Class 12th CBSE Mathematics 29 Questions 100 Marks, Question Paper, Sample Question Paper 2012 2013 Exam CBSE SiteMap

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Class 12th CBSE Mathematics 29 Questions 100 Marks

Class 12th CBSE Mathematics 29 Questions 100 Marks



Class 12th CBSE Mathematics 29 Questions 100 Marks

Sample Paper – 2012
Class – XII
Subject – Mathematics

Section – A

  1. Let A = {3, 5} and B = {7, 11}. And R = {(a, b): a , a – b is odd}, then show that R is an empty relation.
  2. Prove that sin{tan-1(1)} =
  3. If A =  and B =  find A + B.
  4. If A =  verify that  AA‑1 = I
  5. Prove that (a + b + c) is a factor of :
  6. Evaluate :
  7. Evaluate :
  8. Find the unit vector in the direction of the vector:  =
  9. Find λ so that   .                                   A: 3
  10. Find the magnitude of      , if    .                  A:                                                                                     

Section – B

  1. Prove that a relation R on the set Z of all integers defined by: (x, y) ó x – y  is divisible by 4 is an equivalence relation on Z.
  2. Solve :        .                       A: 1/
  3. Show that  x = 2 is a root of the equation:  and solve it completely.            Ans: -3,1,2
  4. The function define d as : f(x) =  is continuous in [ 0,8] find ‘a’ and ‘b’.                                                                                                  Ans  a=3 b=-2
  5. Find       when:  x =  and y = .
  6. Find a point on the curve y = x3 – 3x , where the tangent is parallel to the chord joining the points (1, -2) and (2,2).
  7. Evaluate :   Or dx .
  8. If with reference to the right handed system of mutually perpendicular unit vectors , , , then express  in the form of , where  is parallel to  and  is perpendicular to
  9. If
  10. If  show that
  11. Show that a closed right circular cylinder of given total surface area and maximum volume is such that its height is equal to the diameter of its base.
  12. Obtain the differential equation representing the family of parabolas having vertices at the origin and axis along the positive direction of X-axis.                           Ans: y2 – 2xyy’=0

SECTION – C

  1. Find the shortest distance between the lines  and                                                                                                  Or                                                        Find the image of the point (3,5,3) in the line:                                 A: (-1,1,7)
  2. Find the area of the region { }
  3. Evaluate the integrals from the first Principal
  4. Solve the system of equation using matrix method  2x + 3y + 3z = 5, x – 2y + z = - 4, 3x –y – 2z = 3
  5. Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius r is.
  6. A Cooperative society of farmers has 50 hectares of land to grow two crops X and Y. The profit from crops X and Y per hectare are estimated as Rs 10,500 and Rs 9,000 respectively. To control weeds, a liquid herbicide has to be used for crops X and Y at rates of 20 liters and 10 liters per hectares. Further, not more than 800 liters of herbicide should be used in order to protect fish and wild life using a pond which collects drainage from this land. How much land should be allocated to each crop so as to maximize the total profit of the society?  
  7. A husband and a wife appeared for an interview for two posts. The probability of their selection is 1/7 and 1/5 respectively. What is the probability that:                                                                    (i) both of them will be selected       A:1/35                                                                       (ii) only one of them will be selected         A:2/7                                                                        (iii) at least of them will be selected A:11/35                                                                                (iv) none of them will be selected.       A:24/35                                                                                                                                   Or                                                                               A discrete random variable X has mean score equal to ‘6’ and variance equal to ‘2’. Assuming that the underline distribution is binomial, what is the probability when       Ans:3136/6561

 

Paper Submitted By:

Name            Chetan Jain
Email  jainchetan2004@yahoo.com
Phone No.    9929160320




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