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The Central Board of Secondary Education (CBSE) has released the Maths Sample Paper Class 12 with Solutions for the academic year 2023-2024. **CBSE Class 12 Maths Sample Paper 2023-24 PDF is now available for download at cbseacademic.nic.in.** We have provided Maths Sample Paper Class 12 2024 PDF for both Basis and standard courses in this article.

## Maths Sample Paper Class 12 with Solutions 2024

Sample or model Paper acts as a blueprint of the actual Maths Paper that can help students understand the 12th board exam pattern, types of questions, answer-writing methods, exam difficulty level, and other elements. In addition to the CBSE Class 12 Maths Sample Paper 2023-24, the CBSE also releases the Marking Scheme. Students can use it as a guide to anticipate the types of questions that may be given in their exams, as well as to learn how to answer precisely for a full score.

**Check: CBSE Class 12 Maths Answer Key 2024**

## CBSE Class 12 Maths Sample Paper 2023-24

CBSE Class 12 Maths Sample Paper 2023-24 has the same question format as the real CBSE Class 12 Maths Paper.

- The CBSE Maths sample paper class 12 2024 has a value of 80 marks. Candidates are given three hours to complete the Question paper.
- This Question paper contains – five sections A, B, C, D, and E. Each section is compulsory. However, there are internal choices in some questions.
- Section A has 18 MCQs and 02 Assertion-Reason-based questions of 1 mark each.
- Section B has 5 Very Short Answer (VSA)-type questions of 2 marks each.
- Section C has 6 Short Answer (SA)-type questions of 3 marks each.
- Section D has 4 Long Answer (LA)-type questions of 5 marks each.
- Section E has 3 source-based/case-based/passage-based/integrated units of assessment of 4 marks each with sub-parts.

**Also Read: Class 12 Mathematics Important Questions**

## CBSE Class 12 Maths Sample Paper 2024 PDF with Solutions

The CBSE Class 12 Maths Sample Paper 2023-24 PDF and marking Scheme are now available at cbseacademic.nic.in. Candidates can save the Class 12 Maths Sample Paper PDF from the direct Link given below and start practicing for Class 12th Maths exam preparation.

Class 12 Maths Sample Paper 2023-24 with Solutions PDF Download |

CBSE Class 12 Maths Sample Paper 2024 PDF |

Class 12 Maths Sample Paper 2023- 24 Marking scheme |

## Class 12 Maths Sample Paper with Solutions 2024

The Section A of the Class 12th Math Sample paper consists of 20 questions in total, 1 mark each with 18 MCQ-type questions and 2 Assertion-Reason-type questions.

**Section –A**

**Multiple Choice Questions and ****Each question carries 1 mark**

Q7. The corner points of the bounded feasible region determined by a system of linear constraints are (0, 3) , (1,1) and (3, 0). Let Z px qy where , 0 .p q The condition on p and q so that the minimum of Z occurs at (3, 0) and (1,1) is

(a) p = 2q

(b) p = q/2

(c) p = 3q

(d) p = q

Q11. The feasible region corresponding to the linear constraints of a Linear Programming Problem is given below.

Which of the following is not a constraint to the given Linear Programming Problem?

(a) x+ y ≥ 2 (b) x + 2y ≤ 10 (c) x- y ≥ 1 (d) x – y≤1

Q14 A problem in Mathematics is given to three students whose chances of solving it are 1/2, 1/3, and 1/4 respectively. If the events of their solving the problem are independent then the probability that the problem will be solved is

(a) 1/4

(b) 1/3

(c) 1/2

(d) 3/4

Q15 The general solution of the differential equation ydx-xdy=0; (Given x, y> 0), is of the form

(a) xy = c

(b)x = c y²

(c) y = cx

(d) y = cx²

**ASSERTION-REASON BASED QUESTIONS**

In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R).

Choose the correct answer out of the following choices.

(a) Both (A) and (R) are true and (R) is the correct explanation of (A).

(b) Both (A) and (R) are true but (R) is not the correct explanation of (A).

(c) (A) is true but (R) is false.

(d) (A) is false but (R) is true.

## Maths Sample Paper Class 12 2024: Section B

**Section –B**

**[This section comprises of very short answer type questions (VSA) of 2 marks each] **

Q25. Check whether the function f : R →R defined by f(x) = x³+x , has any critical point/s or not ?

If yes, then find the point/s.

## Class 12th Maths Sample Paper 2024: Section C

**Section – C**

**[This section comprises of short answer type questions (SA) of 3 marks each]**

i) Determine the value of **k**.

(ii) Find **P (x< 2 )**

(iii) Find **P (x> 2 )**

Q30. Solve the following Linear Programming Problem graphically:

Minimize: z= x+2y.

subject to the constraints: x+y≥100, 2x- y ≤0, 2x+ y ≤ 200,x,y ≥0 .

OR

Solve the following Linear Programming Problem graphically:

Maximize: z= – x +2y,

subject to the constraints: x ≥ 3, x+y ≥5, x+2y ≥6, y≥0.

## Maths Sample Paper Class 12 2024: Section D

## CBSE Maths Sample Paper Class 12 2024: Section E

**Section –E**

**[This section comprises three case-study/passage-based questions of 4 marks each with sub-parts.**

**The first two case study questions have three sub-parts (i), (ii), and (iii) of marks 1,1,2 respectively.**

**The third case study question has two sub-parts of 2 marks each.]**

*Q36. Read the following passage and answer the questions given below:*

In an Office three employees Jayant, Sonia and Oliver process incoming copies of a certain form. Jayant processes 50%of the forms, Sonia processes 20% and Oliver the remaining 30% of the forms. Jayant has an error rate of 0.06 , Sonia has an error rate of 0.04 and Oliver has an error rate of 0.03

*Based on the above information, answer the following questions*

(ii) Find the total probability of committing an error in processing the form.

(iii) The manager of the Company wants to do a quality check. During the inspection, he selects a form at random from the day’s output of the processed form. If the form selected at random has an error, find the probability that the form is not processed by Jayant.

Teams A, B, and C went to play a tug-of-war game. Teams A B C, have attached a rope to a metal ring and are trying to pull the ring into their own area.

(ii) Which team will win the game?

(iii) Find the magnitude of the resultant force exerted by the teams.

*Q38. Read the following passage and answer the questions given below:*

The relation between the height of the plant (‘y’ in cm) with respect to its exposure to the sunlight is governed by the following equation

(ii) Does the rate of growth of the plant increase or decrease in the first three days? What will be the height of the plant after 2 days?

CBSE Class 12 Sample Paper 2023-24 |

## Maths Model Question Paper 2024 Class 12

CBSE has also released the Class 12 Maths Model Question Paper 2024 for the students who appeared in upcoming board exams. The CBSE Class 12 Additional MAthss model question paper helps students to understand the scheme of the exam, the questions asked, and the difficulty level of the real exam paper.. Download the CBSE Class 12 Maths Additional Model Question Paper 2024 with solutions from the table below.

Class 12 Maths Model Question Paper 2024 PDF | Solution Key |

Class 12 Maths Model Question Paper 2024 Set 1 | Download PDF |

Class 12 Maths Model Question Paper 2024 Set 2 | Download PDF |