Table of Contents
The CBSE Class 12 Mathematics Paper was held on 9th March 2024. Generally, After taking the exam, Students might be panicked about how many questions they got right. The CBSE Class 12 Maths answer key 2024 includes the correct answers to all questions on the exam. Students can use the answer key to estimate their probable scores. As the exam was concluded, our own experts teachers provided the class 12 Mathematics answer key 2024 for all sets on this page. Students should be aware, nevertheless, that the solution key could not always be right, thus it’s crucial to doublecheck with the official sources.
Class 12 Maths Answer key 2024
The CBSE Class 12 Maths Paper is now over. As per the student’s initial Reactions, the paper was moderate. It would range between moderate to difficult. Students are searching tensely for the CBSE Class 12 Maths Answer Key 2024 after taking the exam. The Adda247 Experience faculty offers you an unofficial Class 12 Maths Answer Key 2024 of all sets, in addition to a thorough explanation, to help you. Students can estimate their results by comparing their responses to every question they attempted in the exam using the Answer Key. We deliver Maths Answer Key 2024 for all sets before anyone else, so be sure to bookmark the page and check it frequently.
CBSE Class 12 Maths Answer key 2024
Mathematics serves as a Core subject in Class 12, and performing well in this subject would benefit students who are preparing for competitive exams such as JEE. The CBSE Class 12 Maths Exam has a total of 100 marks, with 80 for the theory paper and 20 for internal assessment. Let’s take a short look at the CBSE Class 12 Maths Answer key 2024 Highlights.
Particulars  Details 
Exam Conducting Body 
Central Board of Secondary Education (CBSE)

Name of Examination 
CBSE Class 12 Board Examination 2024

Subject  Mathematics 
Mode of Exam  Offline 
Exam Duration  3 Hours 
Medium of Exam  English / Hindi 
Type of Questions 
MCQs, Short and Long Answer Type Questions

