CBSE Question Paper 2009 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. Find the value of x, if

2. Let  be a binary operation on N given by ab = HCF (a, b), a,  Write the value of 224.

3. Evaluate:

4. Evaluate:

5. Write the principal value of .

6. Write the value of the following determinant:

7. Find the value of x from the following:

8. Find the value of p if

9. Write the direction cosines of a line equally inclined to the three coordinate axes.

10.  If  is a unit vector and  then find .

Section B

11.  The length x of a rectangle is decreasing at the rate of 5 cm/minute and the width y is increasing at the rate of 4cm/minute. When (b) the area of the rectangle.

OR

  Find the intervals in which the function f given by

Is strictly increasing or strictly decreasing.

12.  If sing y = x sin (a + y), prove that

OR

If  find

13.  Let  be defined by

 for all

14.  Evaluate:

OR

Evaluate:

15.  If  Show that

16.  On a multiple choice examination with three possible answers (out of which only one is correct) for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing ?

17.  Using properties of determinants, prove the following:

18.  Solve the following differential equation:

19.  Solve the following differential equation:

20.  Find the shortest distance between the following two lines:

21.  Prove the following:

OR

Solve for x:

22.  The scalar product of the vector  with the unit vector along the sum of vectors  and  is equal to one. Find the value of .

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). Also find the distance of the point P(6, 5, 9) from the plane.

24.  Find the area of the region included between the parabola y² = x and the line x + y = 2.

25.  Evaluate:

26.  Using matrices, solves the following system of equations:

X + y + z = 6

X + 2z = 7

3x + y + z = 12

OR

Obtain the inverse of the following matrix using elementary operations:

27.  Coloured balls are distributed in three bags as shown in the following table:

A bag is selected at random and then two balls are randomly drawn from the selected bag. They happen to be black and red. What is the probability that they came from bag I ?

28. A dealer wishes to purchase a number of fans and sewing machines. He has only Rs. 5,760 to invest and has a space for at most 20 items. A fan costs him Rs. 360 and a sewing machine Rs. 240. His expectation is that he can sell a fan at a profit of Rs. 22 and sewing machine at a profit of Rs. 18. Assuming that he can sell all the items that he can buy, how should he invest his money in order to maximize the profit ? Formulate this as a linear programming problem and solve it graphically.

29. If the sum of the length of the hypotenuse and a side of a right-angled triangle is given, show that the area of the triangle is maximum when the angle between them is

OR

  A manufacturer can sell x items at a price of Rs.  each. The cost price of x items is Rs.  Find the number of items he should sell to earn maximum profit.

Previous Question Paper for Class 12 Mathematics

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