🎯 CBSE IP (065) Board Problem Sets

Welcome to the Flügel Information Practices Problem Laboratory. These graded board problem sets test practical Python syntax, SQL analytical queries, and multi-block network design algorithms aligned with the official CBSE Class 12 IP blueprint.

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⚡ Problem 1 (Pandas): Multi-Index Slicing, Boolean Filtering & NaN Imputation

Problem Statement

Given the following quarterly sales dataset stored in a Pandas DataFrame df_sales:

import pandas as pd
import numpy as np

data = {
    'Quarter': ['Q1', 'Q2', 'Q3', 'Q4', 'Q1', 'Q2', 'Q3', 'Q4'],
    'Region': ['North', 'North', 'North', 'North', 'South', 'South', 'South', 'South'],
    'UnitsSold': [120, 150, np.nan, 210, 80, np.nan, 130, 190],
    'UnitPrice': [450, 450, 480, 480, 500, 520, 520, 550]
}
df_sales = pd.DataFrame(data)

1. Write the Python code to replace all NaN values in 'UnitsSold' with the mean units sold in that respective region.
2. Add a calculated column 'TotalRevenue' equal to $\text{UnitsSold}\times \text{UnitPrice}$.
3. Using .loc[], display the 'Quarter' and 'TotalRevenue' for rows where 'TotalRevenue' > 75000 and 'Region' == 'North'.
4. Export the filtered DataFrame to a CSV file named high_revenue_north.csv without writing the integer index.

💡 Interactive Clue SystemStep-by-Step Problem Solving Clues

Try solving with Hint 1 before revealing Hint 2 or 3!

🟡 Hint 1: Physical Intuition & Coordinate Choice

To impute NaN values with column or group mean, use `df['UnitsSold'].fillna(df.groupby('Region')['UnitsSold'].transform('mean'), inplace=True)` or simple `df['UnitsSold'].fillna(df['UnitsSold'].mean(), inplace=True)`.

🟠 Hint 2: Key Governing Equations

Boolean indexing with `.loc` syntax: `df.loc[(condition1) & (condition2), ['Col1', 'Col2']]`.

🟢 Hint 3: Full Step-by-Step Derivation

Substitute I_C = I_cm + M*R^2 and solve for acceleration a_cm.

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🔮 Problem 2 (SQL): Multi-Table Joins with GROUP BY & Aggregate Conditions

Problem Statement

Consider two relational database tables CUSTOMER and ORDERS:

Table: CUSTOMER

CustID	CustName	City	CreditLimit
C101	'Ananya Roy'	'Delhi'	50000
C102	'Dev Sharma'	'Mumbai'	75000
C103	'Pooja Hegde'	'Bengaluru'	60000
C104	'Rajat Verma'	'Delhi'	45000

Table: ORDERS

OrderID	CustID	OrderDate	OrderAmount
O501	C101	2026-01-10	18500
O502	C102	2026-01-12	42000
O503	C101	2026-01-15	12000
O504	C103	2026-01-20	31000
O505	C102	2026-02-05	28000

Write SQL queries for the following requirements:

1. Display the CustName, City, and OrderAmount for all orders placed in the month of January 2026.
2. Display the CustName and total order spending (SUM(OrderAmount)) for each customer who has spent more than ₹30,000 in total.
3. State the Degree and Cardinality of the Cartesian product CUSTOMER $\times$ ORDERS.
4. Write a query to increase the CreditLimit by 15% for all customers living in 'Delhi'.

💡 Interactive Clue SystemStep-by-Step Problem Solving Clues

Try solving with Hint 1 before revealing Hint 2 or 3!

🟡 Hint 1: Physical Intuition & Coordinate Choice

For date matching, use `MONTHNAME(OrderDate) = 'January'` or `MONTH(OrderDate) = 1` or `OrderDate BETWEEN '2026-01-01' AND '2026-01-31'`.

🟠 Hint 2: Key Governing Equations

Aggregate conditions like total order spending $> 30000$ must be placed in `HAVING SUM(OrderAmount) > 30000`, not `WHERE`.

🟢 Hint 3: Full Step-by-Step Derivation

Substitute I_C = I_cm + M*R^2 and solve for acceleration a_cm.

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🌐 Problem 3 (Networks): Complete 5-Mark Campus Layout Specification

Problem Statement

"Vidya Mandir Trust" is setting up a sprawling new educational campus in Pune. The campus consists of 4 main wings: Academic Wing, Administration Wing, Hostel Wing, and Library Wing.

Distance Matrix (in meters):

From Wing	To Wing	Distance
Academic Wing	Administration Wing	$60\text{ m}$
Academic Wing	Hostel Wing	$180\text{ m}$
Academic Wing	Library Wing	$45\text{ m}$
Administration Wing	Hostel Wing	$130\text{ m}$
Administration Wing	Library Wing	$90\text{ m}$
Hostel Wing	Library Wing	$150\text{ m}$

Computer Count Table:

Wing Name	Installed Computers
Academic Wing	160 (Maximum)
Administration Wing	30
Hostel Wing	20
Library Wing	40

Answer the following questions:

1. Suggest the most suitable wing to house the central Server with technical justification.
2. Suggest the optimal wired Cable Layout connecting all wings to minimize cable cost.
3. Specify where Repeater(s) and Switch(es) should be installed with reasons.
4. The management wants to hold live interactive webinars between this Pune campus and their London branch. Which software protocol/technology should be used?

💡 Interactive Clue SystemStep-by-Step Problem Solving Clues

Try solving with Hint 1 before revealing Hint 2 or 3!

🟡 Hint 1: Physical Intuition & Coordinate Choice

Server goes to the wing with the maximum number of computers (80/20 rule).

🟠 Hint 2: Key Governing Equations

Repeaters are required when distance between any two interconnected wings exceeds $70\text{ m} - 100\text{ m}$. Switches are mandatory in EVERY wing.

🟢 Hint 3: Full Step-by-Step Derivation

Substitute I_C = I_cm + M*R^2 and solve for acceleration a_cm.