# class 12 maths sample paper 2022-23 with solutions

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## Class 12 Maths Sample Paper 2022

Class 12 Maths Sample Paper 2022-23 with solutions is given in this article. Here we have also covered the CBSE Class 12 Maths Sample Paper 2023 marking scheme

## Class 12 Maths Sample Paper 2022-23 with Solutions

Class 12 Maths Sample Paper 2022-23 with solutions is given in this article. Here we have also covered the CBSE Class 12 Maths Sample Paper 2022-23 marking scheme

Posted by

soumyadeep Last updated on December 23rd, 2022 09:56 am

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## Class 12 Maths Sample Paper 2022-23

CBSE Class 12 Maths Sample Question Paper 2023 is now available on cbseacademic.nic.in .The Central Board Of Secondary Education has introduced Sample Papers for students of classes 10 and 12 Board. These Sample papers are on its official website. Students can also download the sample papers from here given below.

CBSE has introduced sample papers for all the subjects according to the layout of the question paper which CBSE is going to implement in this session 2022-23. This time, CBSE has introduced only one term examination, which will be conducted in February 2023. Along with CBSE Class 12 Maths Sample Question Paper 2023, CBSE also releases the Marking Scheme of CBSE Class 12 Maths Question Paper 2023. So that students can get a clear idea of the board exam format, question kinds, answer options, and other features with the help of CBSE Class 12 Maths Sample Question Paper 2023.

In this article, we have covered the CBSE Class 12 Maths Sample Paper. The students must solve CBSE Class 12 Maths Sample Paper which is given on this page and bookmark this page to get all the latest updates from CBSE regarding CBSE Annual Exam.

**For Scoring well in Class 12th**Click here

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## Maths Class 12 Sample Paper 2022-23- Questions with Answers

•Time Allowed: 3 Hours

•Maximum 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.

## Class 12 Maths Sample Question Paper 2023-SECTION A

**SECTION A**

**(Multiple Choice Questions)**

**Each question carries 1 mark**

Q1. If A =[aij] is a skew-symmetric matrix of order n, then

(a) 𝑎ij=1/aij ∀ 𝑖,𝑗 (b)𝑎ij≠ 0 ∀ 𝑖,𝑗 (c)𝑎ij = 0 where 𝑖=𝑗 (d) 𝑎ij≠ 0 where i=j

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

Q4. The value of ‘k’ for which the function

(a) 0 (b) -1 (c) 1. (d) 2

Q5. If 𝑓'(𝑥) = 𝑥 + 1/x, then 𝑓(𝑥) is

(a) 𝑥²+ log |𝑥| + 𝐶 (b) 𝑥²/2 + 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

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.

Q.8.The scalar projection of the vector 3𝚤̂− 𝚥̂− 2k̂ on the vector 𝚤̂+2𝚥̂-3k̂ is

## CBSE Maths Sample Paper Class 12 2022

CBSE Sample Papers for Class 12 Maths 2022-23 is available for free download in pdf format along with the marking scheme and solution PDF with a single click. Also, download the unsolved CBSE Maths Sample Paper Class 12 and solve them to check your exam preparation level.

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## CBSE Class 12 Maths Sample Papers 2022-23 with Solution PDF

**CBSE Sample Papers for Class 12 Maths**2022-23 is the resource without which exam preparation cannot be complete. CBSE Class 12 board exam indicates the end of school life, but it also opens doors to new domains where students can just step-in to pursue higher education as per their career desire. Therefore, board exams hold importance in students’ lives as a selection factor for different institutes, colleges and entrance exams that open up a new direction. Students who want to build up their careers in engineering and other streams of Maths must score good marks in Maths subject. The best way to do so is by practising the CBSE Class 12 Sample Papers for Maths. Here, we have provided the latest CBSE Class 12 Maths Sample Paper 2022-23 along with the Marking scheme and Solution PDF of CBSE Sample Paper Class 12 Maths. So, CBSE Class 12 students must practice these Maths Sample Paper to score high marks in board exam.

## CBSE Sample Paper Class 12 Maths 2022-23 with Solutions

For a better knowledge of the marking scheme and question paper pattern, students can make use of the Sample Paper of 2022-23 for free in PDF form.

