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- Date Submitted: 12/19/2010 3:47 AM
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BLUE PRINT - III MATHEMATICS - XII

VSA 1 (1) 1 (1) 4 (1) 4 (1) 10 (4) SA LA TOTAL

S.No.

Topic

1. (a)

Relations and Functions

(b)

Inverse trigonometric

Functions 2 (2) 1 (1) 2 (2) 4 (1) 8 (2) 3 (3) 10 (10) 4 (1) 4 (1) 4 (1) 48 (12) 6 (1) 6 (1) 6 (1) 42 (7) 17 (6) 6 (1) 10 (2) 100 (29) 12 (3) 4 (1) }18 (4) 6 (1) 6 (1) 6 (1) }18 (5) 8 (2) 44 (11) 6 (1) 13 (5)

2. (a)

Matrices

(b)

Determinants

3. (a)

Continuity and

Differentiability

(55)

(b)

Applications of Derivatives

(c)

Integrals

(d)

Applications of Integrals

(e)

Differential equations

4. (a)

Vectors

(b)

3 - dimensional geometry

5.

Linear - Programming

6.

Probability

Total

Sample Question Paper - III

Time : 3 Hours 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 contains 10 questions of 1 mark each, section B is of 12 questions of 4 marks each and section C is of 7 questions of 6 marks each. There is no overall choice. However, an internal choice has been provided in four questions of 4 marks each and two questions of six marks each. Use of calculators is not permitted. However, you may ask for Mathematical tables. SECTION - A 1. 2. 3. 4. 5. Let → R be a function defined as f (x ) = Max. Marks : 100

3.

4.

2x , find f–1 : Range of 5x + 3

Write the range of one branch of sin–1x, other than the Principal Branch. If , find x, 0 < x <

π when A + A´ = I 2

If B is a skew symmetric matrix, write whether the matrix (ABA´) is symmetric or skew symmetric. On expanding by first row, the value of a third order determinant is a11 A11 + a12 A12 + a13 A13. Write the expression for its value on expanding by 2nd column. Where A ij is the cofactor of element a ij .

6.

Write a value of

7.

Write the value of

→ →

8.

Let a and b be two vectors such that a = 3 and b =

→ →

→

→

2 and a x b...