CBSE Class 12 Maths Sample Question Paper 2023: With the release of Class 12 Mathematics Sample Paper 2022-23 (code 041) by CBSE on their official website, it’s now time for the students of Class 12 Mathematics to start preparing for their exams.
“The only way to learn mathematics is to do mathematics.” – Paul Halmos
In other words, the only way to prepare for a Mathematics exam is by doing Mathematics i.e, practising the different questions. You do not have to worry and fall in the downward spiral of finding the right book and guide books. All you require is the prescribed texts by the board.
- Mathematics Part I - Textbook for Class XII, NCERT Publication
- Mathematics Part II - Textbook for Class XII, NCERT Publication
- Mathematics Exemplar Problem for Class XII, Published by NCERT
- Mathematics Lab Manual class XII, published by NCERT
In addition you can make use of previous year papers as well. Besides, now that the board has made available the latest sample papers, utilising these sample papers for 2022-23 and the marking scheme, students must practise the different kinds of questions that can be asked in the CBSE class 12 Mathematics board exams.
If you are lacking any of these resources, Jagran Josh has the latest CBSE class 12 Mathematics syllabus, and the latest sample paper and marking scheme in one place.
Coming to the sample paper, the CBSE 12 Mathematics Sample Question Paper begins with the general instructions for the students to follow.
The general instructions in the beginning of the CBSE Class 12 Mathematics Sample Question Paper 2022-23 are as follows:
TIME - 3 HOURS
MAX. MARKS - 80
General Instructions:
1. This Question paper contains - five sections A, B, C, D and E. Each section is compulsory. However, there are internal choices in some questions.
2. Section A has 18 MCQ’s and 02 Assertion-Reason based questions of 1 mark each.
3. Section B has 5 Very Short Answer (VSA)-type questions of 2 marks each.
4. Section C has 6 Short Answer (SA)-type questions of 3 marks each.
5. Section D has 4 Long Answer (LA)-type questions of 5 marks each.
6. Section E has 3 source based/case based/passage based/integrated units of assessment (4 marks each) with sub parts.
The whole content of the CBSE Class 12 Mathematics Sample Question Paper 2022-23 is given below for easy access.
CBSE Class 12 Maths Sample Question Paper 2023
SECTION A
(Multiple Choice Questions)
Each question carries 1 mark
Q1. If A =[a_{ij}] is a skew-symmetric matrix of order n, then
Q2. If A is a square matrix of order 3, |𝐴′| = −3, then |𝐴𝐴′| =
(a) 9
(b) -9
(c) 3
(d) -3
Q3. The area of a triangle with vertices A, B, C is given by
(a) 0
(b) -1
(c) 1
(d) 2
Q5. If 𝑓′(𝑥) = 𝑥 + 1/𝑥, then 𝑓(𝑥) is
(a) 𝑥^{2} + log |𝑥| + 𝐶
(b) 𝑥^{2}/2 + log |𝑥| + 𝐶
(c) 𝑥/2 + log |𝑥| + 𝐶
(d) 𝑥/2 − log |𝑥| + 𝐶
Q6. If m and n, respectively, are the order and the degree of the differential equation d/dx[(dy/dx)]^{4}=0, then m + n =
(a) 1
(b) 2
(c) 3
(d) 4
Q7. The solution set of the inequality 3x + 5y < 4 is
(a) an open half-plane not containing the origin.
(b) an open half-plane containing the origin.
(c) the whole XY-plane not containing the line 3x + 5y = 4.
(d) a closed half plane containing the origin.