Theory Marks  80 
Practical / Internal Assessment  20 
Total Marks  100 
Passing Marks  33% in aggregate 
Class 12 Maths Exam Paper Pattern 2024
The Class 12 maths paper is based on the Class 12 Maths Syllabus and the pattern of the sample paper supplied by the Board. the question paper has five sections: A, B, C, D, and E. Each section is mandatory. However, certain questions allow for internal choices. Check out the Class 12 Maths Paper sectionwise marks distribution given below,
 Section A consists of 18 multiplechoice questions and 02 assertionreason questions at one mark each.
 Section B contains five Very Short Answer (VSA) questions worth two marks each.
 Section C contains 6 Short Answer (SA) questions for 3 points each.
 Section D has four Long Answer (LA)type questions at 5 points each.
 Section E consists of three 4mark sourcebased/casebased/passagebased/integrated units of assessment, each containing subparts.
Maths Answer Key 2024 of All Sets
After the CBSE Class 12 Maths Exam, we provide the detailed, 100% accurate CBSE Class 12 Maths Answer key 2024 for all sets as soon as possible. Our inhouse experts are constantly assessing the Maths solution key for all sets in detail. Stay connected to us.
Class 12 Maths Answer Key 2024 Set 1: Paper Code (65/2/1)
SECTION A
This section comprises multiple choice questions (MCQs) of 1 mark each.
1. If the sum of all the elements of a 3 x 3 scalar matrix is 9, then the product of all its elements is :
(A) 0
(B) 9
(C) 27
(D) 729
Answer: (C) 27
2. Let f: R+ [5, ∞) be defined as f(x) = 9×2 + 6x – 5, where R, is the set of all nonnegative real numbers. Then, f is:
(A) oneone
(B) onto
(c) bijective
(D) neither oneone nor onto
Answer; (A) oneone
Answer; (D)
Answer: (B)
5. The function f(x) = x³3x² + 12x – 18 is :
(A) strictly decreasing on R
(B) strictly increasing on R
(C) neither strictly increasing nor strictly decreasing on R
(D) strictly decreasing on (∞, 0)
Answer:(B) strictly increasing on R
Answer: (B)
7. The differential equation dy dx differential equation, if F(x, y) is: = F(x, y) will not be a homogeneous
(A) cos x – sin (y/x)
(B) y/x
(C) (x²+y²)/xy
(D) cos²(x/y)
Answer:(A) cos x – sin (y/x)
Answer: (c)
9. The coordinates of the foot of the perpendicular drawn from the point (0, 1, 2) on the xaxis are given by :
(A) (1, 0, 0)
(B) (2, 0, 0)
(C) (√5, 0, 0)
(D) (0, 0, 0)
Answer:(C) (√5, 0, 0)
10. The common region determined by all the constraints of a linear programming problem is called :
(A) an unbounded region
(B) an optimal region
(C) a bounded region
(D) a feasible region
Answer:(D) a feasible region
11. Let E be an event of a sample space S of an experiment, then P(SE) =
(A) P(S∩E)
(B) P(E)
(C) 1
(D) 0
Answer:(C) 1
12. If A = [ajj] be a 3 x 3 matrix, where ajj = i – 3j, then which of the following is false?
(A) a11 < 0
(B) a12 + a21= – 6
(C) a13 > a31
(D) a31= 0
Answer:(C) a13 > a31
13. The derivative of tan1 (x2) w.r.t. x is:
(A) x/1+x4
(B) 2x/1+x4
(C) – 2x/1+x4
(D) 1/4 1+x4
Answer:(B) 2x/1+x4
14. The degree of the differential equation (y”)2 + (y’)³ = x sin (y’) is:
(A) 1
(B) 2
(C) 3
(D) not defined.
Answer:(D) not defined
Answer:
15 (B) j
16 (D) 2, 1, 3
Answer: (B) 2
18. If a line makes an angle of 30° with the positive direction of xaxis, 120° with the positive direction of yaxis, then the angle which it makes with the positive direction of zaxis is:
(A) 90°
(C) 60°
(B) 120°
(D) 0°
Answer: (A) 90°
Questions number 19 and 20 are Assertion and Reason based questions. Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
(B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
(C) Assertion (A) is true, but Reason (R) is false.
(D) Assertion (A) is false, but Reason (R) is true.
19. Assertion (A): For any symmetric matrix A, B’AB is a skewsymmetric matrix.
Reason (R): A square matrix P is skewsymmetric if P’ = – P.
Answer: (D) Assertion (A) is false, but Reason (R) is true.
Answer: (C) Assertion (A) is true, but Reason (R) is false.
SECTIONB
This section comprises very short answer (VSA) type questions of 2 marks each.
OR
(b) Find the domain of the function f(x) = sin1 (x2 – 4). Also, find its range.
22. (a) If f(x) = tan 2×1, then find the value of f'(x) at x = . π 3
OR
(b) If y = cosec (cot1 x), then prove that √1 + x 2 dy dx – x = 0.
23. If M and m denote the local maximum and local minimum values of the function f(x) = x + 1/x (x≠ 0) respectively, find the value of (M – m).
24. Find:
25. Show that f(x) = ex– ex+xtan1 x is strictly increasing in its domain.
SECTION C
This section comprises short answer (SA) type questions of 3 marks each.
SECTION D
This section comprises long answer (LA) type questions of 5 marks each.
32. (a) Show that a function f: RR defined by f(x) = 2x 2/1+x2 is neither oneone nor onto. Further, find set A so that the given function f: R A becomes an onto function.
OR
(b) A relation R is defined on N×N (where N is the set of natural numbers) as:
(a, b) R (c, d) ⇔ ac = bd
Show that R is an equivalence relation.
35. If A₁ denotes the area of region bounded by y2 = 4x, x = 1 and xaxis in the first quadrant and A2 denotes the area of region bounded by y2 = 4x, x = 4, find A1: A2.
SECTION E
This section comprises 3 case study based questions of 4 marks each.
Case Study 1
36. Overspeeding increases fuel consumption and decreases fuel economy as a result of tyre rolling friction and air resistance. While vehicles reach optimal fuel economy at different speeds, fuel mileage usually decreases rapidly at speeds above 80 km/h.
Case Study – 2
37. The month of September is celebrated as the Rashtriya Poshan Maah across the country. Following a healthy and wellbalanced diet is crucial in order to supply the body with the proper nutrients it needs. A balanced diet also keeps us mentally fit and promotes improved level of energy.
A dietician wishes to minimize the cost of a diet involving two types of foods, food X (x kg) and food Y (y kg) which are available at the rate of Rs 16/kg and Rs 20/kg respectively. The feasible region satisfying the constraints is shown in Figure 2. On the basis of the above information, answer the following questions :
(i) Identify and write all the constraints which determine the given feasible region in Figure2.
(ii) If the objective is to minimize cost Z = 16x + 20y, find the values of x and y at which cost is minimum. Also, find minimum cost assuming that minimum cost is possible for the given unbounded region.
Case Study 3
38. Airplanes are by far the safest mode of transportation when the number of transported passengers are measured against personal injuries and fatality totals.
Previous records state that the probability of an airplane crash is 0.00001%. Further, there are 95% chances that there will be survivors after a plane crash. Assume that in case of no crash, all travellers survive.
Let E₁ be the event that there is a plane crash and E₂ be the event that there is no crash. Let A be the event that passengers survive after the journey. On the basis of the above information, answer the following questions:
(i) Find the probability that the airplane will not crash.
(ii) Find P(A  E₁) + P(A  E2).
(iii) (a) Find P(A).
OR
(iii) (b) Find P(E2  A)
Keep refreshing the page to see all of the Class 12 Mathematics Exam Questions and their correct answers.
CBSE Class 12th Maths Answer Key 2024 Set 2
Here we have provided the Answers for Class 12 Set 2 Maths Sections A in the table below
QP Code: 65/3/2 (Set 2)
Question 1  Correct options 
1  (C) ±2 
2  (C) (5/e)x log 5 
3  (D) [0, 6] 
4  (C) π/2 
5  (C) x + 2y ≥ 76, 2x + y ≤ 104, x,y ≥ 0 
6  (A) [ 1/2 0 0 ] [ 0 1/3 0 ] [ 0 0 1/5 ] 
7  (C) a skew symmetric matrix 
8  (C) [1, ∞ ) 
9  (A) 2a 
10  (D) continuous everywhere 
11  (C) f'(x) = 0 and f'(x) does not change its sign from left to right of that point. 
12  (A) 0 
13  (C) first order linear differential equation. 
14  (C) perpendicular vectors 
15  (D) cos α + cos β + cos γ = 1 
16  (B) constraints 
17  (D) 0 
18  (D) aij = { 0, if i ≠ j = { 1, if i = j 
19  (D) Assertion (A) is false, but Reason (R) is true. 
20  (C) Assertion (A) is true, but Reason (R) is false 
Maths Class 12 Answer Key Set 3
Here we have provided the Answers for Class 12 Set 3 Maths Sections A in the table below
QP Code: 65/2/3 (Set 3)
Question 1  Correct options 
1  (D) 1/(e2x – 1)1/2 
2  (D) 2, 2 
3  (B) j 
4  (D) 2, 1, 3 
5  (A) 0 
6  (D) 90° 
7  (C) 27 
8  (A) oneone 
9  (D) 4 
10  (B) 1 
11  (A) strictly decreasing on R 
12  (B) cosx + sinx 
13  (B) y/x 
14  (C) a · b ≤  a   b  
15  (C) (√5, 0, 0) 
16  (D) a feasible region 
17  (C) 1 
18  (D) a13 > a31 
19  (D) Assertion (A) is false, but Reason (R) is true 
20  (D) Assertion (A) is false, but Reason (R) is true. 
Maths Answer Key 2024 Set 1 Question and Answers
Here we have provided the Answers for Class 12 Set 1 Maths Sections A in the table below
QP Code: 65/4/1 (Set 1)
Question 1  Correct options 
1  (D) 25 
2  (A) $7\left\begin{array}{cc}2& \u20131\\ 3& 2\end{array}\right$ 
3  (D) [ 1 0 ] [ 0 1 ] 
4  (D) 1000 
5  (A) 4 
6  (A) e² 
7  (B) 1/4 
8  (C) π/2 
9  (B) x + y = c 
10  (D) 1/y 
11  (D) 11π/6 
12  (D) a rightangled triangle 
13  (C) 3a² 
14  (D) r = λj 
15  (B) 1/2 
16  (C) 120 
17  (D) 1 
18  (A) k > 1 
19  (C) Assertion (A) is true, but Reason (R) is false. 
20  (B) Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A). 
Class 12 Maths Exam Paper Analysis 2024
The Class 12 math exam ended at 1:30 p.m. Following the exam, students can review the comprehensive analysis of the CBSE Class 12 Maths Paper. In CBSE Class12 Maths Exam Analysis 2024, we assesses the question paper based on errors, outofsyllabus questions, and difficulty level. The CBSE class 12 maths exam analysis 2024 has been provided below.
Parameter 
CBSE Class 12 Maths Exam Analysis

