Mathematics Notes

Coding & Decoding

ℹ️

Understanding the Rule

Coding is a method of transmitting messages between sender and receiver which others cannot understand. Decoding is the process of Converting the code back to original form.

Strategy Guide

1
Letter Coding
Letters of a word are replaced by other letters according to a specific rule (e.g. +1, -2, reverse).
2
Number Coding
Words are coded as digits, or digits are coded as letters/symbols.
3
Symbol Mapping
Mathematical operators like +, -, x, / are swapped with other symbols/letters.

Coding-Decoding Lab

Shift alphabets or map symbols to logic.

Alphabet Mapping (Shift 1)

Original

Encoded

IFMMP

Logic Overrides

"If '+' means 'x' and '-' means '/'"

Example: 10 + 5 becomes 10 x 5 = 50

Family Relation Mapper

Building connections using standard symbols.

☐

Male
(Square)

○

Female
(Circle)

Marriage
( Husband + Wife )

⇔

Sibling
( Brother ⇔ Sister )

Vertical
( Parent | Child )

Horizontal
( Sibling Link )

GP(M)

Grandpa

GP(F)

Grandma

A(M)

Father

A(F)

Mother

C1(M)

⇔

C2(F)

⇔

B(M)

Uncle

B(F)

Aunt

C1(M)

⇔

C2(M)

⇔

C3(F)

Total: 3 Generations | Mixed Relations | Standard Notation Visualized

Syllogism Visualizer

Understanding set relationships in logic.

Set B

Set A

Logic Breakdown

ALL

Every member of A is inside B. If A, then B. (Subset relation)

Practice Problems

Chapter Exercises

In a certain code, 'TEACHER' is written as 'VGCEJGT'. How is 'STUDENT' written in that code?

✓ Show Solution

1. Compare TEACHER and VGCEJGT:

T+2=V, E+2=G, A+2=C, C+2=E, H+2=J, E+2=G, R+2=T

2. Rule: Each letter is shifted +2.

3. Apply to STUDENT:

S+2=U, T+2=V, U+2=W, D+2=F, E+2=G, N+2=P, T+2=V

Result: UVWFGPV.

EASY

If '+' means 'x', '-' means '/', 'x' means '+' and '/' means '-', then find the value of: 20 + 5 - 2 x 10 / 5.

✓ Show Solution

1. Replace symbols:

'+' -> 'x' | '-' -> '/' | 'x' -> '+' | '/' -> '-'

2. New equation:

20 \times 5 / 2 + 10 - 5

3. BODMAS:

20 \times 2.5 + 10 - 5 = 50 + 10 - 5 = 55

MEDIUM

A is the brother of B. B is the daughter of C. D is the father of C. How is A related to D?

✓ Show Solution

1. Diagram:

D (☐) is father of C.

C is parent of B (○).

B is sister of A (☐).

2. Generation: D is 2 generations above A.

3. Relation: A is the grandson of D.

MEDIUM

In the code '123' means 'Cold Weather Ahead', '345' means 'Weather Is Good'. What digit represents 'Weather'?

✓ Show Solution

1. Look for common words: 'Weather' appears in both.

2. Look for common digits: '3' appears in both.

3. Result: Weather = 3.

EASY

Statements: All Poets are Thinkers. All Thinkers are Artists. Conclusion: Are all Poets Artists?

✓ Show Solution

1. Venn Diagram: Draw a small circle (Poets) inside a medium circle (Thinkers).

2. Draw the medium circle inside a large circle (Artists).

3. Since Poets are inside Thinkers and Thinkers are inside Artists, Poets are automatically inside Artists.

Result: Yes, All Poets are Artists.

HARD

Introducing a lady, a man said, 'The son of her only brother is the brother of my wife.' How is the lady related to the man?

✓ Show Solution

1. Lady's brother's son = Brother of man's wife.

2. Man's wife's brother = Lady's brother's son.

3. This means the man's father-in-law is the Lady's brother.

4. Relation: Lady is the sister of man's father-in-law.

HARD

If 'GOD' is coded as 7-15-4, how is 'ACT' coded?

✓ Show Solution

1. Check A=1, B=2 sequence:

G=7th letter, O=15th, D=4th.

2. Apply to ACT: A=1, C=3, T=20.

Result: 1-3-20.

EASY

Choose the Venn diagram that best represents: 'Mammal, Cow, Crow'.

✓ Show Solution

1. Relation: Cow is a Mammal. Crow is a Bird (not a mammal).

2. Diagram: A circle (Cow) inside a circle (Mammal), and a separate circle (Crow) outside both.

MEDIUM

CBSE Exam Focus

These questions are curated from previous years' Applied Mathematics papers. Focus on speed and pattern recognition.

Exam Patterns

In a code, 'FIRE' is written as '#*%@' and 'FREE' is written as '#&@@'. How is 'RIFF' written?

