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**CBSE Question Paper 2012 class 12 Mathematics** conducted by Central Board of Secondary Education, New Delhi in the month of March 2012. CBSE previous year question papers with solution are available in myCBSEguide mobile app and cbse guide website. The Best CBSE App for students and teachers is myCBSEguide which provides complete study material and practice papers to cbse schools in India and abroad.

**CBSE Question Paper 2012 class 12 Mathematics **

## Class 12 Mathematics list of chapters

- Relations and Functions
- Inverse Trigonometric Functions
- Matrices
- Determinants
- Continuity and Differentiability
- Application of Derivatives
- Integrals
- Application of Integrals
- Differential Equations
- Vector Algebra
- Three Dimensional Geometry
- Linear Programming
- Probability

## CBSE Question Paper 2012 class 12 Mathematics

**General Instruction:**

- All question are compulsory.
- The question paper consists of 29 questions divided into three section 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.
- All question in Section A are to be answered in one word, one sentence or as per the exact requirement of the questions.
- 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.
- Use of calculators is not permitted.

**Section A**

1. If a line has direction ratios 2, -1, -2, then what are its direction cosines ?

2. Find when the projection of on is 4 units.

3. Find the sum of vectors and .

4. Evaluate:

5. Evaluate

6. If write the minor of the element a_{23}.

7. If write the value of x.

8. Simplify:

9. Write the principal value of .

10. Let be a ‘binary’ operation on N given a b = LCM (a, b) for all Find 5 7.

**Section B**

11. If find .

**OR**

** **If sin y = x sin(a + y), prove that

12. How many times must a man toss a fair coin, so that the probability of having at least one head is more than 80%?

13. Find the vector and cartesian equations of the line passing through the point (1, 2, -4) and perpendicular to the two lines and

14. If are three vectors such that and and find the value of

15. Solve the following differential equation:

16. Find the particular solution of the following differential equations;

given that y=1 when x = 0.

17. Evaluate:

**OR**

Evaluate:

18. Find the point on the curve y = x^{3} – 11x + 5 at which the equation of tangent is y = x – 11.

**OR**

Using differentials, find the approximate value of

19. If show that

20. Using properties of determinants, prove that

21. prove that

**OR**

Prove that

22. Let A = R – {3} and B = R – {1}. Consider the function defined by Show that f is one-one and onto and hence find f^{-1}.

**Section -C**

23. Find the equation of the plane determined by the points A(3, -1, 2), B(5, 2, 4) and C(-1, -1, 6) and hence find the distance between the plane and the point P(6, 5, 9).

24. Of the students in a college, it known that 60% reside in hostel and 40% are day scholars (not residing in hostel). Previous year results report that 30% of all students who reside in hostel attain ‘A’ grade and 20% of day scholars attain ‘A’ grade in their annual examination. At the end of the year, one student is chosen at random from the college and he has an ‘A’ grade, what is the probability that the students is a hostlier?

25. A manufacturer produces nuts and bolts. It takes 1 hour of work on machine A and 3 hours on machine B to produce a package of nuts. It takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts. He earns a profit of Rs.17.50 per package onnuts and Rs.7 per package of bots. How many packages of each should be produced each day so as to maximize his profits if he operates his machines for at the most 12 hours a day? Form the above as a linear programming problem and solve it graphically.

26. prove that

**OR**

Evaluate as a limit of a sum.

27. Using the method of integration, find the area of the region bounded by the lines

and

28. Show that the height of a closed right circular cylinder of given surface and maximum volume, is equal to the diameter of its base.

29. using matrices, solve the following system of linear equations:

X – y + 2z = 7

3x + 4y – 5z = -5

2x – y + 3z = 12

**OR**

Using elementary operations, find the inverse of the following matrix:

**These are questions only. To view and download complete question paper with solution install myCBSEguide App from google play store or login to our student dashboard.**

## Previous Question Paper for Class 12 Mathematics

Download class 12 Mathematics question paper with solution from best CBSE App the myCBSEguide. CBSE class 12 Mathematics question paper 2012 in PDF format with solution will help you to understand the latest question paper pattern and marking scheme of the CBSE board examination. You will get to know the difficulty level of the question paper. CBSE question papers 2012 for class 12 Mathematics have 28 questions with solution.

## Last Year Question Paper 2012

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