CBSE Board Class 12 Math Previous Year Question Papers 2007

MATHEMATICS 
CLASS 12
PREVIOUS PAPER 2007
Time allowed : 3 hours Maximum Marks: 100
General Instuctions  :
(ii) The question paper consists of three sections A,B and C.  Section A is compulsory
for all students. In addition to Section A, every student has to attempt  either
Section B OR Section C.
(ii) For Section A
Question numbers  1 to  8 are of  3 marks each.
Question numbers  9 to  15 are of  4 marks each.
Question numbers  16 to  18 are of  6 marks each.
(iii) For Section B / Section C
Question numbers  19 to  22 are of  3 marks each.
Question numbers  23 to  25 are of  4 marks each.
Question number  26 is of  6 marks.
(iv) All question are compulsory.
(v) Internal choices have been provided in some questions. You have to attempt only
one of the choices in such questions.
(vi) Use of calculator is not permitted. However, you may ask for logarithmic and
statistical table. If required.
1. For the matrix
show that  . Hence find  .

2. Using the properties of determinants, prove the following :

3. Solve the following differential equation :

4. Form the differential equation of the family of curves where A and B are constants.
               OR
Solve the following differential equation :

5. Evaluate :

6. Evaluate :

7. A card is drawn at random from a well-shuffled pack of 52 cards. Find the probability
that it is neither a king nor a heart.

8. An urn contains 6 red and 5 blue balls. Two balls are drawn at random with
replacement. Find the probability of getting
(i) 2 red balls
(ii) 2  blue balls
(iii) one red and one blue ball

9. Evaluate :

10. Evaluate :

11. Find the value of k for which the function is continuous at x = 2.
                  
12. Find the derivative of
w.r.t.   x  from first principle.

13. Find the Boolean expression representing the following switching circuit :
Simplify the expression so obtained.
OR
Examine the validity of the following argument :

14. If prove that ;fn   rks fl) dhft, fd

15. Verify Rolle's theorem for the function 
on [2, 3].

16. Using matrices, solve the following system of equations :

17. Using integration calculate the area of the region bounded by the two parabolas
and  .
                       OR
Evaluate
 as limit of a sum.

18. Find the point on the curve   which is nearest to the point (2, 1).
OR
Show that a right-circular cylinder of given volume, open at the top, has minimum total
surface area, provided its height is equal to the radius of the base.65/2/1 7 P.T.O.

SECTION B

19. Find the projection of on where

20. Find the value of  , which makes the vectors and coplanar.

21. A particle starting with initial velocity of 26 m/sec moves with a uniform acceleration of 6m/sec 2
. Find
(i) the velocity of the particle after 7 seconds.
(ii) how far it will go in 6 seconds.
(iii) its velocity when is has traversed 100 m.

22. Find the resultant of two velocities 6 km/hr and km/hr inclined to one another at an angle of 135°.
OR
A particle is projected with a velocity of 39.2 m/sec at an elevation of 30°. Find
(i) the time of flight.
(ii) the greatest height.

23. A body of mass 50 kg, suspended by two strings of lengths 30 cm and 40 cm fastend to
two points in the same horizontal line 50 cm apart, is in equilibrium. Find the tension
(in Newtons) in each string.

24. Two forces act at a point and are such that if the direction of one is reversed, the
resultant is turned through a right angle. Show that the two forces must be equal in
magnitude.

25. Find the equation of the plane passing through the intersection of the planes
  and the point (1, 1, 1).

26. Find the equation of the sphere which passing through the points (0, 0, 0), (0, 1, -1), (-1, 2, 0)
and (1, 2, 3).

SECTION C

19. Calculate the banker's gain on a bill of Rs. 36,000 due in 5 months at 5% per annum.

20. A bill of exchange drawn on February 4, 2001 at 4 months after date was discounted on
March 26, 2001 at 8% per annum. If the banker’s discount is Rs. 400, find the face value
of the bill.

21. There are two bags I and II. Bag I contains 3 white and 3 red balls and Bag II contains
4 white and 5 red balls. One ball is drawn at random from one of the bags and is found
to be red. Find the probability that it was drawn from bag II.

22. Find the mean variance for the following probability distribution :
X 0  1 2  3
P(X)
                                                 OR
If the mean and variance of a binomial distribution are respectively 9 and 6, find the
distribution.

23. A, B and C entered into a partnership investing Rs. 12,000 for 4 months, Rs. 14,000 for
8 months and Rs. 10,000 for 10 months respectively. Find the share of each in a profit
of Rs. 5,850 if the profit is distributed in the ratio of investments.

24. Find the present  value of an annuity due of Rs. 900 per annum payable at the beginning
of each year for 2 years allowing interest 6% per annum, compounded annually.

25. Given the total cost function for x units of a commidity as
Find
(i) the average cost function.
(ii) the average cost of output of 10 units.
(iii) the marginal cost function
(iv) the marginal cost when 5 units are produced.