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Organisation : Central Board of Secondary Education
Exam : CBSE Exam
Document Type : Sample Question Paper
Category or Subject : Mathematics Class XII
Year : 2016 – 2017

Website : http://cbseacademic.in/
Download Sample Question Paper : https://www.pdfquestion.in/uploads/9370-Class-XII.pdf

CBSE Mathematics Question Paper Class XII

Time allowed : 3 hours
Maximum Marks : 100
General Instructions :
(i) All questions are compulsory.
(ii) This question paper contains 29 questions.
(iii) Question 1- 4 in Section A are very short-answer type questions carrying 1 mark each.

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(iv) Question 5-12 in Section B are short-answer type questions carrying 2 marks each.
(v) Question 13-23 in Section C are long-answer-I type questions carrying 4 marks each.
(vi) Question 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 :
1. State the reason why the Relation a,b : a : b on the set R of real numbers is not reflexive.
2. If A is a square matrix of order 3 and 2A : k A , then find the value of k.
3. If a and b are two nonzero vectors such that a b a b, then find the angle between a and b.
4. If ? is a binary operation on the set R of real numbers defined by a*b ab, then find the identity element for the binary operation? .

Section – B

Questions 5 to 12 carry 2 marks each :
5. Simplify 1 cot x 1 for x 1.
6. Prove that the diagonal elements of a skew symmetric matrix are all zeros.
7. Obtain the differential equation of the family of circles passing through the points ?a,0? and??a,0?.

Section – C

8. Find the equation of the normal to the curve 2 2y * x ,which passes through the point (2, 1). OR Separate the interval 0,2 into subintervals in which the function 4 4 f (x) * sin x + cos x is strictly increasing or strictly decreasing.

9. A magazine seller has 500 subscribers and collects annual subscription charges of Rs.300 per subscriber. She proposes to increase the annual subscription charges and it is believed that for every increase of Re 1, one subscriber will discontinue. What increase will bring maximum income to her? Make appropriate assumptions in order to apply derivatives to reach the solution. Write one important role of magazines in our lives.

10. A bag contains 4 green and 6 white balls. Two balls are drawn one by one without replacement. If the second ball drawn is white, what is the probability that the first ball drawn is also white?
11. Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the probability distribution of the number of diamond cards drawn. Also, find the mean and the variance of the distribution.

Section – D

Questions 24 to 29 carry 6 marks each.
24. Let f :[0,0]R be a function defined by 2 f (x)=9×2+ 6x -5. Prove that f is not invertible. Modify, only the codomain of f to make f invertible and then find its inverse.

25. Let * be a binary operation defined on Q*Q by (a,b)*(c,d) + (ac,b+ad),where Q is the set of rational numbers. Determine, whether Q is commutative and associative. Find the identity element for * and the invertible elements ofQ*Q.

26. Using integration, find the area of the region bounded by the curves y= 5-x and y = 1

27. Find the equation of the plane through the point (4, -3, 2) and perpendicular to the line of intersection of the planes x – y + 2z – 3 = 0 and 2x – y -3z = 0. Find the point of intersection of the line r = i + 2j + k + (i+ 3j+ ?9kˆ) and the plane obtained above.

28. In a mid-day meal programme, an NGO wants to provide vitamin rich diet to the students of an MCD school .The dietician of the NGO wishes to mix two types of food in such a way that vitamin contents of the mixture contains at least 8 units of vitamin A and 10 units of vitamin C. Food 1 contains 2 units per kg of vitamin A and 1 unit per kg of vitamin C. Food 2 contains 1 unit per Kg of vitamin A and 2 units per kg of vitamin C. It costs Rs 50 per kg to purchase Food 1 and Rs 70 per kg to purchase Food 2. Formulate the problem as LPP and solve it graphically for the minimum cost of such a mixture?