CBSE Question Paper 2017 class 12 Mathematics

General Instructions:

1. All questions are compulsory.
2. This question paper consists of 29 questions divided into four sections A, B, C and D. Section A comprises of 4 questions of one mark each, Section B comprises of 8 questions of two marks each, Section C comprises of 11 questions of four marks each and Section D comprises of 6 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 3 questions of four marks each and 3 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
Question numbers 1 to 4 carry 1 mark each.

1. Let A and B are matrices of order 3 × 2 and 2 × 4 respectively. Write order of matrix (AB).
2. Write the equation of tangent drawn to the curve y = sin x at the point (0, 0).
3. Find :
4. Write the angle between the vectors and .

SECTION – B
Question numbers 5 to 12 carry 2 marks each.

5. In the following matrix equation use elementary operation R₂ → R₂ + R₁ and write the equation thus obtained.

6. Find the value of k for which the function

is continuous at x = 2.
7. The radius r of a right circular cone is decreasing at the rate of 3 cm/minute and the height h is increasing at the rate of 2 cm/minute. When r = 9 cm and h = 6 cm, find the rate of change of its volume.
8. Find:
9. Find the differential equation of the family of curves y² = 4 ax.
10. Find the general solution of the differential equation

11. If the points with position vectors and are collinear, find the value of λ.
12. A firm has to transport at least 1200 packages daily using large vans which carry 200 packages each and small vans which can take 80 packages each.

The cost for engaging each large van is ` 400 and each small van is Rs.200.Not more than Rs.3,000 is to be

spent daily on the job and the number of large vans cannot exceed the number of small vans. Formulate this problem as a LPP given that the objective is to minimize cost.

SECTION – C
Question numbers 13 to 23 carry 4 marks each.

13. Prove that :
14. then using properties of determinants, find the value of where x, y, z ≠ 0.
OR Using elementary operations, find the inverse of the following matrix A
.
15. If x = a (cos θ + θ sin θ) and y = a (sin θ – θ cos θ), then find .