**CBSE Class 12 Maths Sample Paper 2022-23**

Students can download the CBSE Sample Paper for Class 12 Maths 2021-22 Term 2 exam based on the latest exam pattern and reduced term wise CBSE Sample Paper Class 12 Maths from the link below:

**CBSE Class 12 Maths Sample Paper 2022 Term 2 PDF**

**CBSE Class 12 Maths Marking Scheme and Solution 2022 Term 2 PDF**

**CBSE Class 12 Maths Sample Mock Paper 2022 Term 2**

**CBSE Class 12 Maths Mock Solutions 2022 Term 2**

### Watch The Below Video for CBSE Class 12 Maths Pre Board Mock Paper

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To acquire an extra edge over competitors, try to get a good grip on the basic concepts and fundamentals of the Mathematics subject. Math exam includes different questions based on theorem, formulas, and some of them are asked indirectly in the exam to increase the difficulty level of the paper. So, make sure to revise as many times as possible. The key strategy to ace the CBSE Class 12 Maths exam is a continuous practice. Solve different questions of CBSE Sample Paper for Class 12 to get a good grip on Maths subject. Students can also access the sample papers for other subjects of Class 12 by visiting here.

## CBSE Sample Paper Class 12 Maths (Based on Previous Year Pattern)

Students can access the CBSE Class 12 Maths sample paper from the link shown below in the table. After solving the CBSE Sample Paper Class 12 Maths, they can check their answer sheet from the solution file. We have also provided the unsolved CBSE Class 12 Maths Sample Papers. Class 12 students must download them and practice 1 set of CBSE Maths Sample Paper Class 12 daily. These sets of CBSE Sample Paper Class 12 Maths help student to realise their strength and weakness. After knowing them, they can prepare accordingly for the exam.

### Access Latest CBSE Sample Paper for Class 12 Maths

CBSE Maths Sample Paper Class 12 Set 1 Access Solution

CBSE Maths Sample Paper Class 12 Set 2

CBSE Maths Sample Paper Class 12 Set 3

CBSE Maths Sample Paper Class 12 Set 4

CBSE Maths Sample Paper Class 12 Set 5

CBSE Maths Sample Paper Class 12 Set 6

CBSE Maths Sample Paper Class 12 Set 7

CBSE Maths Sample Paper Class 12 Set 8

CBSE Maths Sample Paper Class 12 Set 9

CBSE Maths Sample Paper Class 12 Set 10

### CBSE Class 12 Maths Sample Papers Released by CBSE

Every year CBSE releases the CBSE sample papers on its official site to help students in understanding the question paper pattern and marking scheme of the paper. Here we have compiled the year-wise Maths sample papers. Students can download them from the table below.

### Download CBSE Sample Paper Class 12 Maths with Marking Scheme

CBSE Class 12 Maths Sample Paper 2022 Term 1 Marking Scheme and Answers

CBSE Class 12 Maths Sample Paper 2021 Marking Scheme and Answers

CBSE Class 12 Maths Sample Paper 2020 with Marking Scheme and Answers

CBSE Class 12 Maths Sample Paper 2019 Marking Scheme and Answers

CBSE Class 12 Maths Sample Paper 2018 Marking Scheme and Answers

CBSE Class 12 Maths Sample Paper 2017 Marking Scheme and Answers

CBSE Class 12 Maths Sample Paper 2016 Marking Scheme and Answers

CBSE Class 12 Maths Sample Paper 2015 Marking Scheme and Answers

CBSE Maths Paper is scoring and less time consuming as compared to other subjects. Scoring marks in Maths is easy if concepts are strong. Students must write down all the important formulas at one place and paste in their study room. They should daily go through these formulas so that it will be at their fingertips. Solving different types of questions from the CBSE Maths Sample Paper Class 12 with speed and accuracy will help them in scoring high marks. Also, they get an idea of types of questions which can be asked in the Maths paper.

We hope students have found this information on “CBSE Sample Paper Class 12 Maths” useful. Keep learning and stay tuned for further updates on CBSE and other competitive exams. Download the BYJU’S App and subscribe to YouTube channel to access interactive study videos.

## CBSE Class 12 Maths Sample Paper 2023 with Solutions

Download Class 12 Maths Sample Paper and solution. Practice Maths Sample Paper for Class 12 as per the new exam pattern.

