Sample Question Paper (With value based questions) Issued by CBSE for 2013 Examination Mathematics Class–XII Blue Print S. No.

Topics

VSA

SA

LA

Total

—

4(1)

—

—

2(2)

4(1)

—

10(4)

2(2)

—

6(1)

—

1(1)

4(1)

—

13(5)

1(1)

12(3)

—

—

(b) Applications of Derivatives

—

—

6(1)

44(11)

(c) Integration

—

12(3)

—

—

(d) Application of Integrals

—

—

6(1)

—

1(1)

—

6(1)

—

2(2)

4(1)

—

—

(b) 3-dimensional Geometry

1(1)

4(1)

6(1)

17(6)

5.

Linear Programming

—

—

6(1)

6(1)

6.

Probability

—

4(1)

6(1)

10(2)

10(10)

48(12)

42(7)

100(29)

1. (a) Relations and Functions (b) Inverse Trigonometric Functions 2. (a) Matrices (b) Determinants 3. (a) Continuity and Differentiability

(e) Differential Equations 4. (a) Vectors

Total

Note: — Number of questions are given within brackets and marks outside the brackets. — The Question Paper will include question(s) based on values to the extent of 5 marks.

CBSE Sample Question Paper–2013 (with Value Based Questions) Time allowed: 3 hours

Maximum 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 7 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 calculator is not permitted. You may ask for logarithmic tables, if required.

SECTION–A Question numbers 1 to 10 carry 1 mark each. 1. Using principal values, write the value of 2 cos -1 é 2. Evaluate tan -1 ê 2 cos æç 2 sin -1 è ë

1 1 + 3 sin -1 . 2 2

1 öù ÷ . 2 ø úû

é1 0 0ù é xù é 1 ù 3. Write the value of x + y + z, if ê 0 1 0ú ê yú = ê -1ú . ê úê ú ê ú êë 0 0 1 úû êë z úû êë 0 úû 4. If A is a square matrix of order 3 such that |adj A| = 225, find |A’| é cos q sin q ù 5. Write the inverse of the matrix ê ú. ë - sin q cos q û 6. The contentment obtained after eating x-units of a new dish at a trial function is given by the Function C(x) = x3 + 6x2 + 5x + 3. If the marginal contentment is defined as rate of change of (x) with respect to the number of units consumed at an instant, then find the marginal contentment when three units of dish are consumed. æ d2y ö d 2 y dy ÷÷ - 2 7. Write the degree of the differential equation çç + 1 = 0. è dx 2 ø dx 2 dx

(iii)

CBSE Sample Question Paper

® ® ® ® 2 8. If a and b are two vectors of magnitude 3 and , respectively such that a ´ b is a unit vector, 3 ®

®

write the angle between a and b . ®

®

®

®

9. If a = 7i$ + j$ - 4k$ and b = 2i$ + 6j$ + 3k$, find the projection of a on b . 10. Write the distance between the parallel planes 2x - y + 3z = 4 and 2x - y + 3z = 18.

SECTION–B Question numbers from 11 to 22 carry 4 marks each. 11. Prove that the function f : N ® N, defined by f ( x) = x 2 + x + 1 is one – one but not onto. 12. Show that sin [cot -1 {cos(tan -1 x)}] =

x2 + 1 x2 + 2

OR æ1 - x 2 ö æ 2x ö æ 2x ö p Solve for x: 3 sin -1 ç ÷ + 2 tan -1 ç - 4 cos -1 ç ÷ ÷= . 2 è1 + x 2 ø è1 - x 2 ø 3 è1 + x ø 13. Two schools A and B decided to award prizes to their students for three values: honesty (x), punctuality (y) and obedience (z). School A decided to award a total of `11,000 for these three values to 5, 4 and 3 students, respectively, while school B decided to award `10,700 for these three values to 4, 3 and 5 students, respectively. If all the three prizes together amount to `2,700 then (i) Represent the above situation by a matrix equation and form Linear equations by using matrix multiplication. (ii) Is it possible to solve the system of equations so obtained using matrices? (iii) Which value you prefer to be rewarded most and why? 14. If x = a(q - sin q) and y = a(1 - cos q), find 15. If y =

sin -2 x 1 - x2

, show that (1 - x 2 )

d2y dx

2

d2y dx 2

- 3x

.

dy - y = 0. dx

ì x 2 + ax + b , 0 £ x < 2 ï 16. The function f ( x) is defined as f ( x) = í 3x + 2, 2 £ x £ 4 . If f ( x) is continuous on [0, 8], ï 2ax + 5b , 4

Topics

VSA

SA

LA

Total

—

4(1)

—

—

2(2)

4(1)

—

10(4)

2(2)

—

6(1)

—

1(1)

4(1)

—

13(5)

1(1)

12(3)

—

—

(b) Applications of Derivatives

—

—

6(1)

44(11)

(c) Integration

—

12(3)

—

—

(d) Application of Integrals

—

—

6(1)

—

1(1)

—

6(1)

—

2(2)

4(1)

—

—

(b) 3-dimensional Geometry

1(1)

4(1)

6(1)

17(6)

5.

