NCERT Solutions for Class 12 Maths Exercise 1.3: The "Composition of Functions" of Class 12 Maths Chapter 1 is an important topic and is not too...

NCERT Solutions for Class 12 Maths Exercise 1.3

October 24, 2024**CBSE Important Questions Class 12 Maths:** The CBSE Class 12 Maths has total 13 chapters in Mathematics – I and Mathematics – II. Students should solve the previous year question papers and sample questions to develop a strong understanding of all the topics, do revision and know the topics in which they need better clarity or practice. Also, solving CBSE important questions Class 12 Maths can help students cover more topics in lesser time.

In this article, we have provided some chapter-wise important questions. This activity can enable students know their strengths and weaknesses and learn how to solve all necessary questions in a stipulated time. Scroll down to get Maths Class 12 CBSE important questions.

Below is the overview of CBSE Class 12 board exams. Students are advised to check it once before moving to the important MCQs of Maths for Class 12.

Board Name | Central Board of Secondary Education / CBSE |

Exam Name | CBSE Board Class 12 Exam |

Level of Exam | National |

Exam Frequency | Once a Year |

Exam Mode | Offline |

Mode of Registration | Offline Mode For Regular Students Online Mode For Private Students |

Official Website | cbse.gov.in |

Students are advised to solve the in-text questions, miscellaneous exercises, sample questions and previous year question papers apart from the important questions so that they practice all the topics. Below are some of the chapter-wise CBSE important questions Class 12 Maths:

Students can learn the CBSE class 12 Maths important questions from below:

- Let f : W → W be defined as f(n) = n – 1, if n is odd and f(n) = n + 1, if n is even. Show that f is invertible. Find the inverse of f. Here, W is the set of all whole numbers.
- If f : R → R is defined by f(x) = x 2 – 3x + 2, find f (f(x)).
- Let A = {1, 2, 3}. Then number of relations containing (1, 2) and (1, 3) which are reflexive and symmetric but not transitive is – (A) 1 (B) 2 (C) 3 (D) 4
- Number of binary operations on the set {a, b} are – (A) 10 (B) 16 (C) 20 (D ) 8

Students can solve Maths Class 12 CBSE important questions from below:

- If A and B are symmetric matrices, prove that AB – BA is a skew symmetric matrix.
- Show that the matrix B′AB is symmetric or skew symmetric according as A is symmetric or skew symmetric.
- A manufacturer produces three products x, y, z which he sells in two markets. Annual sales are indicated below: Market Products I 10,000 2,000 18,000

II 6,000 20,000 8,000.

(a) If unit sale prices of x, y and z are 2.50, 1.50 and 1.00, respectively, find the total revenue in each market with the help of matrix algebra.

(b) If the unit costs of the above three commodities are 2.00, 1.00 and 50 paise respectively. Find the gross profit.

- If A and B are square matrices of the same order such that AB = BA, then prove by induction that ABn = Bn A. Further, prove that (AB)n = An Bn for all n ∈ N.

Students can solve Maths Class 12 CBSE important questions from below:

- cos (a cos x + b sin x), for some constant a and b.
- x
^{x}+ x^{a}+ a^{x}+ a^{a}, for some fixed a > 0 and x > 0, for some fixed a > 0 and x > 0 - Using the fact that sin (A + B) = sin A cos B + cos A sin B and the differentiation, obtain the sum formula for cosines.
- Does there exist a function which is continuous everywhere but not differentiable at exactly two points? Justify your answer.

Students can solve Maths Class 12 CBSE important questions from below:

- The two equal sides of an isosceles triangle that have a fixed base b, are reducing at the rate of 3 cm per second. How fast is the area reducing, when the two equal sides are equal to the base ?
- Find the equation of the normal to curve x
^{2}= 4y which passes through the point (1, 2). - A tank having rectangular base and rectangular sides and open ingat the top, is to be built such that its depth is 2 m and its volume is 8m
^{3}. If constructing the tank costs Rs 70 per sq metres for its base and Rs 45 per square metre for its sides, then what is the cost of least expensive tank? - The sum of perimeter of a square and a circle is k, where k is a constant. You have to prove that the addition of their areas is least when the side of the square is twice the radius of the circle.

From the table below, students can download the question bank and additional practice questions on Maths Class 12 CBSE important questions for CBSE 12th Maths all chapters:

CBSE Class 12 Maths Important Questions | Download Link |

CBSE Class 12 Maths Question Bank | Download Here |

CBSE Class 12 Maths Additional Practice Questions | Download Here |

Here are some of the most frequently asked questions on CBSE important questions Class 12 Maths:

**Q.1. Is solving CBSE Class 12 Maths important questions helpful for board exam?****Ans. **Yes, solving the important MCQs of Maths for Class 12 helps students to repeatedly practice and memorise formulas. Students are also able to improve their problem-solving speed and accuracy.

**Q.2. From where can I get the CBSE Class 12 Maths important questions for Matrices and Determinants?****Ans. **In this article, we have given direct links for downloading question bank and additional questions for practice. Students can practice questions for Matrices and Determinants from them, apart from solving previous years papers and sample questions on Embibe for.

**Q.3. Where can I download important questions for Class 12 Maths chapter-wise?****Ans.** Students can download chapter-wise important questions for Class 12 Maths from the links provided in this article.

**Q.4. How do Embibe important questions Maths Class 12 help in getting good marks in the board exam?****Ans.** The important questions on Class 12 Maths at Embibe prepares students to solve any type of question by introducing them to different levels of questions when they solve Embibe mock tests. This gives exam confidence and reduces fear of failure or making silly mistake in the board exam.

**Q.5. What are the most important chapter in Class 12 Maths?****Ans. **All the CBSE Class 12 Maths chapters are important and questions can be asked from any chapter. Students are advised to gain conceptual clarity in all chapters and solve sufficient practice problems.

*We hope this article on CBSE Important Questions Class 12 Maths was helpful to you. Stay tuned to **Embibe** for all the latest updates. *