CBSE Class 12 Maths Previous Year Question Paper 2014 - Binary Operations
This CBSE Class 12 Maths Previous Year Question Paper from 2014 focuses on the topic of Binary Operations. It includes several 1-mark questions designed to test fundamental understanding and calculation skills related to binary operations. Students are required to compute specific values based on given binary operation definitions, such as <math>a*b = a + 4b^2</math>, <math>a*b = ab/5</math>, <math>a*b = LCM(a,b)</math>, and <math>a*b = 2a + b</math>. Solving these previous year questions helps students familiarize themselves with the exam pattern, identify key concepts within the Binary Operations chapter, and enhance their problem-solving abilities for the board examinations.
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Quick info
| Board | CBSE |
|---|---|
| Class | 12 |
| Subject | Maths |
| Session | 2014 |
| Language | English |
| Type | Previous Year Question Paper |
| Exam type | Board Exam |
Paper pattern
This paper contains 1-mark questions related to Binary Operations.
Topics covered
Paper topics
- Binary Operations
- LCM
- Real Numbers
- Integers
- Natural Numbers
Important topics
- Binary Operations on Real Numbers
- Binary Operations on Natural Numbers
- Properties of Binary Operations
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Question paper text
Binary Operations
1 Mark Questions
1. Let *: <math>R \times R \rightarrow R</math> given by <math>(a,b) \rightarrow a + 4b^2</math> be a binary operation. Compute (-5)* <math>(2*0)</math>.
All India 2014C
<math>(-5) * (2 * 0) = (-5) * (2 + 4(0)^{2})</math> <math>ab \rightarrow a + 4b^2</math>
<math>= (-5) * (2) = -5 + 4(2)^2 = -5 + 16 = 11</math> (1)
- Let * is a binary operation on the set of all non-zero real numbers, given by <math>a * b = \frac{ab}{E}</math> for all <math>a, b \in R - \{0\}</math>. Find the value of x, given
that <math>2 * (x * 5) = 10</math>. Delhi 2014
...(i)
Given, <math>a * b = \frac{ab}{5}</math>, <math>\forall a, b \in R - \{0\}</math> Also given, <math>2 * (x * 5) = 10</math> <math>\Rightarrow 2*\left(\frac{x\cdot 5}{5}\right)=10</math> [from Eq. (i)]
<math>\Rightarrow</math> <math>2 * x = 10 \Rightarrow \frac{2x}{5} = 10 \Rightarrow x = 25</math> (1)
3. Let * is a binary operation on N given by <math>a*b = LCM(a,b)</math> for all <math>a,b \in N</math>. Find <math>5*7</math>. Delhi 2012; Foreign 2008 Given, <math>a * b = LCM(a, b), \forall a, b \in N</math> <math>\therefore</math> 5 * 7 = LCM (5, 7) = 35
4. Let *: <math>R \times R \rightarrow R</math> is defined as <math>a * b = 2a + b</math>. Find (2 * 3) * 4. All India 2012
Given, *: <math>R \times R \rightarrow R</math> such that <math>a * b = 2a + b</math>. On putting <math>a = 2</math> and <math>b = 3</math>, we get
<math>(2 * 3) = 2 (2) + 3 = 4 + 3 = 7</math>
<math>\therefore</math> (2 * 3) * 4 = 7 * 4 = 2 (7) + 4 = 14 + 4 = 18(1)
5. If the binary operation * on the set of integers Z, is defined by <math>a * b = a + 3b^2</math>, then find the value of <math>8*3</math>. All India 2012C
Frequently asked questions
What is this document?
This is a CBSE Class 12 Maths Previous Year Question Paper from 2014, focusing on the topic of Binary Operations.
What is the main topic covered?
The main topic covered is Binary Operations, including various definitions and calculations.
How does solving this paper help students?
Solving this previous year question paper helps students understand the exam pattern, practice Binary Operations concepts, and improve their scores in the CBSE board exams.
What is the marking scheme for these questions?
The questions provided in this extract are all 1-mark questions.
What kind of problems are included?
Problems include computing values of binary operations with given functions and solving for variables in binary operation equations.
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