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German Continuous and Indefinite is same


In German there is NO separate grammatical tense equivalent to the English “continuous / progressive” form (am doing, is going, are eating).

So in most situations:

> English present simple = English present continuous = German Pr盲sens

German uses one tense (Pr盲sens) and context decides whether the action is habitual, happening now, temporary, or scheduled.

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 1. The Core Idea



German speakers simply do not mark the difference grammatically.

They rely on:

* time words
* context
* tone

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2. How German Shows “Continuous” Meaning Instead

Instead of changing verb form, German adds time indicators


馃憠 gerade is the closest natural equivalent to “-ing”

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Important Insight (Very Useful)


So German collapses:

> I read books
> I am reading books
> I do read books

into:

> **Ich lese B眉cher**

Only context changes interpretation.



Same verb form every time.

Conclusion

German does not grammatically separate:

* simple present
* present continuous
* near future

They are all expressed using Pr盲sens + context words.

So yes — functionally:

German continuous and indefinite (simple present) are the same tense.

The meaning changes through adverbs, not verb structure.




The Layered Approach to Retirement Planning in India: Stop Chasing 10–15 Crores and Start Building Freedom One Step at a Time

The Layered Approach to Retirement Planning in India: Stop Chasing 10–15 Crores and Start Building Freedom One Step at a Time

You open a retirement calculator, punch in your current expenses, and the screen spits out ₹10 crore… ₹12 crore… sometimes even ₹15 crore.

Your stomach drops. You quietly close the tab and tell yourself, “This is not for people like me.”

The problem isn’t that we earn too little. The problem is that traditional retirement calculators force us to buy our entire dream retirement on day one — groceries, medical emergencies, eating out, vacations, international travel, everything — from the very first month we stop working.

That’s not a plan. That’s a fantasy. And fantasies create paralysis.

Here’s a completely different way to think about retirement that actually works in India: the layered financial freedom ladder.

Instead of one terrifying finish line, you climb five manageable stages. Each stage gives you real peace of mind before you reach the next one. And the best part? Stage 1 — bare survival with dignity — is often far closer than you think.

Stage 1: Bare Essential Freedom (Survival with Dignity)

This is the most important and most misunderstood stage. It doesn’t buy you a luxurious life. It buys you self-respect.

Meet “Monty” — a regular salaried Indian who just wants to never beg, borrow, or tolerate nonsense at work.

His monthly survival budget (today’s prices, family of 3–4, child education handled separately because it ends):

  • Groceries & basic food: ₹25,000
  • Electricity + water: ₹5,000
  • Cooking gas: ₹1,000
  • Wi-Fi + phones + basic TV: ₹4,000
  • Health + term insurance premiums: ₹5,000
  • Fuel (two-wheeler or local transport): ₹2,000
  • Medicines + small health expenses: ₹2,000
  • House maintenance + miscellaneous: ₹6,000

Total: ₹50,000 per month

No eating out. No movies. No maid. No vacations. No upgrades. This is self-respect money, not happiness money.

Now the magic number.

Assumptions (very India-realistic):

  • Retire at 40, live till 80 (40 years)
  • Portfolio return: 9% (achievable with 60–70% equity index funds + debt)
  • Inflation: 7%
  • Real return: 2%

Corpus needed at retirement: ≈ ₹1.7 crore

Not 10. Not 15. 1.7 crore.

When people see this number, something shifts in their brain. The impossible suddenly becomes possible. That mental shift is where real financial freedom begins.

Stage 2: The 10% Health Buffer (Separate Medical Corpus)

Never mix retirement corpus and medical expenses. Insurance reduces risk, but it doesn’t make bills disappear.

Simple rule I follow: Keep at least 10% of your retirement corpus in a completely separate medical buffer (liquid, in debt funds or liquid funds).

For Stage 1 (₹1.7 cr) → ₹15–20 lakh separate for health.

This one decision removes 80% of retirement anxiety for most families.

Stage 3: Making the Plan Robust (Ultra-Conservative Assumptions)

Now that fear is gone, let’s stress-test.

New assumptions:

  • Return: 8% (more conservative)
  • Life expectancy: 90 (50 years in retirement)
  • Inflation still 7%

Corpus needed for the same ₹50,000/month: ≈ ₹2.4 crore

The jump isn’t scary anymore because you already secured Stage 1 in your mind.

Stage 4: Comfortable Freedom

Work isn’t killing you anymore. You want occasional eating out, a maid, movies, small upgrades, and one domestic vacation a year.

Expenses rise to ₹1 lakh per month.

Using original assumptions → ≈ ₹4.8 crore

Stage 5: Luxury / Ultra-Safe Freedom

You want zero stress. You assume portfolio only matches inflation (7% return = 0% real return) and plan for 50 years.

  • ₹50,000/month → ₹3 crore
  • ₹1 lakh/month → ₹6 crore






 If your retirement plan includes vacations and luxury before you have secured bare survival and medical safety, you don’t have a plan. You have anxiety wearing a spreadsheet.

Stop asking: “How much do I need for everything in life?”

Start asking: “What is the next layer I need to secure?”

Build it in the right order — survival → medical → robust → comfort → luxury — and you will reach financial freedom much faster than the scary calculators want you to believe.

Start with Stage 1.

The rest will feel surprisingly doable once the first layer is in place.