✓ Show Solution

1. Map letters to symbols:

F=#, I=*, R=%, E=@, R=% , E=@, E=@

Note: 'FREE' uses '&' for R? Let's re-map.

F=#, I=*, R=%, E=@ from FIRE.

F=#, R=&, E=@, E=@ from FREE.

Wait, R is mapped to % in FIRE and & in FREE? This usually means position-based or unique mapping.

Assuming RIFF from FIRE mapping: % * # #.

MEDIUM

Relation Problem: Pointing to a photograph, Shikha said 'He is the only son of the mother of my sister's brother.' How is the man related to Shikha?

✓ Show Solution

1. 'Shikha's sister's brother' = Shikha's brother.

2. 'Mother of Shikha's brother' = Shikha's mother.

3. 'Only son of Shikha's mother' = Shikha's brother.

Result: Brother.

EASY

Coding Logic: If BLUE is coded as 42, find code for READ.

✓ Show Solution

1. Position sum: B(2)+L(12)+U(21)+E(5) = 40 (Not 42). Try +2?

2. Position sum + Number of letters:

40 + 4 = 44

? No.

3. Try reverse positions: B(25)+L(15)+U(6)+E(22) = 68. No.

4. Try fixed logic: Maybe sum of positions + 2?

40 + 2 = 42

5. Applying to READ: R(18)+E(5)+A(1)+D(4) = 28.

6. Ans:

28 + 2 = 30

HARD

Venn Type: Out of 100 students, 60 like Math, 40 like Science and 20 like both. How many like NEITHER?

✓ Show Solution

1. Total like Math or Science =

n(M) + n(S) - n(M \cap S) = 60 + 40 - 20 = 80

2. Neither = Total - Either =

100 - 80 = 20

MEDIUM

Family Tree: A and B are sisters. R and S are brothers. A's daughter is R's sister. What is B's relation to S?

✓ Show Solution

1. A & B are Sisters.

2. A's daughter is sister of R and S.

3. This means R and S are A's sons.

4. B is the sister of S's mother (A).

Result: B is S's Maternal Aunt (Masi).

MEDIUM

Coding & Decoding

ℹ️

Understanding the Rule

Coding is a method of transmitting messages between sender and receiver which others cannot understand. Decoding is the process of Converting the code back to original form.

Strategy Guide

1
Letter Coding
Letters of a word are replaced by other letters according to a specific rule (e.g. +1, -2, reverse).
2
Number Coding
Words are coded as digits, or digits are coded as letters/symbols.
3
Symbol Mapping
Mathematical operators like +, -, x, / are swapped with other symbols/letters.

Coding-Decoding Lab

Shift alphabets or map symbols to logic.

Alphabet Mapping (Shift 1)

Original

Encoded

IFMMP

Logic Overrides

"If '+' means 'x' and '-' means '/'"

Example: 10 + 5 becomes 10 x 5 = 50

Family Relation Mapper

Building connections using standard symbols.

☐

Male
(Square)

○

Female
(Circle)

Marriage
( Husband + Wife )

⇔

Sibling
( Brother ⇔ Sister )

Vertical
( Parent | Child )

Horizontal
( Sibling Link )

GP(M)

Grandpa

GP(F)

Grandma

A(M)

Father

A(F)

Mother

C1(M)

⇔

C2(F)

⇔

B(M)

Uncle

B(F)

Aunt

C1(M)

⇔

C2(M)

⇔

C3(F)

Total: 3 Generations | Mixed Relations | Standard Notation Visualized

Syllogism Visualizer

Understanding set relationships in logic.

Set B

Set A

Logic Breakdown

ALL

Every member of A is inside B. If A, then B. (Subset relation)

Practice Problems

Chapter Exercises

In a certain code, 'TEACHER' is written as 'VGCEJGT'. How is 'STUDENT' written in that code?

✓ Show Solution

1. Compare TEACHER and VGCEJGT:

T+2=V, E+2=G, A+2=C, C+2=E, H+2=J, E+2=G, R+2=T

2. Rule: Each letter is shifted +2.

3. Apply to STUDENT:

S+2=U, T+2=V, U+2=W, D+2=F, E+2=G, N+2=P, T+2=V

Result: UVWFGPV.

EASY

If '+' means 'x', '-' means '/', 'x' means '+' and '/' means '-', then find the value of: 20 + 5 - 2 x 10 / 5.

✓ Show Solution

1. Replace symbols:

'+' -> 'x' | '-' -> '/' | 'x' -> '+' | '/' -> '-'

2. New equation:

20 \times 5 / 2 + 10 - 5

3. BODMAS:

20 \times 2.5 + 10 - 5 = 50 + 10 - 5 = 55

MEDIUM

A is the brother of B. B is the daughter of C. D is the father of C. How is A related to D?

✓ Show Solution

1. Diagram:

D (☐) is father of C.

C is parent of B (○).

B is sister of A (☐).

