
1. 🧾 In Indian Education:
Form-IV usually refers to the fourth year of school (Class 4) in some older or regional education systems.
In CBSE or modern systems, this terminology is rarely used.
2. 📊 In Government or Employment Records (India):
Form IV is often used in official documentation or compliance registers.
For example:
Under the Factories Act, Form IV is a register of adult workers.
Under the Minimum Wages Act, Form IV may be a wage register.
In labor law, Form IV may refer to overtime or register of employment.
3. 🏢 In Business/Corporate Law:
Under some regulatory acts (like Shops & Establishment or ESI), Form-IV might be a return form or compliance submission format.
4. 📑 In Other Countries:
In some countries like Kenya, Uganda, etc., “Form IV” refers to the fourth year of secondary/high school education.
We are given:
Speed of the train = 60 km/hr
Time to cross a pole = 9 seconds
We are to find the length of the train
🧠 Concept:
When a train crosses a pole, the distance covered = length of the train.
So,
Distance=Speed×Time\text{Distance} = \text{Speed} × \text{Time}
But we must ensure that the speed and time are in the same units.
🔄 Step 1: Convert speed to m/s
To convert km/h to m/s, multiply by 5/18:
60 km/hr=60×518=30018=16.67 m/s60 \text{ km/hr} = 60 × \frac{5}{18} = \frac{300}{18} = 16.67 \text{ m/s}
🔢 Step 2: Use the formula
Length of train=Speed×Time=16.67×9≈150 meters\text{Length of train} = \text{Speed} × \text{Time} = 16.67 × 9 ≈ 150 \text{ meters}
✅ Final Answer:
The length of the train is 150 meters.
We are given:
Kamal invested ₹9000 for 12 months
Sameer invested ₹8000 but joined after 5 months ⇒ so he invested for (12 − 5) = 7 months
Total profit = ₹6970
We are to find Sameer’s share of the profit
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🟢 Step 1: Calculate profit-sharing ratio
Profit is shared in the ratio of (Capital × Time)
Kamal’s share = 9000 × 12 = 108000
Sameer’s share = 8000 × 7 = 56000
Now simplify the ratio:
Kamal : Sameer = 108000 : 56000
Divide both by 1000 ⇒ 108 : 56
Simplify further: divide both by 4 ⇒ 27 : 14
So the profit-sharing ratio is:
➡️ Kamal : Sameer = 27 : 14
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🟢 Step 2: Total parts = 27 + 14 = 41 parts
Sameer’s share = (14 / 41) × 6970
Now calculate:
1441×6970=9758041=2380\frac{14}{41} × 6970 = \frac{97580}{41} = 2380
✅ Final Answer:
Sameer’s share of the profit is ₹2,380.
We are given:
(999)2−(998)2(999)^2 – (998)^2
This is a classic difference of squares identity:
a2−b2=(a−b)(a+b)a^2 – b^2 = (a – b)(a + b)
Let’s apply it:
a = 999
b = 998
So:
(999)2−(998)2=(999−998)(999+998)=1×1997=1997(999)^2 – (998)^2 = (999 – 998)(999 + 998) = 1 × 1997 = 1997
✅ Final Answer:
1997