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Disclaimer: This is not financial advice. Numbers are illustrative based on reasonable assumptions. Past performance is no guarantee of future results. Please consult a SEBI-registered financial advisor before making any decisions.


If a block and tackle system with convenient direction has 3 movable pulleys then its velocity ratio

 If a block and tackle system with convenient direction has 3 movable pulleys, then its velocity ratio

1. is either 6 or 7 2.should be 6 3.should be 7 4. is 3






PYQ Boards Imp formulas | 3D Geometry Class 12 Chapter 11 Maths | CBSE NCERT with Solutions PDF

 


Important Concepts Covered in This Revision Lecture

(Chapter 11 – Three-Dimensional Geometry | Class 12 NCERT CBSE | Extremely Useful for 2026 Boards)

  • Cartesian equation of a linexx1a=yy1b=zz1c\frac{x - x_1}{a} = \frac{y - y_1}{b} = \frac{z - z_1}{c}
  • Vector form of a liner=a+b\vec{r} = \vec{a} + \lambda \vec{b}
  • Parametric form / Any point on the line Using parameter 位 (or t, 渭): x=x1+a, y=y1+b, z=z1+cx = x_1 + a\lambda,\ y = y_1 + b\lambda,\ z = z_1 + c\lambda
  • Direction ratios (DRs) and Direction cosines (DCs) of a line
  • Condition for two lines to be parallela1a2=b1b2=c1c2\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}
  • Condition for two lines to be perpendiculara1a2+b1b2+c1c2=0a_1a_2 + b_1b_2 + c_1c_2 = 0
  • Direction ratios of line joining two points(x1,y1,z1)(x_1, y_1, z_1) and (x2,y2,z2)(x_2, y_2, z_2)x2x1, y2y1, z2z1x_2 - x_1,\ y_2 - y_1,\ z_2 - z_1
  • Mid-point formula in 3D(x1+x22, y1+y22, z1+z22)\left( \frac{x_1+x_2}{2},\ \frac{y_1+y_2}{2},\ \frac{z_1+z_2}{2} \right)
  • Foot of the perpendicular from a point to a line (most frequent 4–6 mark question)
  • Image (reflection) of a point in a given line Key properties used:
    1. Foot of perpendicular Q is the mid-point of A and A'
    2. Line AA' is perpendicular to the given line → Solve using parametric point + perpendicular condition
  • Equation of the line joining a point and its image (A and A')
  • Distance of a point from a line = 7 units type questions → Use distance formula between point and general point on line → solve quadratic in 位 → two possible points P1, P2
  • Line perpendicular to two given lines (common normal) Direction ratios = b1×b2\vec{b_1} \times \vec{b_2} (vector cross product)
  • Shortest distance between two skew lines (non-parallel, non-intersecting) (a2a1)(b1×b2)b1×b2
  • Equation of a line parallel to a given line and passing through a given point Same DRs, new point
  • Conversion between Cartesian and vector forms of a line
  • Case-study/application-based questions (metro lines, solar panels, pedestrian pathway) that combine parallel, perpendicular, shortest distance, and equation of line concepts



CBSE Class 12 Maths | 3D Geometry Chapter 11 Revision + 2025 Board Questions Full Solution | 2026 Boards Complete last-minute revision of Three Dimensional Geometry Class 12 CBSE Chapter 11 with all 2025 board paper questions solved step-by-step. Perfect for CBSE 2026 students targeting 95%+ in Maths! q1 Find the image A' of the point A(1, 6, 3) in the line x/1=y-1/2=z-2/3  Also, find the equation of the line joining A and A'. q2. Find the image A' of the point A(2, 1, 2) in the line l : 7 = 41 + 2j + 2k + 2 (i - j -k). Also, find the equation of line joining AA'. Find the foot of perpendicular from point A on the line l. q3 Find a point P on the line x+5/1=y+3/4=z-6/-9 from point Q(2, 4,-1) is 7 units. Also, find the equation of line joining P and Q. q4. Initially, two metro lines, Line A and Line B, each consisting of multiple stations are designed. The track for Line A is represented by Class 12 3d chapter cbse pdf Class 12 3D Geometry NCERT PDF 3D Geometry Class 12 NCERT Solutions PDF Class 12 3d chapter cbse solutions 3D Geometry Class 12 Notes PDF download 3D Geometry Class 12 PYQ boards PDF Class 12 3d chapter cbse notes Class 12 Maths Chapter 11 PDF 00:00 imp formulas 06:00 q1 13:38 q2 25:45 q3 34:30 q4 3d geometry class 12 three dimensional geometry class 12 class 12 maths chapter 11 3d geometry cbse 2026 3d geometry 2025 board paper image of point in a line foot of perpendicular 3d geometry shortest distance between skew lines cbse class 12 maths 2026 class 12 maths revision 3d geometry important questions direction ratios class 12 equation of line in 3d cbse 2025 maths solutions 3d geometry case study metro case study 3d geometry class 12 maths chapter 11 ncert 3d geometry one shot 3d geometry revision 2026 class 12 maths board exam 2026 cbse class 12 maths important questions 3d geometry pyq previous year questions 3d geometry class 12 maths chapter wise revision cbse maths 2026 strategy 3d geometry ncert solutions vector form of line class 12 cartesian form of line perpendicular lines in 3d parallel lines in 3d