Badhai ho dosto โ ye aakhri chapter hai! ๐ 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 1โ2 questions aate hain aur DI se 1โ2. 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! ๐ช
1. Number Series ke 7 Types โญ
| Type | Example | Pattern |
|---|---|---|
| Addition (fix) | 3, 7, 11, 15, โฆ | +4 har baar |
| Addition (badhta hua) | 2, 6, 12, 20, 30, โฆ | +4, +6, +8, +10 |
| Multiplication | 3, 6, 12, 24, โฆ | ร2 har baar |
| Square | 1, 4, 9, 16, โฆ | 1ยฒ, 2ยฒ, 3ยฒ, 4ยฒ |
| Cube | 1, 8, 27, 64, โฆ | 1ยณ, 2ยณ, 3ยณ, 4ยณ |
| Mixed (รn + k) | 5, 11, 23, 47, โฆ | ร2 + 1 |
| Prime / special | 2, 3, 5, 7, 11, โฆ | Prime numbers |
Step 2: Agla antar = 12 โ 30 + 12 = 42 โ
Step 2: Check: 5ร2+1 = 11 โ, 11ร2+1 = 23 โ, 23ร2+1 = 47 โ
Step 3: Agla = 47ร2+1 = 95 โ
Step 2: Agla โ15 โ 63 โ 15 = 48 โ
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 25โ1, 26 โ 27โ1).
4. Aakhir mein alternate (ek chhod ke) numbers dekho โ do series mili hui ho sakti hain.
2. Odd One Out (bemel number)
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:
| Mahina | Sales (units) |
|---|---|
| January | 200 |
| February | 300 |
| March | 400 |
| April | 500 |
(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
(b) 25% ka sector kitne degree? โ 25 ร 3.6 = 90ยฐ โ
(c) Total kharcha โน12,000 hai aur khaane ka sector 108ยฐ โ khaana = 30% of 12000 = โน3600
| % | Degree | % | Degree |
|---|---|---|---|
| 10% | 36ยฐ | 30% | 108ยฐ |
| 20% | 72ยฐ | 50% | 180ยฐ |
| 25% | 90ยฐ | 75% | 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).
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.
Antar bahut bada โ ร2, ร3 check karo
5, 11, 23, 47 โ antar 6, 12, 24 (dugna ho raha) โ matlab rule ร2 + 1 hai. Antar khud dugna ho to multiply wala pattern hai.
24 = 25โ1 ยท 26 = 27โ1 ยท 63 = 64โ1
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.
% ร 3.6 = degree
10% = 36ยฐ, 25% = 90ยฐ, 30% = 108ยฐ, 50% = 180ยฐ. Ye chaar yaad rahe to pie ka har sawal 10 second ka.
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.
| Ch | Topic | Sabse zaroori baat |
|---|---|---|
| 1 | Number System | BODMAS โ 'of' รท se pehle; รท & ร left-to-right; 1 se n tak = n(n+1)/2 |
| 2 | HCF & LCM | HCF ร LCM = product; bada maango โ HCF, chhota โ LCM |
| 3 | Fractions & Surds | Compare = cross-multiply; โ(a+b) โ โa + โb |
| 4 | Percentage | a + b + ab/100; x% zyada โ x/(100+x) kam; 1/8 = 12.5% |
| 5 | Ratio & Partnership | Share = part/total ร qty; profit โ paisa ร time |
| 6 | Average | Sum = avg ร n; average speed = 2xy/(x+y) |
| 7 | Profit & Loss | Profit% CP par, discount% MP par; CP = 100 maan lo |
| 8 | SI & CI | SI = PRT/100; 2 saal CI = 2R + Rยฒ/100; antar = P(R/100)ยฒ |
| 9 | Time & Work | LCM method; leak = minus efficiency |
| 10 | Speed & Distance | ร5/18; platform = train + platform ki lambai |
| 11 | Mensuration 2D | ยฝ wale teen (triangle, rhombus, trapezium); circle ฯrยฒ, 2ฯr |
| 12 | Mensuration 3D | Cone = โ cylinder; 1 litre = 1000 cmยณ; maap k โ volume kยณ |
| 13 | Algebra & Geometry | aยฒโbยฒ = (a+b)(aโb); polygon exterior sum 360ยฐ |
| 14 | Series & DI | Pehle antar likho; pie: 1% = 3.6ยฐ |
Q1. Find the next number: 2, 6, 12, 20, 30, ?
Q2. Find the next number: 3, 6, 12, 24, ?
Q3. Find the next number: 1, 4, 9, 16, ?
Q4. Find the next number: 1, 8, 27, 64, ?
Q5. Find the next number: 5, 11, 23, 47, ?
Q6. Find the next number: 2, 3, 5, 7, 11, ?
Q7. Find the next number: 120, 99, 80, 63, ?
Q8. Find the odd one out: 3, 5, 7, 9, 11
Q9. In a pie chart, a sector has an angle of 108ยฐ. The percentage it represents is:
Q10. In a pie chart, 25% of the total is shown by an angle of:
Q11. In a school of 1200 students, 30% are girls. The number of boys is:
Q12. The sales of a shop in four months are 200, 300, 400 and 500 units. The average monthly sales is:
Q13. (Revision โ Ch 4) What is 15% of 400?
Q14. (Revision โ Ch 8) The simple interest on โน2000 at 5% per annum for 2 years is:
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 ร2 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%).
๐ 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! ๐