class xii mathematics study material
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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
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relation
X
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for suitable value of domain
, x > 0 & p + , x > 0
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either consistent or inconsistent according as
the system may be have either infinite many solutions or no solutions.
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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 .
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1identify
2 31 1
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inflexion
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(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
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y =4ax2
is
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; n 1
= log x + c
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7. + cot x.( )
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involved in equation
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or (whose diagonals are given by p & q ) p q
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4.2 31 2
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