Linear Programming

—

—

6(1)

6(1)

6.

Probability

—

4(1)

6(1)

10(2)

10(10)

48(12)

42(7)

100(29)

1. (a) Relations and Functions (b) Inverse Trigonometric Functions 2. (a) Matrices (b) Determinants 3. (a) Continuity and Differentiability

(e) Differential Equations 4. (a) Vectors

Total

Note: — Number of questions are given within brackets and marks outside the brackets. — The Question Paper will include question(s) based on values to the extent of 5 marks.

CBSE Sample Question Paper–2013 (with Value Based Questions) Time allowed: 3 hours

Maximum 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 7 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 calculator is not permitted. You may ask for logarithmic tables, if required.

SECTION–A Question numbers 1 to 10 carry 1 mark each. 1. Using principal values, write the value of 2 cos -1 é 2. Evaluate tan -1 ê 2 cos æç 2 sin -1 è ë

1 1 + 3 sin -1 . 2 2

1 öù ÷ . 2 ø úû

é1 0 0ù é xù é 1 ù 3. Write the value of x + y + z, if ê 0 1 0ú ê yú = ê -1ú . ê úê ú ê ú êë 0 0 1 úû êë z úû êë 0 úû 4. If A is a square matrix of order 3 such that |adj A| = 225, find |A’| é cos q sin q ù 5. Write the inverse of the matrix ê ú. ë - sin q cos q û 6. The contentment obtained after eating x-units of a new dish at a trial function is given by the Function C(x) = x3 + 6x2 + 5x + 3. If the marginal contentment is defined as rate of change of (x) with respect to the number of units consumed at an instant, then find the marginal contentment when three units of dish are consumed. æ d2y ö d 2 y dy ÷÷ - 2 7. Write the degree of the differential equation çç + 1 = 0. è dx 2 ø dx 2 dx

(iii)

CBSE Sample Question Paper

® ® ® ® 2 8. If a and b are two vectors of magnitude 3 and , respectively such that a ´ b is a unit vector, 3 ®

®

write the angle between a and b . ®

®

®

®

9. If a = 7i$ + j$ - 4k$ and b = 2i$ + 6j$ + 3k$, find the projection of a on b . 10. Write the distance between the parallel planes 2x - y + 3z = 4 and 2x - y + 3z = 18.

SECTION–B Question numbers from 11 to 22 carry 4 marks each. 11. Prove that the function f : N ® N, defined by f ( x) = x 2 + x + 1 is one – one but not onto. 12. Show that sin [cot -1 {cos(tan -1 x)}] =

x2 + 1 x2 + 2

OR æ1 - x 2 ö æ 2x ö æ 2x ö p Solve for x: 3 sin -1 ç ÷ + 2 tan -1 ç - 4 cos -1 ç ÷ ÷= . 2 è1 + x 2 ø è1 - x 2 ø 3 è1 + x ø 13. Two schools A and B decided to award prizes to their students for three values: honesty (x), punctuality (y) and obedience (z). School A decided to award a total of `11,000 for these three values to 5, 4 and 3 students, respectively, while school B decided to award `10,700 for these three values to 4, 3 and 5 students, respectively. If all the three prizes together amount to `2,700 then (i) Represent the above situation by a matrix equation and form Linear equations by using matrix multiplication. (ii) Is it possible to solve the system of equations so obtained using matrices? (iii) Which value you prefer to be rewarded most and why? 14. If x = a(q - sin q) and y = a(1 - cos q), find 15. If y =

sin -2 x 1 - x2

, show that (1 - x 2 )

d2y dx

2

d2y dx 2

- 3x

.

dy - y = 0. dx

ì x 2 + ax + b , 0 £ x < 2 ï 16. The function f ( x) is defined as f ( x) = í 3x + 2, 2 £ x £ 4 . If f ( x) is continuous on [0, 8], ï 2ax + 5b , 4