(a) 7√14
(b) 7/14
(c) 6/13
(d) 7/2
Q9. The value of ∫^{3}_{ 2} x/x^{2}+1dx is
(a) 𝑙𝑜𝑔4
(b) 𝑙𝑜𝑔3/2
(c) 1/2𝑙𝑜𝑔2
(d) 𝑙𝑜𝑔9/4
Q10. If A, B are non-singular square matrices of the same order, then (𝐴𝐵^{-1})^{-1} =
(a)𝐴^{-1}𝐵
(b)𝐴^{-1}𝐵^{-1}
(c)𝐵𝐴^{-1}
(d) 𝐴𝐵
Q11. The corner points of the shaded unbounded feasible region of an LPP are (0, 4), (0.6, 1.6) and (3, 0) as shown in the figure. The minimum value of the objective function Z = 4x + 6y occurs at
(a)(0.6, 1.6) 𝑜𝑛𝑙𝑦
(b) (3, 0) only
(c) (0.6, 1.6) and (3, 0) only
(d) at every point of the line-segment joining the points (0.6, 1.6) and (3, 0)
(a) 3
(b) √3
(c) -√3
d) √3, −√3
Q13. If A is a square matrix of order 3 and |A| = 5, then |𝑎𝑑𝑗𝐴| =
(a) 5
(b) 25
(c) 125
(d) 1/5
Q14. Given two independent events A and B such that P(A) =0.3, P(B) = 0.6 and P(𝐴′ ∩ 𝐵′) is
(a) 0.9
(b) 0.18
(c) 0.28
(d) 0.1
Q15. The general solution of the differential equation 𝑦𝑑𝑥 − 𝑥𝑑𝑦 = 0 𝑖𝑠
(a) 𝑥𝑦 = 𝐶
(b) 𝑥 = 𝐶𝑦^{2}
(c) 𝑦 = 𝐶𝑥
(d) 𝑦 = 𝐶𝑥^{2}
Q16. If 𝑦 = 𝑠𝑖𝑛^{-1}𝑥, then (1 − 𝑥^{2})𝑦_{2} 𝑖𝑠 equal to
(a) 𝑥𝑦^{1}
(b) 𝑥𝑦
(c) 𝑥𝑦^{2}
(d) 𝑥^{2}
(a) √2
(b) 2√6
(c) 24
(d) 2√2
Q18. P is a point on the line joining the points 𝐴(0,5, −2) and 𝐵(3, −1,2). If the x-coordinate of P is 6, then its z-coordinate is
(a) 10
(b) 6
(c) -6
(d) -10
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.
SECTION - B
This section comprises of very short answer type-questions (VSA) of 2 marks each
Q22. A man 1.6 m tall walks at the rate of 0.3 m/sec away from a street light that is 4 m above the ground. At what rate is the tip of his shadow moving? At what rate is his shadow lengthening?
𝑶𝑹
Find the direction ratio and direction cosines of a line parallel to the line whose equations are
6𝑥 − 12 = 3𝑦 + 9 = 2𝑧 − 2
SECTION - C
(This section comprises of short answer type questions (SA) of 3 marks each)
Q26. Find: ∫dx/√3-2x-x^{2}
Q27. Three friends go for coffee. They decide who will pay the bill, by each tossing a coin and then letting the “odd person” pay. There is no odd person if all three tosses produce the same result. If there is no odd person in the first round, they make a second round of tosses and they continue to do so until there is an odd person. What is the probability that exactly three rounds of tosses are made?
OR
Find the mean number of defective items in a sample of two items drawn one-by-one without replacement from an urn containing 6 items, which include 2 defective items. Assume that the items are identical in shape and size.'
Q29. Solve the differential equation: 𝑦𝑑𝑥 + (𝑥 − 𝑦^{2})𝑑𝑦 = 0
OR
Solve the differential equation: 𝑥𝑑𝑦 − 𝑦𝑑𝑥 = √𝑥^{2}+𝑦^{2} 𝑑𝑥
Q30. Solve the following Linear Programming Problem graphically:
Maximize Z = 400x + 300y subject to 𝑥 + 𝑦 ≤ 200, 𝑥 ≤ 40, 𝑥 ≥ 20, 𝑦 ≥ 0
Q31. Find ∫(x^{3}+x+1)/(x^{2}-1)/dx
SECTION - D
(This section comprises of long answer-type questions (LA) of 5 marks each)
Q32. Make a rough sketch of the region {(𝑥, 𝑦): 0 ≤ 𝑦 ≤ 𝑥^{2}, 0 ≤ 𝑦 ≤ 𝑥, 0 ≤ 𝑥 ≤ 2} and find the area of the region using integration.