## CBSE Class 12 Maths Sample Paper 2023 with Solutions

Home Class 12 Maths Sample Paper 2023

## Class Class 12 Maths Sample Paper 2023

**Maths Sample Paper Class 12:**Central Board of Secondary Education has released the official Maths Sample Paper Class 12 exam along with the other subject sample papers on www.cbseacademic.nic.in. All students are advised to buckle up their preparation and be punctual for the board exam. The Class 12 Maths Sample Paper would be of great help in practicing as per the revised exam pattern. In this article, we have provided direct links for downloading Maths Sample Paper Class 12 along with its solution PDF.

## CBSE Class 12 Maths Sample Paper PDF

CBSE has released the Class 12 Maths Sample Paper as per the Class 12 Maths Syllabus along with the solution/marking scheme in PDF format. The students are advised to go through the Maths Sample Paper Class 12 at least once before the examination so as to get familiar with the new pattern to be followed. Download the CBSE Class 12 Maths Sample Paper PDF from the below link and practice.

**CBSE Class 12 Maths Sample Paper Download PDF**

**CBSE Class 12 Maths Sample Paper Solution**

## Class 12 Maths Sample Paper and Solution 2023

Maths is one of the important subjects in boards examination. It comprises a total of 100 Marks. CBSE has released the official sample paper, you can go through this sample question to understand the level of questions the examiner can ask in the board exam. Go through these questions so as to score well in exams.

### Section A

**Q1.**If A =[aij] is a skew-symmetric matrix of order n, then

**Solution:**(c) In a skew-symmetric matrix, the (i, j)th element is negative of the (j, i)th element. Hence, the (i, i)th element = 0

**Q2.**If A is a square matrix of order 3, |𝐴′| = −3, then |𝐴𝐴′| =

(a) 9 (b) -9 (c) 3 (d) -3

**Solution:**(a) |𝐴𝐴′| = |𝐴||𝐴′| = (−3)(−3) = 9

**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

**Solution:**(b) The strict inequality represents an open half plane and it contains the origin as (0, 0) satisfies it.

**Q8.**The scalar projection of the vector 3𝚤̂− 𝚥̂− 2𝑘 on the vector 𝚤̂+ 2𝚥̂− 3𝑘 is

(a) 7/**√**14 (b) 7/14 (c) 6/13 (d) 7/2

**Solution:**(a) 7/

**√**14

**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)

**Solution:**(d) The minimum value of the objective function occurs at two adjacent corner points (0.6, 1.6) and (3, 0) and there is no point in the half plane 4𝑥 + 6𝑦 < 12 in common with the feasible region. So, the minimum value occurs at every point of the line segment joining the two points.

**Q13.**If A is a square matrix of order 3 and |A| = 5, then |𝑎𝑑𝑗𝐴| =

(a) 5 (b) 25 (c) 125 (d)1/5

**Solution:**(b) = 25

**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

**Solution:**(c) P(𝐴′ ∩ 𝐵 ′) = 𝑃(𝐴′) × 𝑃(𝐵′) (As A and B are independent, 𝐴 ′𝑎𝑛𝑑 𝐵′ are also independent.) = 0.7 × 0.4 = 0.28

**Q15.**The general solution of the differential equation 𝑦𝑑𝑥 − 𝑥𝑑𝑦 = 0 𝑖𝑠 (a) 𝑥𝑦 = 𝐶 (b) 𝑥 = 𝐶𝑦² (c) 𝑦 = 𝐶𝑥 (d) 𝑦 = 𝐶𝑥²

**Solution:**𝑦𝑑𝑥 − 𝑥𝑑𝑦 = 0

⟹ 𝑦𝑑𝑥 − 𝑥𝑑𝑦 = 0

⟹ 𝑑𝑦/𝑦 = 𝑑𝑥/𝑥

**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

**Solution:**(b) The line through the points (0, 5, -2) and (3, -1, 2) is 𝑥/0-3 = 𝑦-5/-1-5 = 𝑧+2/2-2 𝑜𝑟, 𝑥 /3 = 𝑦 − 5/ −6 = 𝑧 + 2/4.

Any point on the line is (3𝑘, −6𝑘 + 5,4𝑘 − 2), where k is an arbitrary scalar. 3𝑘 = 6 ⟹ 𝑘 = 2

The z-coordinate of the point P will be 4 × 2 − 2 = 6

### Section B

**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?

**Solution:**Let AB represent the height of the street light from the ground. At any time t seconds, let the man represented as ED of height 1.6 m be at a distance of x m from AB and the length of his shadow EC be y m.

Using the similarity of triangles, we have 4/1.6= x+y/y= 3y=2x

Guys, does anyone know the answer?