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14CHAPTER

Number Series + Data Interpretation + Mixed Practice

Aakhri chapter! Series ka pattern, graph padhna, aur poore course ka revision. Ab tayyar ho! ๐Ÿ

Badhai ho dosto โ€” ye aakhri chapter hai! ๐ŸŽ‰ Isme teen cheezein hain:

1. Number Series โ€” numbers ki line di hoti hai, agla number batana hota hai (pattern pehchano). 2. Data Interpretation (DI) โ€” table, bar graph ya pie chart se data padh ke sawal. 3. Mixed Practice โ€” pichle 13 chapters ka revision.

Series se CET mein 1โ€“2 questions aate hain aur DI se 1โ€“2. DI mein naya kuch nahi hai โ€” bas percentage, average aur ratio (Chapter 4, 5, 6) hi data par lagane hote hain. Chalo khatam karte hain! ๐Ÿ’ช

1. Number Series ke 7 Types โญ

TypeExamplePattern
Addition (fix)3, 7, 11, 15, โ€ฆ+4 har baar
Addition (badhta hua)2, 6, 12, 20, 30, โ€ฆ+4, +6, +8, +10
Multiplication3, 6, 12, 24, โ€ฆร—2 har baar
Square1, 4, 9, 16, โ€ฆ1ยฒ, 2ยฒ, 3ยฒ, 4ยฒ
Cube1, 8, 27, 64, โ€ฆ1ยณ, 2ยณ, 3ยณ, 4ยณ
Mixed (ร—n + k)5, 11, 23, 47, โ€ฆร—2 + 1
Prime / special2, 3, 5, 7, 11, โ€ฆPrime numbers
โœ๏ธ Solved Example 1 โ€” 2, 6, 12, 20, 30, ? Step 1: Antar nikalo: 4, 6, 8, 10 (har baar 2 zyada)
Step 2: Agla antar = 12 โ†’ 30 + 12 = 42 โœ“
โœ๏ธ Solved Example 2 โ€” 5, 11, 23, 47, ? Step 1: Antar 6, 12, 24 โ€” badh raha hai, to shayad multiply wala rule hai
Step 2: Check: 5ร—2+1 = 11 โœ“, 11ร—2+1 = 23 โœ“, 23ร—2+1 = 47 โœ“
Step 3: Agla = 47ร—2+1 = 95 โœ“
โœ๏ธ Solved Example 3 โ€” 120, 99, 80, 63, ? Step 1: Ghat raha hai: โˆ’21, โˆ’19, โˆ’17 (har baar 2 kam)
Step 2: Agla โˆ’15 โ†’ 63 โˆ’ 15 = 48 โœ“
๐Ÿ“Œ Series solve karne ka 4-step tarika 1. Pehle antar (difference) nikalo โ€” fix hai ya badh/ghat raha hai?
2. Antar mein pattern na mile to รท ya ร— check karo (agla รท pichla).
3. Phir bhi na mile to squares/cubes ke aas-paas dekho (24 โ‰ˆ 25โˆ’1, 26 โ‰ˆ 27โˆ’1).
4. Aakhir mein alternate (ek chhod ke) numbers dekho โ€” do series mili hui ho sakti hain.

2. Odd One Out (bemel number)

โœ๏ธ Solved Example โ€” 3, 5, 7, 9, 11 mein bemel kaun? Sab prime hain, par 9 = 3 ร— 3 composite hai โ†’ answer 9 โœ“
Aise sawal mein dekho: sab prime hain? sab even/odd? sab square/cube hain? sab kisi ek se divide hote hain?

3. DATA INTERPRETATION โ€” Table

Table mein data rows-columns mein hota hai. Sawal hamesha total, average, percentage ya ratio ka hota hai:

MahinaSales (units)
January200
February300
March400
April500
โœ๏ธ Is table se 3 sawal (a) Average sales? (200+300+400+500) รท 4 = 1400/4 = 350
(b) March ki sales total ka kitna %? 400/1400 ร— 100 = 28.57%
(c) Jan aur April ka ratio? 200 : 500 = 2 : 5
Dekha? Naya kuch nahi โ€” Chapter 4, 5, 6 wala hi kaam hai!