2. Generation: D is 2 generations above A.

3. Relation: A is the grandson of D.

MEDIUM

In the code '123' means 'Cold Weather Ahead', '345' means 'Weather Is Good'. What digit represents 'Weather'?

✓ Show Solution

1. Look for common words: 'Weather' appears in both.

2. Look for common digits: '3' appears in both.

3. Result: Weather = 3.

EASY

Statements: All Poets are Thinkers. All Thinkers are Artists. Conclusion: Are all Poets Artists?

✓ Show Solution

1. Venn Diagram: Draw a small circle (Poets) inside a medium circle (Thinkers).

2. Draw the medium circle inside a large circle (Artists).

3. Since Poets are inside Thinkers and Thinkers are inside Artists, Poets are automatically inside Artists.

Result: Yes, All Poets are Artists.

HARD

Introducing a lady, a man said, 'The son of her only brother is the brother of my wife.' How is the lady related to the man?

✓ Show Solution

1. Lady's brother's son = Brother of man's wife.

2. Man's wife's brother = Lady's brother's son.

3. This means the man's father-in-law is the Lady's brother.

4. Relation: Lady is the sister of man's father-in-law.

HARD

If 'GOD' is coded as 7-15-4, how is 'ACT' coded?

✓ Show Solution

1. Check A=1, B=2 sequence:

G=7th letter, O=15th, D=4th.

2. Apply to ACT: A=1, C=3, T=20.

Result: 1-3-20.

EASY

Choose the Venn diagram that best represents: 'Mammal, Cow, Crow'.

✓ Show Solution

1. Relation: Cow is a Mammal. Crow is a Bird (not a mammal).

2. Diagram: A circle (Cow) inside a circle (Mammal), and a separate circle (Crow) outside both.

MEDIUM

CBSE Exam Focus

These questions are curated from previous years' Applied Mathematics papers. Focus on speed and pattern recognition.

Exam Patterns

In a code, 'FIRE' is written as '#*%@' and 'FREE' is written as '#&@@'. How is 'RIFF' written?

✓ Show Solution

1. Map letters to symbols:

F=#, I=*, R=%, E=@, R=% , E=@, E=@

Note: 'FREE' uses '&' for R? Let's re-map.

F=#, I=*, R=%, E=@ from FIRE.

F=#, R=&, E=@, E=@ from FREE.

Wait, R is mapped to % in FIRE and & in FREE? This usually means position-based or unique mapping.

Assuming RIFF from FIRE mapping: % * # #.

MEDIUM

Relation Problem: Pointing to a photograph, Shikha said 'He is the only son of the mother of my sister's brother.' How is the man related to Shikha?

✓ Show Solution

1. 'Shikha's sister's brother' = Shikha's brother.

2. 'Mother of Shikha's brother' = Shikha's mother.

3. 'Only son of Shikha's mother' = Shikha's brother.

Result: Brother.

EASY

Coding Logic: If BLUE is coded as 42, find code for READ.

✓ Show Solution

1. Position sum: B(2)+L(12)+U(21)+E(5) = 40 (Not 42). Try +2?

2. Position sum + Number of letters:

40 + 4 = 44

? No.

3. Try reverse positions: B(25)+L(15)+U(6)+E(22) = 68. No.

4. Try fixed logic: Maybe sum of positions + 2?

40 + 2 = 42

5. Applying to READ: R(18)+E(5)+A(1)+D(4) = 28.

6. Ans:

28 + 2 = 30

HARD

Venn Type: Out of 100 students, 60 like Math, 40 like Science and 20 like both. How many like NEITHER?

✓ Show Solution

1. Total like Math or Science =

n(M) + n(S) - n(M \cap S) = 60 + 40 - 20 = 80

2. Neither = Total - Either =

100 - 80 = 20

MEDIUM

Family Tree: A and B are sisters. R and S are brothers. A's daughter is R's sister. What is B's relation to S?

✓ Show Solution

1. A & B are Sisters.

2. A's daughter is sister of R and S.

3. This means R and S are A's sons.

4. B is the sister of S's mother (A).

Result: B is S's Maternal Aunt (Masi).

MEDIUM

Logical Reasoning

Coding & Decoding

Understanding the Rule

Strategy Guide

Letter Coding

Number Coding

Symbol Mapping

Coding-Decoding Lab

Alphabet Mapping (Shift 1)

Logic Overrides

Family Relation Mapper

Syllogism Visualizer

Logic Breakdown

ALL

Practice Problems

Chapter Exercises

CBSE Exam Focus

Exam Patterns

Loading Knowledge...

Logical Reasoning

Coding & Decoding

Understanding the Rule

Strategy Guide

Letter Coding

Number Coding

Symbol Mapping

Coding-Decoding Lab

Alphabet Mapping (Shift 1)

Logic Overrides

Family Relation Mapper

Syllogism Visualizer

Logic Breakdown

ALL

Practice Problems

Chapter Exercises

CBSE Exam Focus

Exam Patterns