Model Question Paper - 5: Ii P.U.C Mathematics
Model Question Paper - 5: Ii P.U.C Mathematics
Model Question Paper - 5: Ii P.U.C Mathematics
II P.U.C
MATHEMATICS (35)
(i)
The question paper has five parts namely A, B, C, D and E. Answer all the parts.
(ii)
Use the graph sheet for the question on Linear programming in PART E.
PART A
10 1=10
2.
3.
Give an example of a relation which is reflexive and symmetric but not transitive.
(
).
Find the value of
Define a scalar matrix.
4.
If|
5.
6.
Differentiate
Evaluate:
1.
with respect to
7.
Find the vector components of the vector with initial point (2,1) and terminal point
(-5,7).
8
What is the equation of the plane that cuts the coordinate axes at (a,0,0),(0,b,0) and
(0,0,c).
9. Define the term corner point in the L. P. P.
10. If E is an event of a sample space S of an experiment then find P(S/F).
PART
B
10 2=20
defined on
(
( )
by
is associative or not.
).
5
14.
Let A(1,3), B(0,0) and C(k,0) be the vertices of triangle ABC of area 3 sq. units .Find k using
determinant method.
15
16.
Find
17.
Find the intervals in which the function f given by f(x)=x 2-4x+6 is strictly increasing.
18.
Evaluate:
19.
Evaluate:
, If
, -
is not differentiable at
20.
a and b
21.
If either
or
with an example.
22.
23.
then
) and
and
).
24. A fair die is rolled. Consider the events E={1,3,5), F={2,3} and G={2,3,4,5}.
Find (i)P(E/F) (ii) P(E/G)
PART C
10 3=30
28.
If
, find
.
]
/
0
+ as
*(
.
1
( )
( )
, in the interval ,
- where
30.
Find two positive numbers whose sum is 16 and the sum of whose cubes is minimum.
31.
Find
32.
Evaluate:
33.
34.
35.
)(
dx.
36.
Show that the points A(-1,4,-3), B(3,2,-5) C(-3,8,-5) and D(-3,2,1) are coplanar.
37.
Find the Cartesian and vector equation of the line that passes through the points (3,-2,-5)
and (3,-2,6)
38.
A die is thrown. If E is the event the number appearing is a multiple of 3 and F be the
event The number appearing is even. Then find whether E and F are independent?
PART D
6 5=30
39.
If
40.
If
41.
, where
) , prove that (
42.
If
43.
A particle moves along the curve 6y=x2+2. Find the points on the curve at which the ycoordinate is changing 8 times as fast as the x- coordinate.
44.
46.
47.
Derive the formula to find the shortest distance between the two skew lines
48.
PART E
1 10=10
49. (a) A manufacturer produces nuts and bolts. It takes 1 hour of work on machine A and 3
hours on machine B to produce a package of nuts. It takes 3 hours on machine A and 1
hour on machine B to produce a package of bolts. He earns a profit of Rs 17.50 per
package on nuts and Rs 7.00 per package on bolts. How many packages of each should
be produced each day so as to maximize his profit, if he operates his machines for at the
most 12 hours a day?
6
(b)
50. (a)
(b)
Prove that |
Prove that
|=(a-b)(b-c)(c-a).
( )
( )
| |
|.