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Class 12th CBSE Mathematics 29 Questions 100 Marks

Class 12th CBSE Mathematics 29 Questions 100 Marks

**Sample Paper -2012**

**Class – XII**

**Mathematics**

** SECTION A**:

1. If f: R be given by f ( x) = then find

2. Find the value of Sin-1 ( sin )

3. If A = and A + AT = I. Find the value of

4. Find the value of ‘x’ if

5. Find the constant ‘c’ if A =

6. Evaluate

7. Evaluate

8. Find

9. Find the value of

10. Find a unit vector perpendicular to each of the vectors

**OR**

**OR **

**OR **

**OR **

__SECTION C:__

23. Using elementary transformation find the inverse of the matrix

24. Show that all the rectangles inscribed in given circle square has the maximum area

**OR **

A water tank has the shape of an inverted right circular cone with its axis vertical and

vertex lowermost .Its semi vertical angle is tan-1 ( 0.5) .Water is poured in to it at a

constant rate of 5 cubic meter per hour .Find the rate at which the level of the water is

rising at the instant when the depth of the water tank is 4m.

25. Prove that = =

**OR **

Evaluate limit as a sum

26. Find the area of the region bounded by the parabolas y2 = 4ax and x2 = 4by

27. A doctor is to visit a patient .From the past experiences , it is known that the probabilities

that he will come by train , bus , scooter or by other means of transport are respectively

. The probabilities that he will be late are , if he comes by

train , bus, and scooter respectively , but if he come by other means of transport , then he

will not be late .When he arrives he is late .What is the probability that he comes by train ?

28. A line makes angles with the diagonals of a cube , prove that

29. A manufacturing company produces two models A and B of a product .Each piece of

model A requires 9 labour hours for fabricating and 1 hour for finishing .Each piece of

model B requires 12 labour hours for fabricating and 3 hour for finishing. For fabricating

and finishing the maximum labour hours available are 180 and 30 respectively .The

company makes a profit of Rs.8000 on each piece of model A and Rs.12000 on each piece

of model B .How many pieces of model A and model B should manufactured per week to

get a maximum profit ? What is the maximum profit ( Solve as a linear programming

problem)

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