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CBSE Class 12 Maths Answer Key 2024: The Central Board of Secondary Education has conducted the CBSE Class 12 Maths Examination 2024 on March 09, 2024. The exam has been started at 10:30 am and lasted till 01:30 pm at various examination centers across the country. As the CBSE Class 12th Mathematics Examination 2024 has been successfully conducted students can able to download the CBSE Class 12 Maths Answer Key 2024 with a complete Mathematics Question Paper Analysis by simply clicking on the direct link that has been shared in our article below. However students must understand that the answer key may not always be accurate, so cross-checking with the official sources is very important.
Class 12 Maths Answer Key 2024
The CBSE Class 12th Mathematics Exam 2024 has been conducted today i.e., March 09, 2024 from 10:30 am. The question paper is expected to comprise a diverse range of topics, testing students’ understanding of mathematical concepts acquired throughout the academic year. Students are allotted a time duration of 3 hours to complete the Mathematics Exam and an extra 15 minutes will be given to read the question paper. The Maths question paper will be divided into five different sections A, B, C, D, and E. Each section is compulsory. However, there are internal choices in some questions. Section A comprises MCQs and Assertion-Reason-based questions of 1 mark each. Whereas Section B has Short Answer (VSA)-type questions of 2 marks each.
CBSE Class 12 Maths Answer Key 2024
The CBSE Class 12th Mathematics board exam 2024 has been conducted in offline mode i.e., pen and paper mode. The CBSE Class 12th Mathematics exam 2024 will be for a total of 100 marks out of which 80 marks will be for the Theory exam and the rest 20 marks will be for the Internal Assessments.
CBSE Class 12 Mathematics Answer Key 2024 | |
Exam Conducting Body | Central Board of Secondary Education |
Name of Examination | CBSE Class 12th Board Examination 2024 |
Category | Answer Key |
Status | Released |
CBSE Class 12 Mathematics Exam Date 2024 | March 09, 2024 |
CBSE Class 12 Maths Answer Key 2024 release date | March 2024 |
Mode of Answer Key Availability | Online Mode |
Class 12th Maths Total Marks | 80 |
Negative Marking | No negative marking |
Official Website | https://www.cbse.nic.in/ |
Note: Keep refreshing the article page to get all the Class 12 Mathematics Exam Questions and their right answer. We will keep on updating all the SET 1, 2, 3, and 4 questions and answers. Stay Connected!
Class 12 Maths Answer Key 2024 All Set
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 9
(D) 729
Answer 1: (A) 0
2. Let f: R4 [5,∞) be defined as f(x) = 9×2 + 6x – 5, where R₁ is the set of all non-negative real numbers. Then, f is:
(A) one-one
(B) onto
(C) bijective
(D) neither one-one nor onto
Answer 2: (C) bijective
Answer 3: (D) 4
Answer 4: (B) 1
5. The function f(x) = x³-3x² + 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 5: (B) strictly increasing on R
Answer 6: (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 7:(A) cos x – sin (y/x)
Answer 8: (c)
9. The coordinates of the foot of the perpendicular drawn from the point (0, 1, 2) on the x-axis are given by:
(A) (1, 0, 0)
(B) (2, 0, 0)
(C) (√5,0,0)
(D) (0, 0, 0)
Answer 9: (D) (0, 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 10: (D) a feasible region
11. Let E be an event of a sample space S of an experiment, then P(S|E) =
(A) P(S∩E)
(B) P(E)
(C) 1
(D) 0
Answer 11: (C) 1
12. If A = [ajj] be a 3 x 3 matrix, where ajj = i – 3j, then which of the following is false?
(A) a_{11} < 0
(B) a_{12} + a_{21}= – 6
(C) a_{13} > a_{31}
(D) a_{31}= 0
Answer 12: (C) a_{13} > a_{31}
13. The derivative of tan-1 (x2) w.r.t. x is:
(A) x/1+x^{4}
(B) 2x/1+x^{4}
(C) – 2x/1+x^{4}
(D) 1/4 1+x^{4}
Answer 13:
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 14:
18. If a line makes an angle of 30° with the positive direction of x-axis, 120° with the positive direction of y-axis, then the angle which it makes with the positive direction of z-axis is:
(A) 90°
(C) 60°
(B) 120°
(D) 0°
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 skew-symmetric matrix.
Reason (R): A square matrix P is skew-symmetric if P’ = – P.
SECTION-B
This section comprises very short answer (VSA) type questions of 2 marks each.
OR
(b) Find the domain of the function f(x) = sin-1 (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 (cot-1 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) = e^{x}– e-^{x}+x-tan^{-1} x is strictly increasing in its domain.
SECTION C
This section comprises short answer (SA) type questions of 3 marks each.
OR
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+x^{2} is neither one-one 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) ⇔ a-c = b-d
Show that R is an equivalence relation.
35. If A₁ denotes the area of region bounded by y^{2} = 4x, x = 1 and x-axis in the first quadrant and A2 denotes the area of region bounded by y^{2} = 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 well-balanced 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 Figure-2.
(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).
Class 12 Mathematics Exam Paper Analysis 2024
Most of the students who appeared for the CBSE Class 12th Mathematics Exam today i.e., March 09, 2024 found the paper a bit difficult and well-structured. Students also said that the paper was moderately lengthy. Students have mentioned that all questions were based on the syllabus and followed the same format as the latest CBSE class 12 Mathematics sample paper 2024. Experts have said that the question paper was good as it posed many difficulties in front of students during the exam
- The overall class 12th mathematics question paper was moderate to difficult.
- Section A- Moderately Challenging, Section B- Average, Section C- Average, Section D- Average, Section E- Easy
- All the questions were from the syllabus.
- The MCQs and Assertion Reasoning were a bit tricky and lengthy at the same time
- Very short answer type and short answer type questions were average. It was a mix of easy and difficult questions
- The case study was comparatively easier than the rest of the sections in the paper
- The middle sections will help students score better
- The question paper was aligned with the sample paper format and marking scheme
CBSE Class 12 Maths Question Paper 2024 PDF Download
The Central Board of Secondary Education (CBSE) has conducted the Class 12th Mathematics Exam 2024 today March 09, 2024. The CBSE Question Papers are valuable resources as after the successful conduction of the exam, these question papers help the students to evaluate their performance in the exams. These question papers will help the students preparing to appear in the class 12th exams next year to provide an overview of the question paper, and the types of questions asked in the examination. The direct link to download the CBSE Class 12 Mathematics Question Paper 2024 PDF has been shared here.
Class 12 Maths Question Paper 2024 PDF | |
Set Number | Question Paper PDF Link |
SET 1 | Class 12 Mathematics Question Paper 2024 SET 1 65-2-1 |
SET 2 | Soon |
SET 3 | Soon |
Class 12 Maths Answer Key 2024 PDF Download
The CBSE Class 12 Mathematics Exam 2024 has been conducted today i.e., March 09, 2024. Students who appear in the class 12th Mathematics examination will get the chance to evaluate their Maths exam performance by calculating approximate scores through the Class 12 Mathematics Answer Key. The direct link to download the CBSE Board Class 12 Mathematics Answer Key 2024 will be available here to the students.
CBSE Class 12 Maths Exam Analysis 2024
As the CBSE conducted the Class 12 Mathematics Board Exam 2024, Students can watch the video below on CBSE Class 12 Maths Exam Analysis 2024 by Adda247.