Overall difficulty level of the paper  Moderate 
Difficulty level of Section A  Moderate to hard 
Difficulty level of Section B  Moderate 
Difficulty level of Section C  Moderate 
Difficulty level of Section D  Moderate 
Difficulty level of Section E  Easy 
Overall expected a good score  65+ 
Class 12 Maths Question Paper Analysis 2024: Students’ Review
Outside, We talked to the students who appeared in the Class 12th Math Exam to know what they were thinking about the paper. Check out the students reviews on the Class 12 Maths Question Paper 2024 below:
 The question paper was moderate. It would vary from moderate to challenging.
 The paper was relatively lengthy.
 Section A was the most difficult part of the paper because of the tough MCQs and AssertionReasoning.
 The MCQs and Assertion Reasoning were both tough and lengthy.
 Both very short answer and short response questions were average. There was a mix of easy and difficult questions.
 The case study was relatively easy than the rest of the components in the paper.
 The paper included applicationbased questions (case study/assertion reasoning).
 There were no questions that weren’t on the syllabus.
 The question paper was aligned with the sample paper format and the marking scheme
Class 12 Maths Paper Analysis 2024 : Experts’ Review
After exam completion, we talked to some teachers as subject experts to know their reviews on math questions paper.
 MCQs consist of a decent mix of easy and tough questions.
 The case study was comparatively easy than the other components.
 The question paper was completely based on the sample paper format.
 The middle parts improve student scores. Applicationbased questions require students to think,
 apply formulas, and locate appropriate answers.
CBSE Class 12 Maths Board Exam Paper PDF Download
The Central Board of Secondary Education (CBSE) held the Class 12 Mathematics Exam 2024 on March 9, 2024. CBSE Question Papers are essential resources since they allow students to analyze their test performance after the exam has been successfully conducted. Download the CBSE Class 12 Maths Question Paper 2024 PDF for all sets from the table below.
CBSE Class 12 Maths Question Paper 2024 PDF download  
Set 1  Download Now 
Set 2  Available Soon 
Set 3  Available Soon 
Math Answer Key 2024 with Solutions
Watch the video where Anu Ma’am detailed the analysis of Math Question paper 2024.
Answer Key Maths Class 12 2024 & Marking Scheme
The CBSE Class 12 Maths Answer Key 2024 & marking scheme helps students to predict the scores in the Exam. Check out the Class 12 Maths Paper Marking Scheme Tabulated below.
Sections  Number of Questions  Marks  Type of Questions  Difficulty Level 
Section A  18  1 x 18  Multiple Choice Questions 
EasyModerate

