Economy

Sample Paper – 2011
Class – XII
Subject - Mathematics
Time   : 3 Hours                                                                                       Max. Marks : 100

General Instructions

1.   All questions are compulsory.

2. The question paper consists of 29 questions divided into three sections A,B and C.

      Section A comprises of 10 questions of one mark each, section B comprises of 12

      questions of four marks each and section C comprises of   07 questions of six marks each.

3.   All questions in Section A are to be answered in one word, one sentence or as per the exact

      requirement of the question.

4.   There is no overall choice. However, internal choice has been provided in 4 questions of four

      marks each and 2 questions of six marks each. You have to attempt only one of the alternatives

      in all such questions.

5.   Use of calculators is not permitted. You may ask for logarithmic tables, if required.

SECTION - A

1. Find the domain of the function e3logx.

2. Find a branch of the function cos-1 other than the principal value branch.

3. If A is a 3x3 matrix such that |A|=5 then what is |adjA| ?

4. What is the minimum value of   | sin4x + 3| ?

5. Write square matrices A and B of order 2 such that AB=0, A≠0 and B≠0.

6. If   [pic] and [pic] are any two vectors such that |[pic].[pic]| =   |[pic]x[pic]| then what is the angle between

    [pic] and [pic]?

7. If the lines [pic] and [pic] are perpendicular then find the value of k.

[pic]

9. If [pic] and [pic] are unit vectors such that |[pic]+[pic]| =1 then what is |[pic]-[pic]|?

10. If A is a square matrix of order 3 such that |A| = 4 then find A(adjA).

SECTION_- B

11.Solve for x:

                                [pic]

                                                Or

    Simplify:

                [pic]

[pic]

13. Using properties of determinants, prove that

          [pic]...