CBSE Board Class 12 Math Previous Year Question Papers 2009

Previous Paper – 2009
Class – XII
Subject – MATHEMATICS 
M.M.  100         Time: 3 hours
General Instructions:
(1). All questions are compulsory
(2).  The question paper consists of 29 questions divided into three  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 07  questions of six marks each.
(3). All questions in section A are to be answered in one word, one sentence or as per the     exact requirement of the question.
(4). There is no overall choice. However internal choice has been in 04 questions of six marks each. You have to attempt only one of the alternative in all such questions.
(5). Use of calculator is not permitted. However, you may ask for logarithmic and statistical   Tables, if required.
Section – A

Q. 1 A matrix A of order 3× 3 has determinant 5. What is the value of   ?

Q. 2 For what value of x, the following matrix is singular ?
                        
Q. 3 Evaluate the determinants.
                          
Q. 4 What is the principal value of?

Q.5 Give an example of a relation which is reflexive and transitive but not
         Symmetric;

Q.6 The radius of a circle is increasing at the rate of 0.7 cm/s. what is the rate
         of increasing of its circumference  ?

Q.7 Find the projection of the vector  = , on the vector
   
Q.8 Find if for a unit vector  ,

Q.9 Show that the points (2,3,4), (-1,-2,1),(5,8,7) are collinear.

SECTION – B

Q.10 Write the function in the simplest form  , x

Q11 Show that the function f(x) =   is the continuous at every x
        but fails to be differentiable at x = -2.
                                                                                                                               
Q.12 Using properties of determinants, prove that

Q.13 Find the equation of the tangent line to the curve y = x2 - 2x+7  is parallel to the line
        2x - y + 9 = 0 .

Q 14   Evaluate     
         
Q.15    Evaluate  .

Q.16 Evaluate    as the limit of the sum.

Q.17 Find the area of the parallelogram whose adjacent sides are represented
         by the vectors   and .

Q.18 Find the shortest distance between the lines, whose equations are
                
 Q.19.Prove that the image of the point (3,-2,1) in the plane 3x – y + 4z = 2 lies on the plane, x + y + z + 4=0 .

Q .20 There  are 5% defective items in a large bulk of items. What is the Probability that a
           sample of 10 items will include not more than one defective  items ? 
      
SECTION - C
   
 Q.21 Consider f : R given by f(x) = 9x2+6x-5. Show that f is Invertible. Find the inverse of f.

Q.22 A point on the hypotenuse of a triangle is at distance a and b from the Sides of the
          triangle. Show that the minimum length of the hypotenuse is

Q.23 Find the area of the region bounded by the curve y = x2+2, and the lines y =x, x = 0
          and x = 3.

Q.24 Solve the differential equation
           (tan-1y - x)dy = (1 + y2) dx.

Q.25 Find the vector equation of the line passing through the (1,2,3) and parallel to the
          planes      = 5 and    = 6.
                  
Q.26 Two godowns A and B have grain capacity of 100 quintals and 50 quintals
          respectively.They supply to 3 ration shops, D,E and F whose requirements
           Are 60,50 and 40 quintals respectively. The cost of Transportation per
          quintal from the godowns to the shops are given in the following table ;
          How should the supplies be transported in order that the Transportation cost
          is minimum ? what is the minimum cost?

Q.27 A factory has two machines A and B. past record shows that machine A produced 60%
          of the items of output and machine B produced 40% Of the items. Further, 2% of the
          items produced by the machine A and 1% produced by the machine B were defective.
          All the items are put into One stockpile and then one item is chosen at random from
         this and is Found to be defective. What is the probability that it was produced by
         machine B?