4. DI โ€” Pie Chart (gol chart) โญ

โญ Poora circle = 360ยฐ = 100% 1% = 3.6ยฐ ยท Degree โ†’ % : (angle รท 360) ร— 100 ยท % โ†’ Degree : % ร— 3.6
โœ๏ธ Solved Examples (a) Ek sector 108ยฐ ka hai โ†’ % = 108/360 ร— 100 = 30% โœ“
(b) 25% ka sector kitne degree? โ†’ 25 ร— 3.6 = 90ยฐ โœ“
(c) Total kharcha โ‚น12,000 hai aur khaane ka sector 108ยฐ โ†’ khaana = 30% of 12000 = โ‚น3600
%Degree%Degree
10%36ยฐ30%108ยฐ
20%72ยฐ50%180ยฐ
25%90ยฐ75%270ยฐ

5. DI โ€” Bar Graph

  • Har bar ki unchai padho (y-axis se) โ€” yahi value hai.
  • Sawal wahi: total, average, sabse zyada/kam, do bar ka ratio ya % zyada/kam.
  • % increase nikalte waqt neeche purani (pichhle saal ki) value โ€” Chapter 4 wala rule!

6. Mixed Practice โ€” Poore course ka nichod

CET mein Maths ke 10 sawal alag-alag chapters se mile-jule aate hain. Ye rahe har chapter ke sabse zaroori points ek jagah โ€” quiz se pehle ek baar padh lo (poori list niche "Poore Course ka Revision" section mein hai).