Section B  5  2 x 5  Very Short Answer Questions  Moderate 
Section C  6  3 x 6  Short Answer Questions 
ModerateDifficult

Section D  4  5 x 4  Long Answer Questions 
Moderate (Tricky)

Section E  3  4 x 3  CaseBased Questions 
ModerateDifficult

Total  35  70  –  – 
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 CBSE Class 12 Chemistry Answer Key 2024
 Class 12 Physics Answer Key 2024
 CBSE Class 12 Physical Education Answer Key 2024
Answer Key of Maths Class 12 Last Year Questions
Candidates can also check the CBSE Class 12th Maths Answer Key from last year, which is provided here.
1. Sin [π/3 + sin^{1}(1/2)] is equal to
(a) 1
(b) 1/2
(c) 1/3
(d) 1/4
Answer: (a) 1
2. Let A = {3,5}. Then number of reflexive relations on A is
(a) 2
(b) 4
(c) 0
(d) 8
Answer: (a) 2
3.
(a) ±1
(b) 1
(c) 1
Answer: (d)
5. The value of the determinant
(a) 10
(b) 8
(c) 7
(d) 7
Answer: (d) 7
6. The function f(x) = [x], where [x] denotes the greatest integer less than or equal to x, is continuous at
(a) x = 1
(b) x = 1.5
(c) x = 2
(d) x = 4
Answer: (c) x = 2
7. The derivative of x^{2x}w.r.t. x is
(a) x^{2x1}
(b) 2x^{2x}logx
(c) 2x^{2x}(1 + logx)
(d) 2x^{2x}(1 – logx)
Answer: (c) 2x^{2x}(1 + logx)
Answer: (a) (1, ∞)
Answer: (a) only at x = 0
Answer: (c) tanx – secx + c
Answer: (a) 0
Answer: (c) 5
Answer: (b)