Q33. Define the relation R in the set 𝑁 × 𝑁 as follows:
For (a, b), (c, d) ∈ 𝑁 × 𝑁, (a, b) R (c, d) iff ad = bc. Prove that R is an equivalence relation in 𝑁 × 𝑁.
OR
Given a non-empty set X, define the relation R in P(X) as follows:
For A, B ∈ 𝑃(𝑋), (𝐴, 𝐵) ∈𝑅 iff 𝐴 ⊂ 𝐵. Prove that R is reflexive, transitive and not symmetric.
OR
The equations of motion of a rocket are:
𝑥 = 2𝑡, 𝑦 = −4𝑡, 𝑧 = 4𝑡, where the time t is given in seconds, and the coordinates of a moving point in km. What is the path of the rocket? At what distances will the rocket be from the starting point O(0, 0, 0) and from the following line in 10 seconds?
SECTION - E
(This section comprises of 3 case-study/passage-based questions of 4 marks each with two sub-parts. First two case study questions have three sub-parts (i), (ii), (iii) of marks 1, 1, 2 respectively. The third case study question has two sub-parts of 2 marks each.)
Q36. Case-Study 1: Read the following passage and answer the questions given below.
The temperature of a person during an intestinal illness is given by
𝑓(𝑥) = −0.1𝑥^{2} + 𝑚𝑥 + 98.6,0 ≤ 𝑥 ≤ 12, m being a constant, where f(x) is the temperature in °F at x days.
(i) Is the function differentiable in the interval (0, 12)? Justify your answer.
(ii) If 6 is the critical point of the function, then find the value of the constant m.
(iii) Find the intervals in which the function is strictly increasing/strictly decreasing.
OR
(iii) Find the points of local maximum/local minimum, if any, in the interval (0, 12) as well as the points of absolute maximum/absolute minimum in the interval [0, 12]. Also, find the corresponding local maximum/local minimum and the absolute maximum/absolute minimum values of the function.
Q37. Case-Study 2: Read the following passage and answer the questions given below.
In an elliptical sport field the authority wants to design a rectangular soccer field with the maximum possible area. The sport field is given by the graph of x^{2}/a^{2}+y^{2}/b^{2}=1.
(i) If the length and the breadth of the rectangular field be 2x and 2y respectively, then find the area function in terms of x.
(ii) Find the critical point of the function.
(iii) Use First derivative Test to find the length 2x and width 2y of the soccer field (in terms of a and b) that maximize its area.
OR
(iii) Use Second Derivative Test to find the length 2x and width 2y of the soccer field (in terms of a and b) that maximize its area.
Q38. Case-Study 3: Read the following passage and answer the questions given below.
There are two antiaircraft guns, named as A and B. The probabilities that the shell fired from them hits an airplane are 0.3 and 0.2 respectively. Both of them fired one shell at an airplane at the same time.
(i) What is the probability that the shell fired from exactly one of them hit the plane?
(ii) If it is known that the shell fired from exactly one of them hit the plane, then what is the probability that it was fired from B?
CBSE Class 12 Mathematics Sample Paper 2022-23 in pdf format to download and print.
Download CBSE Class 12 Mathematics Sample Question Paper 2022-23
The marking scheme of the CBSE Class 12 Mathematics Sample Paper 2022-23 in pdf format is attached below.
Download CBSE Class 12 Mathematics Marking Scheme 2022-23
Remember that “The only way to learn mathematics is to do mathematics.” – Paul Halmos. Thus, using both CBSE Class 12 Mathematics Sample Paper 2022-23 and the marking scheme, students should practice more to score higher in their board exams.
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Best of luck to all the candidates.