MARKS DISTRIBUTION

MATHEMATICS (041)

CLASS XII 2015-16Three Hours

One paper Marks : 100

Unit Marks

I. RELATIONS AND FUNCTIONS 10

II. ALGEBRA 13

III. CALCULUS 44

IV. VECTORS AND THREE - DIMENSIONAL GEOMETRY 17

V. LINEAR PROGRAMMING 06

VI. PROBABILITY 10

Total 100

3

4

5

6

7

8

9

10

relation

X

11

12

13

14

15

16

for suitable value of domain

, x > 0 & p + , x > 0

17

18

19

20

21

22

either consistent or inconsistent according as

the system may be have either infinite many solutions or no solutions.

23

24

4. Show that the matrix satisfies the equation A 4A + 1 = 0 where I is 2 2

and 0 is 2 2 zero matrix using this equation, find A .

2

1identify

2 31 1

25

26

27

28

29

30

31

32

33

34

35

inflexion

36

(iii) the test fails if f (a) = 0 and f (a) = 0. In this case we apply 1 derivative test.I stII

III IV III III

IV III IV

OR

f (a) & f (a) if f (a) 0 then f has max or min value at x = a (is called point) if f (a) = 0

and f (a) < 0 then f is max at x = 4 and f (a) = 0, & f (a) > 0 then f is min at x = a

m m

m m

from bottom.

decreasing

37

y =4ax2

is

38

39

40

41

; n 1

= log x + c

42

43

44

7. + cot x.( )

45

46

47

48

49

50

51

involved in equation

52

53

54

55

56

or (whose diagonals are given by p & q ) p q

57

58

6

6

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

4.2 31 2

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98