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Maths
Class - XII 1999(CBSE)
You are on Set no 1 Question 22 to
30
Q22) Evaluate  o3f(x) dx, when f(x) = |x| + |x - 1|
+ |x - 2| (Marks 4)
Q23) Prove, using the properties of determinants (Marks
4)
 |
b+c
c+a a+b
c+a a+b
b+c
a+b b+c c+a |
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=
2 |
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a
b c
b c
a
c a b |
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Q24) A particle moves along the curve 6y = x3 + 2.
Find the points on the curve at which the y-coordinate is changing 8
times as fast as x-coordinate. (Marks 4)
Q25)
Find the derivative of cos (3x + 2) w.r.t. x from
the first principal. (Marks 4)
Q26) Given the following pairs of values of variables x &
y:
| x: |
3 |
5 |
7 |
12 |
20 |
22 |
24 |
| y: |
30 |
25 |
24 |
16 |
11 |
9 |
5 | (i) Find the karl Pearson's coefficient of
Correlation.
(ii) Interpret the result
(iii) Confirm your
interpretation with the help of a scatter diagram. (Marks
6)
Q27) Find the cartesian as well as vector equations of the
planes through the intersection of the planes
 . (2 + 6 ) + 12 = 0 and . (3 - + 4 ) = 0 which are at unit
distance from origin. (Marks 6)
Q28)
The Slope of the
tangent at any point of a curve is  times the slope of the
straight line joining the point of contact to the origin, formulate
the differential equation representing the problem and hence find
the equation of the curve. (Marks 6)
Q29) If
| A = |
 |
1 2
2
2 1 2
2 2 1 |
 |
find A-1 and hence prove that
A2 - 4A - 5I = 0. (Marks 6)
Q30) An open tank with a square
base and vertical sides is to be constructed from a metal sheet so
as to hold a given quantity of water. Show that the cost of the
material will be least when the depth of the tank is half of its
width. (Marks 6)
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