# 10th Maths Guide PDF | CBSE, STATE BOARD

If you are a student of class X, then today I am going to share with you a very important book 10th Maths Guide PDF which is also very beneficial for your board exam. Because with its help you will be able to solve maths questions easily and you will also be able to get good marks in class.

By the way, we all know how important the tenth board is for us. That’s why we put all our hard work to pass class 10th with good marks. If you have the right teacher and study materials, then you can easily pass the 10th board with very good marks in maths subject. Each and every question in this book is solved in a very easy way so that a student can easily understand.

### Sample

1. Find A × B, A × A and B × A

(i) A = {2, −2, 3} and B = {1, −4}

A × B = {2, −2, 3} × {1, −4}

= {(2, 1), (2, −4), (−2, 1), (−2, −4), (3, 1), (3, −4)}

A × A = {2, −2,3} × {2, −2, 3}

= {(2, 2), (2, −2), (2, 3), (−2, 2), (−2, −2), (−2, 3), (3, 2), (3, −2), (3, 3)}

B × A = {1, −4} × {2, −2,3}

= {(1, 2), (1, −2), (1, 3), (−4, 2), (−4, −2), (−4, 3)}

2. If A = {5, 6}, B = {4, 5, 6}, C = {5, 6, 7}, show that A × A = (B × B) ∩ (C × C).

A × A = (B × B) ∩ (C × C)

LHS: A × A = {5,6} × {5,6}

= {(5, 5), (5, 6), (6, 5), (6, 6)} ……….(1)

RHS:

B × B = {4,5,6} × {4,5,6}

= {(4,4), (4,5), (4,6), (5,4), (5, 5),

(5, 6), (6,4), (6, 5), (6, 6)}

C × C = {5,6,7} × {5,6,7} = {(5, 5), (5, 6), (5,7), (6, 5), (6, 6), (6,7), (7,5), (7,6), (7,7)}

(B × B) ∩ (C × C) = {(5, 5), (5, 6), (6, 5), (6, 6)}……….(2)

From (1) and (2), A × A = (B × B) ∩ (C × C)

3. A × (B − C) = (A × B) − (A × C)

LHS: B − C = {2,3,5,7} − {2} = {3,5,7}

A × (B − C) = {1,2,3,4,5,6,7} × {3,5,7}

= {(1, 3), (1, 5), (1, 7), (2, 3), (2, 5), (2, 7), (3, 3), (3, 5), (3, 7), (4, 3), (4, 5), (4, 7),

(5, 3), (5, 5), (5, 7), (6, 3), (6, 5), (6, 7), (7, 3), (7, 5), (7, 7)}…………(1)

RHS: A × B = {1,2,3,4,5,6,7} × {2,3,5,7}

= {(1,2), (1,3), (1,5), (1,7), (2,2), (2,3), (2,5), (2,7), (3,2), (3,3), (3,5), (3,7), (4,2), (4,3),

(4,5), (4,7), (5,2), (5,3), (5,5), (5,7), (6,2), (6,3), (6,5), (6,7), (7,2), (7,3), (7,5), (7,7)}

A × C = {1,2,3,4,5,6,7} × {2} = {(1,2), (2,2), (3,2), (4,2), (5,2), (6,2), (7,2)}

(A × B) − (A × C)

= {(1,2), (1,3), (1,5), (1,7), (2,2), (2,3), (2,5), (2,7), (3,2), (3,3), (3,5), (3,7), (4,2), (4,3),

(4,5), (4,7), (5,2), (5,3), (5,5), (5,7), (6,2), (6,3), (6,5), (6,7), (7,2), (7,3), (7,5), (7,7)}

− {(1,2), (2,2), (3,2), (4,2), (5,2), (6,2), (7,2)}

= {(1, 3), (1, 5), (1, 7), (2, 3), (2, 5), (2, 7), (3, 3), (3, 5), (3, 7), (4, 3), (4, 5), (4, 7),

(5, 3), (5, 5), (5, 7), (6, 3), (6, 5), (6, 7), (7, 3), (7, 5), (7, 7)}…………(2)

From (1) and (2)

A × (B − C) = (A × B) − (A × C)

### What’s New

• Easy Solution for all Exercise Problems in Textbook
• Exam-Based Creative Exercises
• For self-evaluation, ‘Try Your Self’.
• Concept Corner for each Exercise
• Answers for Progress Check & Thinking Corner
• Text Book MCQ Questions with Simple solution
• QR Code Questions with Simple solution
• Exam-based Creative MCQ