โœ๏ธ Type 1 โ€” Agla number batao Pehle antar dekho, phir guna, phir square/cube. 90% series in teen mein se ek hoti hai.
โœ๏ธ Type 2 โ€” Beech ka gayab number (?) Series ke beech mein ? ho to dono taraf se pattern check karo โ€” pichle se aage aur agle se peeche. Dono match karein tabhi answer sahi hai.
โœ๏ธ Type 3 โ€” Odd one out "Bemel chuno" โ€” check karo: sab prime? sab perfect square? sab kisi number se divide? Jo pattern tod raha ho wahi answer.
โœ๏ธ Type 4 โ€” Pie chart ka degree โ†” % Angle diya โ†’ % = angle/3.6. % diya โ†’ angle = % ร— 3.6. Aur "kitne rupaye" poocha ho to % ร— total.
โœ๏ธ Type 5 โ€” Table/bar se average ya % badhotri Average = sab jodo รท ginti (Ch 6). % badhotri = (antar รท purani value) ร— 100 (Ch 4). Data alag hai, formula wahi purana.
Trick 1: Pehle antar likho, hamesha
Numbers ke neeche difference likho
2, 6, 12, 20, 30 ke neeche 4, 6, 8, 10 likh do โ€” pattern turant dikh jayega. Ye ek aadat 70% series solve kar deti hai.
Trick 2: Tezi se badhe to ร— wala rule
Antar bahut bada โ†’ ร—2, ร—3 check karo
5, 11, 23, 47 โ€” antar 6, 12, 24 (dugna ho raha) โ†’ matlab rule ร—2 + 1 hai. Antar khud dugna ho to multiply wala pattern hai.
Trick 3: Square-cube ke aas-paas dekho
24 = 25โˆ’1 ยท 26 = 27โˆ’1 ยท 63 = 64โˆ’1
Number kisi square/cube ke ekdum paas ho to series shayad nยฒยฑ1 ya nยณยฑ1 wali hai. Squares 1-15 aur cubes 1-10 yaad hone chahiye.
Trick 4: Pie chart ka 3.6 wala jaadu
% ร— 3.6 = degree
10% = 36ยฐ, 25% = 90ยฐ, 30% = 108ยฐ, 50% = 180ยฐ. Ye chaar yaad rahe to pie ka har sawal 10 second ka.
Trick 5: DI mein pehle TOTAL nikalo
Total nikala = aadhe sawal hal
Table dikhte hi sab jod ke total likh lo. Uske baad %, average, ratio โ€” sabke sab isi ek number se ban jaate hain.
โŒ Galti 1: Pehle do numbers dekh ke rule maan lena 3, 6, 12 dekh ke "ร—2" maan liya, par ho sakta hai 3, 6, 12, 21 (+3, +6, +9) ho. Pura pattern teen-chaar numbers par check karo, tabhi answer do.
โŒ Galti 2: Ghatti hui series mein sign ulta karna 120, 99, 80, 63 mein antar โˆ’21, โˆ’19, โˆ’17 hai. Agla โˆ’15 hai (โˆ’13 nahi) โ€” antar ka pattern bhi dhyan se dekho.
โŒ Galti 3: Pie chart mein degree ko % samajh lena 108ยฐ ka matlab 108% nahi, 30% hai. Pehle degree ko % mein badlo (รท3.6), tab total par lagao.
โŒ Galti 4: DI mein galat row/column padhna Jaldi mein "March" ki jagah "May" ka data utha lena โ€” sabse dukhad galti. Sawal padh ke row par ungli rakh ke value uthao.
โŒ Galti 5: % badhotri mein nayi value neeche lagana Ye Chapter 4 wali hi galti hai โ€” neeche hamesha purani value. 400 se 500 hua to 25% badha (20% nahi).
Series solve karne ka pehla step?tap ๐Ÿ‘†
Antar (difference) likho
Antar khud dugna ho raha ho to?tap ๐Ÿ‘†
ร—2 wala rule check karo (jaise ร—2+1)
2, 6, 12, 20, 30 โ†’ agla?tap ๐Ÿ‘†
42 (+4,+6,+8,+10,+12)
5, 11, 23, 47 โ†’ agla?tap ๐Ÿ‘†
95 (ร—2 + 1)
1, 8, 27, 64 โ†’ agla?tap ๐Ÿ‘†
125 (cubes)
3, 5, 7, 9, 11 mein bemel?tap ๐Ÿ‘†
9 (baaki sab prime)
Pie chart: pura circle = ?tap ๐Ÿ‘†
360ยฐ = 100%
1% kitne degree?tap ๐Ÿ‘†
3.6ยฐ
108ยฐ = kitna %?tap ๐Ÿ‘†
30% (108 รท 3.6)
25% = kitne degree?tap ๐Ÿ‘†
90ยฐ
DI mein sabse pehla kaam?tap ๐Ÿ‘†
Total nikalo
% badhotri mein neeche kya?tap ๐Ÿ‘†
Purani value
BODMAS mein 'of' kab?tap ๐Ÿ‘†
Divide se PEHLE (Ch 1)
Successive % change formula?tap ๐Ÿ‘†
a + b + ab/100 (Ch 4)
Average speed (barabar doori)?tap ๐Ÿ‘†
2xy/(x+y) (Ch 6, 10)
Time & Work ka fast method?tap ๐Ÿ‘†
LCM method (Ch 9)
2 saal ka CI rate (10%)?tap ๐Ÿ‘†
21% (Ch 8)
Cone ka volume?tap ๐Ÿ‘†
โ…“ฯ€rยฒh (Ch 12)
ChTopicSabse zaroori baat
1Number SystemBODMAS โ€” 'of' รท se pehle; รท & ร— left-to-right; 1 se n tak = n(n+1)/2
2HCF & LCMHCF ร— LCM = product; bada maango โ†’ HCF, chhota โ†’ LCM
3Fractions & SurdsCompare = cross-multiply; โˆš(a+b) โ‰  โˆša + โˆšb
4Percentagea + b + ab/100; x% zyada โ†’ x/(100+x) kam; 1/8 = 12.5%
5Ratio & PartnershipShare = part/total ร— qty; profit โˆ paisa ร— time
6AverageSum = avg ร— n; average speed = 2xy/(x+y)
7Profit & LossProfit% CP par, discount% MP par; CP = 100 maan lo
8SI & CISI = PRT/100; 2 saal CI = 2R + Rยฒ/100; antar = P(R/100)ยฒ
9Time & WorkLCM method; leak = minus efficiency
10Speed & Distanceร—5/18; platform = train + platform ki lambai
11Mensuration 2Dยฝ wale teen (triangle, rhombus, trapezium); circle ฯ€rยฒ, 2ฯ€r
12Mensuration 3DCone = โ…“ cylinder; 1 litre = 1000 cmยณ; maap k โ†’ volume kยณ
13Algebra & Geometryaยฒโˆ’bยฒ = (a+b)(aโˆ’b); polygon exterior sum 360ยฐ
14Series & DIPehle antar likho; pie: 1% = 3.6ยฐ
๐ŸŽฏ Exam ki raat ka plan Ye table + har chapter ke flip-cards ek baar dekh lo. Naya topic mat padho โ€” jo aata hai usko pakka karo. Aur CET mein Maths ke 10 sawal hain, koi negative marking nahi โ€” isliye har sawal attempt karo, chhodna mat! ๐Ÿ’ช
๐ŸŽฏ Score: 0 / 0 Total questions: 14
Practice (exam-style)

Q1. Find the next number: 2, 6, 12, 20, 30, ?

