CBSE Question Paper 2008 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. Evaluate:

2. Find the value of x and y if:

3. If f(x) = x + 7 and g(x) = x – 7, x∈x∈ R, find (fog) (7)

4. Evaluate:

5. Evaluate:

6. Fined the co-factor a₁₂ in the following:

7. For what value of λ are the vectors  and

8. Find the angle between the vectors  and

9. Find a unit vector in the direction of

10. Evaluate:

Section B

11. Solve the following differential equation:

12. Solve the followng differential euation:

Give that y =when x = 1

OR

Solve the following differential equation:

 if y = 1 when x = 1

13. Find trhe shortest distance between the following lines:

 and

OR

Find the point on the line  at a distance  from the point (1, 2, 3)

14. A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability distribution of number of successes.

15. if  and  find a vector  such that  and 

OR

 If  and  and  show that the angle between  is 60°.

16. Let , Express A as sum of two matrices such that one is symmetric and the other is skew symmetric.

OR

If  verify that

17. For What value of k is the following function continuous at x = 2 ?

18. Find the equation of tangent to the curve  at

19. (i) Is the binary operation *, defined on set N, given by a*b for all  commutative ?

(ii) Is the above binary operation * associative ?

20. Solve for x :

21. Evaluate:

22. If  find

Section C

23. Using properties of determinants, prove the following:

24. Evaluate:

25. Using integration, find the area of the region enclosed between the circles  and

26. An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers. The probability of an accident involving a scooter, a car and a truck are 0.01, 0.03 and 0.15 respectively. One of the insured persons meets with an accident. What is the probability that he is a scooter driver.

27. Find the equation of the plane passing through the point (-1, -1, 2) and perpendicular to each of the following planes:

 and

OR

Find the equation of the plane passing the points (3, 4, 1) and (0, 1, 0) and parallel to the line

28. A factory owner purchases two types of machines, A and B for his factory.
The requirements and the limitations for the machines are follows:

He has maximum are 9000 m² available, and 72 skilled labourers who can operate both the machines. How many machines of each type should he buy to maximize the daily output ?

29. Show that the rectangle of maximum area that can be inscribed in a circle is a square.

OR

Show that the height of the cylinder of maximum volume that can be inscribed in a cone of height h is