Model Question Paper Mathematics Class Xii Worksheet Page 6
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1
2
3
4
5
6
71
1
husband’s selection is
and that of the wife’s selection is
. Find the probabil-
7
5
ity that only one of them will be selected.
Part-C
32.
Obtain the inverse of the following matrix using elementary operations.
⎛
⎞
0 1 2
⎜
⎟
=
A
1 2 3
⎜
⎟
⎝
⎠
3 1 1
OR
−
⎛
⎞
2
3
5
⎜
⎟
=
−
–1
–1
If
, find A
. Using A
, solve the system of equations:
A
3
2
4
⎜
⎟
−
⎝
⎠
1
1
2
2x – 3y + 5z = 11
3x + 2y – 4z = –5
x + y – 2x = –3
–1
33.
Show that the function f given by f (x) = tan
(sinx + cosx), x > 0 is always an
π
⎛
⎞
strictly increasing function in
⎜
⎟
0,
⎝
⎠
4
OR
An open box is to be constructed by removing equal squares from each corner
of a 3 metre by 8 metre rectangular sheet of aluminium and folding up the
sides. Find the volume of the largest such box.
2
2
2
34.
Find the area of the region enclosed between the two circles x
+ y
= 4 and (x – 2)
2
+ y
= 4.
OR
2
2
Prove that the curves y
= 4x and x
= 4y divide the area of the square bounded by
x
=
0,
x = 4, y = 4 and y = 0 into three equal parts.
35.
A dietician has to develop a special diet using two foods P and Q. Each packet
(containing 30g) of food P contains 12 units of calcium, 4 units of iron, 6 units of
cholesterol and 6 units of vitamin A. Each packet of the same quantity of food Q
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