … bindu triangles mein jamte hain; 1, 4, 9, 16, 25, … bindu squares bharte hain; aur 1, 8, 27, 64, 125, … chhote cubes jamkar bade cubes banaate hain.

3. 36 triangle aur square ki tarah: 6 by 6 binduon ka square, aur 1, 2, 3, 4, 5, 6, 7 aur 8 binduon ki rows waala triangle (1 + 2 + … + 8 = 36).

4. 1, 7, 19, 37 hexagonal numbers hain. Antar 6, 12, 18 hain, isliye agla antar 24 aur agla number 37 + 24 = 61 hai.

5. 2 aur 3 ki powers ki tasveerein: 2 ki powers: ek bindu (1), jude do bindu (2), square (4), cube (8), kone se jude do cubes (16), jaisa chapter dikhaata hai; ya ek ped jo har level pe 2 shaakhaon mein bante. 3 ki powers: ek bindu (1), 3 binduon ki row (3), 3 × 3 square (9), aise teen squares jama karke 3 × 3 × 3 cube (27); ya ek ped jo har level pe 3 mein bante.

Sequences ke rishte (pages 6–7)

Pehle 10 odd numbers ka jod: 10 by 10 square ki L-shaped tasveer se 100.

Pehle 100 odd numbers ka jod: 100 by 100 square ki kalpana se 10,000.

Figure it Out: sequences ke rishte (pages 8–9)

1. Binduon ke square grid ki tirchi rows mein 1, 2, 3, …, n, …, 3, 2, 1 bindu hote hain (baayein tasveer), isliye counting numbers ko upar aur neeche jodne se square n × n milta hai.

2. 1 + 2 + 3 + … + 99 + 100 + 99 + … + 3 + 2 + 1 = 100 × 100 = 10,000.

3. All 1’s ko jodne pe 1, 1 + 1, 1 + 1 + 1, … = 1, 2, 3, 4, …: counting numbers milte hain. Upar aur neeche jodne pe 1, 1 + 1 + 1, 1 + 1 + 1 + 1 + 1, … = 1, 3, 5, 7, …: odd numbers milte hain.

4. Counting numbers jodne pe 1, 3, 6, 10, 15, …: triangular numbers milte hain. Chhoti tasveer: binduon ki seedhi jiske columns mein 1, 2, 3, 4, … bindu hon.

5. 1 + 3 = 4, 3 + 6 = 9, 6 + 10 = 16, 10 + 15 = 25, …: squares. Binduon ke square ko seedhi ki tarah kaatne se do triangles milte hain, ek doosre se ek kadam chhota (daayein tasveer).

6. 1, 1 + 2, 1 + 2 + 4, 1 + 2 + 4 + 8, … = 1, 3, 7, 15, 31, …. 1 jodne pe 2, 4, 8, 16, 32, …: 2 ki powers. Kyun: 1 + 2 + 4 mein 1 jodo to 1 + 1 + 2 + 4 = 2 + 2 + 4 = 4 + 4 = 8; wo 1 jodi banaata jaata hai aur double hota jaata hai. Isliye har jod 2 ki agli power se ek kam hai.

7. 6 × 1 + 1 = 7, 6 × 3 + 1 = 19, 6 × 6 + 1 = 37, 6 × 10 + 1 = 61, 6 × 15 + 1 = 91: hexagonal numbers. Tasveer: binduon ka hexagon ek beech ka bindu hai jiske chaaron taraf binduon ke 6 triangles hain, har ek triangular number.

8. 1, 1 + 7, 1 + 7 + 19, 1 + 7 + 19 + 37, … = 1, 8, 27, 64, …: cubes. Tasveer: chhote cubes se bane cube ko ek kone se dekho; hexagon dikhta hai. Har hexagonal number us kone se dikhne waale chhote cubes ki parat hai, aur use hataane se agla chhota cube bachta hai. Isliye parton ka jod cube hai.

9. Apne kuch patterns:

• Cubes jodne se triangular numbers ke squares milte hain: 1 = 1 × 1, 1 + 8 = 9 = 3 × 3, 1 + 8 + 27 = 36 = 6 × 6, 1 + 8 + 27 + 64 = 100 = 10 × 10.
• 2 se lagaataar even numbers jodne pe aise numbers milte hain jo ek counting number aur uske agle ka guna hain: 2 = 1 × 2, 2 + 4 = 6 = 2 × 3, 2 + 4 + 6 = 12 = 3 × 4.
• Har teesra Virahānka number even hai: 2, 8, 34, …

Figure it Out: shapes ke patterns (page 11)

1. Table 3 ke patterns: regular polygons: bhujaayein 3, 4, 5, …, 10; complete graphs: 1, 3, 6, 10, 15 lines; stacked squares: 1, 4, 9, 16, 25 chhote squares; stacked triangles: 1, 4, 9, 16, 25 chhote triangles; Koch snowflake: 3, 12, 48, 192, 768 segments.

2. Har sequence ki agli shape: 11 bhujaaon waala regular polygon; complete graph K7, 7 bindu aur 21 lines; 36 squares ka 6 by 6 dher; 6 rows aur 36 triangles waala triangles ka dher; aur agla Koch snowflake, 3,072 segments ke saath. Aakhri wala haath se banaana bahut mushkil hai: uske segments bahut chhote ho jaate hain.

Figure it Out: shapes aur numbers (pages 11–12)

1. Regular polygons ki bhujaayein 3, 4, 5, 6, 7, 8, 9, 10, … hain: 3 se counting numbers. Kone bhi yahi sequence dete hain, kyunki band shape mein har bhuja do konon pe khatam hoti hai aur har kona do bhujaaon ko jodta hai: ghoomte hue bhuja, kona, bhuja, kona, … milte hain jab tak shuruaat pe na laut aao.

2. Complete graphs ki lines 1, 3, 6, 10, 15 hain: triangular numbers. Har naya bindu pichhle saare binduon se judta hai, isliye K3 mein K2 se 2 lines zyaada, K4 mein 3, K5 mein 4 aur K6 mein 5.

3. Stacked squares mein 1, 4, 9, 16, 25 chhote squares hain: squares, kyunki n bhuja waali shape mein n chhote squares ki n rows hain.

4. Stacked triangles mein 1, 4, 9, 16, 25 chhote triangles hain: phir squares. Rows mein 1, 3, 5, 7, 9 triangles hain, jo odd numbers hain, aur odd numbers jodne se squares milte hain.

5. Koch snowflake mein 3, 12, 48, 192, 768, … segments hain: har segment ki jagah 4 aate hain, isliye har baar ginti 4 se guna hoti hai, yaani 3 guna 4 ki powers.