CBSE 12^{th} Maths Sample Paper 2018 is available here (along with Answer Key or Marking Scheme) for download in PDF format. In order to help the students, CBSE has recently released this Sample Paper.
With the help of this Sample Paper, students preparing for CBSE Class 12^{th} Maths board exam 2018 will easily get acquainted with the new examination pattern, blue print, marking scheme and the level of questions which can be asked in CBSE Class 12 Maths board exam 2018.
CBSE Class 12 Syllabus 2017-2018: All Subjects
Complete CBSE Class 12^{th} Maths Sample Paper 2018 is given below
Sample Question Paper
Mathematics (041)
Class XII: 2017-18
Time allowed: 3 hours Maximum Marks: 100
General Instructions
• All questions are compulsory.
• This question paper contains 29 questions.
• Question 1- 4 in Section A are very short-answer type questions carrying 1 mark each.
• Questions 5-12 in Section B are short-answer type questions carrying 2 marks each.
• Questions 13-23 in Section C are long-answer-I type questions carrying 4 marks each.
• Questions 24-29 in Section D are long-answer-II type questions carrying 6 marks each.
Section A
Questions 1 to 4 carry 1 mark each.
Question 1:
Let A= {1, 2, 3, 4}. Let R be the equivalence relation on A × A defined by (a, b) R (c, d) iff a + d = b + c. Find the equivalence class [(1, 3)].
Question 2:
If A = [a_{ij}] is a matrix of order 2×2, such that |A| = ‒15 and C_{ij} represents the cofactor of a_{ij}, a then find a_{21} c_{21} + a_{22} c_{22}.
CBSE Class 12 Mathematics Question Paper: 2017
Question 3:
Question 4:
Determine whether the binary operation * on the set N of natural numbers defined by a*b = 2^{ab} is associative or not.
Section B
Questions 5 to 12 carry 2 marks each
Question 5:
If 4sin^{‒1} x + cos^{‒1} x = π, then find the value of x.
Question 6:
Question 7:
Question 8:
Find the approximate change in the value of 1/x^{2}, when x change from x = 2 to x = 2.002.
Question 9:
Question 10:
Verify that ax^{2} + by^{2} = 1 is a solution of the differential equation x (yy_{1} + y_{1}^{2}) = yy_{1}.
Question 11:
Question 12:
If A and B are two events such that P (A) = 0.4, P (B) = 0.8 and P (B|A) = 0.6, then find P (A|B).
Section C
Questions 13 to 23 carry 4 marks each
Question 13:
NCERT Exemplar: CBSE Class 12 Mathematics - All Chapters
Question 14:
OR
Question 15:
Question 16:
OR
Question 17:
A person wants to plant some trees in his community park. The local nursery has to perform this task. It charges the cost of planting trees by the following formula:
C (x) = x^{3} ‒ 45 x^{2} + 600x, where x is the number of trees and C(x) is the cost of planting x trees in rupees. The local authority has imposed a restriction that it can plant 10 to 20 trees in one community park for a fair distribution. For how many trees should the person place the order so that he has to spend the least amount?
How much is the least amount? Use calculus to answer these questions. Which value is being exhibited by the person?
Question 18:
Question 19:
Find the particular solution of the differential equation: y e^{y} dx = (y^{3} + 2xe^{y}) dy, y (0) = 1
OR
Show that (x ‒ y) dy = (x + 2y) is a homogenous differential equation. Also, find the general solution of the given differential equation.
Question 20:
Question 21:
Question 22:
Bag I contains 1 white, 2 black and 3 red balls; Bag II contains 2 white, 1 black and 1 red balls; Bag III contains 4 white, 3 black and 2 red balls. A bag is chosen at random and two balls are drawn from it with replacement. They happen to be one white and one red. What is the probability that they came from Bag III.
Question 23:
Four bad oranges are accidentally mixed with 16 good ones. Find the probability distribution of the number of bad oranges when two oranges are drawn at random from this lot. Find the mean and variance of the distribution.
Section D
Questions 24 to 29 carry 6 marks each
Question 24:
Question 25:
Question 26:
Using integration, find the area in the first quadrant bounded by the curve y = x|x|, the circle x^{2} + y^{2} = 2 and the y-axis.
Question 27:
NCERT Solutions for Class 12 Mathematics
Question 28:
Question 29:
A company produces two different products. One of them needs 1/4 of an hour of assembly work per unit, 1/8 of an hour in quality control work and Rs1.2 in raw materials. The other product requires 1/3 of an hour of assembly work per unit, 1/3 of an hour in quality control work and Rs 0.9 in raw materials. Given the current availability of staff in the company, each day there is at most a total of 90 hours available for assembly and 80 hours for quality control. The first product described has a market value (sale price) of Rs 9 per unit and the second product described has a market value (sale price) of Rs 8 per unit. In addition, the maximum amount of daily sales for the first product is estimated to be 200 units, without there being a maximum limit of daily sales for the second product.
Formulate and solve graphically the LPP and find the maximum profit.
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Marking Scheme of CBSE Class 12 Maths Sample Paper 2018 in PDF format |
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