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 line $\frac{x - x_1}{a} = \frac{y - y_1}{b} = \frac{z - z_1}{c}$
Vector form of a line $\vec{r} = \vec{a} + \lambda \vec{b}$
Parametric form / Any point on the line Using parameter λ (or t, μ): $x = x_1 + a\lambda,\ y = y_1 + b\lambda,\ z = z_1 + c\lambda$
Direction ratios (DRs) and Direction cosines (DCs) of a line
Condition for two lines to be parallel $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$
Condition for two lines to be perpendicular $a_1a_2 + b_1b_2 + c_1c_2 = 0$
Direction ratios of line joining two points $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ $x_2 - x_1,\ y_2 - y_1,\ z_2 - z_1$
Mid-point formula in 3D $\left( \frac{x_1+x_2}{2},\ \frac{y_1+y_2}{2},\ \frac{z_1+z_2}{2} \right)$
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 λ → two possible points P1, P2
Line perpendicular to two given lines (common normal) Direction ratios = $\vec{b_1} \times \vec{b_2}$ (vector cross product)
Shortest distance between two skew lines (non-parallel, non-intersecting) $∣ \frac{(\vec{a_{2}} - \vec{a_{1}}) \cdot (\vec{b_{1}} \times \vec{b_{2}})}{∣ \vec{b_{1}} \times \vec{b_{2}} ∣} $
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

Amazon Basics Rechargeable LED Table Lamp Review: Features, Battery Life, Drawbacks & Real-User Verdict

In this article, I share a detailed hands-on review, including the lamp’s best features, battery performance, everyday usability, and the one major drawback that buyers often discover too late.

👉 Watch the full video review here: https://youtu.be/URIiMSa2Yo4

⭐ 1. Design & Flexibility: A Lamp That Moves the Way You Need

One of the first things you notice is the lamp’s highly flexible neck. Unlike rigid metal stems, this one bends effortlessly, allowing you to adjust it to any position—perfect for studying in bed, reading a book on a couch, or directing focused light onto your laptop keyboard.

Key design benefits:

Lightweight and portable
Fully flexible stem for angle adjustment
Minimalist design suitable for bedrooms, study tables, and home offices

This feature alone makes it one of the most user-friendly study lamps in its price range.

⭐ 2. Three Light Modes: White, Yellow & Mixed

Lighting preferences change depending on the task—white for reading, yellow for relaxing, and mixed for balanced usage.
The Amazon Basics lamp offers three touch-sensitive modes:

Cool White Light – Bright and sharp; ideal for reading textbooks or writing notes
Warm Yellow Light – Comfortable for evening use and reduces eye strain
Mixed Light Mode – A blend of both, suitable for long study sessions

Switching between modes is intuitive:
✔ Tap once → White
✔ Tap twice → Yellow
✔ Tap thrice → Mixed
✔ Tap again → OFF

This simplicity makes it ideal for students and working professionals alike.

⭐ 3. Adjustable Brightness: Press-and-Hold Dimming

The lamp also offers smooth brightness control.
All you need to do is press and hold the touch button:

The brightness gradually decreases
Hold again to increase the light intensity

This dimmable feature is extremely useful during late-night study sessions when harsh lighting can cause fatigue.

⭐ 4. Battery Life: 4–6 Hours on a Full Charge

With regular use, the lamp delivers around 4 to 5 hours of continuous light, depending on the mode and brightness level.

A fully charged battery easily lasts an entire evening of studying or binge-reading. Once the brightness begins to fade, it's a sign that the lamp needs recharging.

This makes the lamp perfect for:

Hostel rooms
Power cuts
Late-night reading
Portable table lighting without messy cables

⭐ 5. The Major Drawback: Charging Socket Loosens Over Time

Here’s where things get tricky—and this is the main reason many users hesitate to repurchase the product.

After a few months of constant plugging and unplugging, the DT-type charging socket tends to loosen.
Once loose, the lamp stops charging properly, and eventually becomes unusable.

In my experience:

This issue appeared on multiple units
It is a recurring manufacturing flaw
Once the port loses grip, repairing it is difficult

For a lamp designed to be recharged daily, this becomes a critical long-term problem.

⭐ 6. Packaging & What You Get Inside

Amazon Basics usually maintains good packaging standards.

Inside the box, you will find:

The Rechargeable LED Table Lamp
A DT-type charging cable
A user instruction manual

Note:
An adapter is not included, but you can use any standard mobile charging adapter from home.

⭐ 7. Should You Buy This Lamp in 2025? – Verdict

The Amazon Basics Rechargeable LED Table Lamp is ideal if you want:

A budget-friendly study lamp
Multiple light modes
Flexible design
Adjustable brightness
Portability

However, the recurring charging socket issue makes it a risky long-term investment.

✔ Buy it if:

You need a short-term or occasional-use lamp.

✘ Avoid it if:

You want a lamp that lasts for years without charging problems.

⭐ Conclusion: A Good Lamp Held Back by One Serious Flaw

Based on features alone, the lamp performs exceptionally well for its price.
But durability is where it struggles.

If Amazon improves the charging port in future versions, this could easily become one of the best budget study lamps in India.

For a complete demonstration—flexibility, modes, dimming, charging, and live usage—
👉 Watch the full video review here: https://youtu.be/URIiMSa2Yo4

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