๐Ÿ’ก Antar +4, +6, +8, +10 โ†’ agla +12 โ†’ 30 + 12 = 42.
Practice (exam-style)

Q2. Find the next number: 3, 6, 12, 24, ?

๐Ÿ’ก Har baar ร—2 โ†’ 24 ร— 2 = 48.
Practice (exam-style)

Q3. Find the next number: 1, 4, 9, 16, ?

๐Ÿ’ก Squares: 1ยฒ, 2ยฒ, 3ยฒ, 4ยฒ โ†’ agla 5ยฒ = 25.
Practice (exam-style)

Q4. Find the next number: 1, 8, 27, 64, ?

๐Ÿ’ก Cubes: 1ยณ, 2ยณ, 3ยณ, 4ยณ โ†’ agla 5ยณ = 125.
Practice (exam-style)

Q5. Find the next number: 5, 11, 23, 47, ?

๐Ÿ’ก Rule ร—2 + 1 โ†’ 47 ร— 2 + 1 = 95.
Practice (exam-style)

Q6. Find the next number: 2, 3, 5, 7, 11, ?

๐Ÿ’ก Prime numbers ki series โ†’ agla prime 13.
Practice (exam-style)

Q7. Find the next number: 120, 99, 80, 63, ?

๐Ÿ’ก Antar โˆ’21, โˆ’19, โˆ’17 โ†’ agla โˆ’15 โ†’ 63 โˆ’ 15 = 48.
Practice (exam-style)

Q8. Find the odd one out: 3, 5, 7, 9, 11

๐Ÿ’ก Baaki sab prime hain; 9 = 3 ร— 3 composite hai.
Practice (exam-style)

Q9. In a pie chart, a sector has an angle of 108ยฐ. The percentage it represents is:

๐Ÿ’ก 108/360 ร— 100 = 30% (ya 108 รท 3.6).
Practice (exam-style)

Q10. In a pie chart, 25% of the total is shown by an angle of:

๐Ÿ’ก 25 ร— 3.6 = 90ยฐ (chauthai circle).
Practice (exam-style)

Q11. In a school of 1200 students, 30% are girls. The number of boys is:

๐Ÿ’ก Boys = 70% of 1200 = 840 (girls 360).
Practice (exam-style)

Q12. The sales of a shop in four months are 200, 300, 400 and 500 units. The average monthly sales is:

๐Ÿ’ก (200+300+400+500)/4 = 1400/4 = 350.
Practice (exam-style)

Q13. (Revision โ€” Ch 4) What is 15% of 400?

๐Ÿ’ก (15/100) ร— 400 = 60.
Practice (exam-style)

Q14. (Revision โ€” Ch 8) The simple interest on โ‚น2000 at 5% per annum for 2 years is:

๐Ÿ’ก PRT/100 = 2000 ร— 5 ร— 2/100 = โ‚น200.

Series mein hamesha pehle antar likho โ€” na mile to ร—/รท dekho, phir square/cube, phir alternate numbers. Antar khud dugna ho to rule ร—2 ยฑ k hai. Odd-one-out mein "sab prime/square hain kya" check karo. DI mein naya kuch nahi โ€” total nikalo, phir percentage (Ch 4), average (Ch 6) aur ratio (Ch 5) lagao; pie chart mein 1% = 3.6ยฐ (108ยฐ = 30%).

๐ŸŽ‰ Aur yahin course poora hua โ€” 14 chapters, 196 MCQs! Ab upar wale "Poore Course ka Revision" table ko apna final-day notes bana lo. CET mein Maths ke 10 sawal hain aur negative marking nahi โ€” har sawal attempt karna. All the best! ๐Ÿ†