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CBSE Class 12 Maths Sample Paper: 2018

Jan 9, 2018 10:38 IST
    CBSE Sample Paper 2018 for Class 12 Maths
    CBSE Sample Paper 2018 for Class 12 Maths

    CBSE 12th 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 12th 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 12th 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 = [aij] is a matrix of order 2×2, such that |A| = ‒15 and Cij represents the cofactor of aij, a then find a21 c21 + a22 c22.

    CBSE Class 12 Mathematics Question Paper: 2017

    Question 3:

    CBSE 12th Maths Sample Paper: Question number 3

    Question 4:

    Determine whether the binary operation * on the set N of natural numbers defined by a*b = 2ab 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:

    CBSE 12th Maths Sample Paper: Question number 6

    Question 7:

    CBSE 12th Maths Sample Paper: Question number 7

    Question 8:

    Find the approximate change in the value of 1/x2, when x change from x = 2 to x = 2.002.

    Question 9:

    CBSE 12th Maths Sample Paper: Question number 9

    Question 10:

    Verify that ax2 + by2 = 1 is a solution of the differential equation x (yy1 + y12) = yy1.

    Question 11:

    CBSE 12th Maths Sample Paper: Question number 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:

    CBSE 12th Maths Sample Paper: Question number 13

    NCERT Exemplar: CBSE Class 12 Mathematics - All Chapters

    Question 14:

    CBSE 12th Maths Sample Paper: Question number 14

    OR

    CBSE 12th Maths Sample Paper: Question number 14 (Optional)

    Question 15:

    CBSE 12th Maths Sample Paper: Question number 15

    Question 16:

    CBSE 12th Maths Sample Paper: Question number 16

    OR

    CBSE 12th Maths Sample Paper: Question number 16 (Optional)

    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) = x3 ‒ 45 x2 + 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:

    CBSE 12th Maths Sample Paper: Question number 18

    Question 19:

    Find the particular solution of the differential equation: y ey dx = (y3 + 2xey) dy, y (0) = 1

    OR

    Show that (xy) dy = (x + 2y) is a homogenous differential equation. Also, find the general solution of the given differential equation.

    Question 20:

    CBSE 12th Maths Sample Paper: Question number 20

    Question 21:

    CBSE 12th Maths Sample Paper: Question number 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:

    CBSE 12th Maths Sample Paper: Question number 24

    Question 25:

    CBSE 12th Maths Sample Paper: Question number 25

    Question 26:

    Using integration, find the area in the first quadrant bounded by the curve y = x|x|, the circle x2 + y2 = 2 and the y-axis.

    Question 27:

    CBSE 12th Maths Sample Paper: Question number 27

    NCERT Solutions for Class 12 Mathematics

    Question 28:

    CBSE 12th Maths Sample Paper 2018: Question number 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.

    Download

    CBSE Class 12 Maths Sample Paper 2018 in PDF format

    Marking Scheme of CBSE Class 12 Maths Sample Paper 2018 in PDF format

     

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