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Maths
Class - XII 1998 (CBSE)
You are on Set no 1 Question 21 to
30
Q21) For the function
f(x) = -2x3 - 9x2 - 12x + 1, find the interval
(s):
(i) in which f(x) is increasing.
(ii) in which f(x) is
decreasing.
Q22) Find from the
first principle derivative of  cosec x w.r.t. x.
Q23) Find the value
of
2
0 |
 |
(3x2 -
2)dx as limit of
sum. |
Q24) Evaluate
|
3
dx
(1 - x)(1 +
x2) |
Q25) Draw a rough
sketch and find the area of the region bounded by the two parabolas
y2 = 4x and x2 = 4y by using methods of
integration.
Q26) If A
=
 |
4 -5
-11
1 -3 1
2
3 -7 |
 |
, find
A-1 |
Using A-1, solve
the following system of equations:
4x - 5y - 11z = 12
x - 3y +
z = 1
2x + 3y - 7z = 2
Q27) Define the line of
shortest distance between two skew lines. Find the shortest distance
and the vector equation of the line of shortest distance between the
lines given by
 = 2 - 3 +  (2
- )
and
=
4 + 3 +  (3 + +)
Q28) A wet porous
substance in open air loses it's moisture at the rate proportional
to the moisture content. If a sheet hung in wind loses half of it's
moisture during the first hour, when will it have lost 95% moisture,
weather conditions remaining the same
Q29) A rectangle is
inscribed in a semi circle of radius 'r' with one of it sides on the
diameter of the semi circle. Find the dimensions of the rectangle so
that it's area is maximum. Find also this area.
Q30) Calculate Karl
Pearson's coeff of correlation between x and y for the following
data:
| x: |
16 |
18 |
21 |
20 |
22 |
26 |
27 |
15 |
| y: |
22 |
25 |
24 |
26 |
25 |
30 |
33 |
14 |
Also, give the
interpretation of coeff of correlation thus obtained
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