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