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 –
                         1. How many matrices of order 3 x 3 are possible with each entry as 0 or 1?
                         2. For any 2 x 2 matrix A, if A (adj A) =, then find |A|
                         3. If A= 
                         4. If f(x) = [ x ] and g (x) = │x │, then evaluate (f o g) (1/2) – (g o f) (-1/2)
5. How many relations can be defined from a non- empty sets A to B if n(A)=2and n(B)=3
6. A matrix A of order 3 x 3 has determinant 7, what is the value of |3A|?
7. If A is a square matrix such that A² = A, then find (I + A)² - 3A.
8. If   is a skew symmetric, find value of x.
9. If   the function f : R R defined by, find the inverse of   f  and f-(23).
10. If * be a binary operation defined on the set of integers as a*b=a+b+1 for a, b € I, find inverse element.
11. If X+Y=,Find X and Y
12. If A is 3x4 matrix and B is a matrix such that AB and BA are both defined, find order of mat B.
13. For what value of  x if
14. If A is a square matrix of order 3 such that = 25, find
15. If f(x) = 8x3 and g(x) = x⅓ , find g o f.
16. Show that the matrix A=  is Skew-symmetric.
11.By using properties of determinants show that
12. Prove by using properties of determinant 
13. If A = , then prove that aA-1 =
14. If A =  and B=,Find BA and  hence solve equations x-y =3, 2x +3y +4z =17,y+2z =7
15.Let A =NXN and Let * be a binary operation on A defined by  (a,b)*(c,d) = (ad+bc,bd) for all(a,b),(c,d) €  NXN. Determine if * is commutative, associative. Also find the identity and inverse if they exist.
 16. Using properties of determinants show that        = 0
17. Let A = ,   B =    Verify that  ( AB)T =  BT AT.
18 Using properties of determinants, show that  = 2abc(a+b+c) 3

19. If a, b, c are in AP, show that =0.
20. By using properties of determinants show that:
21. Using properties of determinants, prove that: maths_10_clip_image078  
22. Show that A = , satisfies the equation x² +  4x – 42 = 0.Hence find A-1.
23.Using properties of determinants, prove that:                                          24.If a,b,c are in A.P then find the value of the determinant
25. Prove using properties that  = 3(a+b+c)(ab+bc+ca) .
26. Show that the function F: R - {-1} ®R - {-1}, given by f(x) = is a bijection.Also find f 
 27.  If A= , then by induction show that, if a& b are constants.
 28. Prove that :   = (1 – x2)
29. maths_10_clip_image086
30. Express A =as sum of a symmetric and skew symmetric matrix.

                                                                        SECTION-C (6x6=36 Marks)            
31. If A =  find  A-1 and hence solve the equations:  2x – 3y + 5z = 11, 3x + 2y – 4z = -5, x +  y - 2z  = - 3.
32. If A =  find A-1. Hence solve the equations: x – y + z = 4,    x – 2y – 2z = 9,   2x + y + 3z = 1
33. Show that   = 2 xyz (x + y + z) 3
34. Prove that   
35. Consider f : R+ --> [-5, ∞) given by f(x) = 9x² + 6x – 5.  Show that f is bijective. Also find the inverse of  f.
 36. Using elementary row transformation find the inverse of the matrix  
  37. A= 
38. Prove using properties that maths_10_clip_image082
39.Using matrices solve  system of equations:x+3y+4z = 8,2x+y+2z =5,5x+y+z =7
40. Let f : N → R be a function defined as f(x) = 4x2 + 12 x + 15. Show that f : N → S where, S is the range
 of f , is invertible. Find f -1.
41. If A =  
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Name         Esther praveen
Phone No. 043340191



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