MATHEMATICS
Previous year question paper with solutions for MATHEMATICS Mar-2015
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Question paper 1
SECTION - A
1. If functions
and 
are defined by 
and 
respectively find got 
Answer:
2. Write down the value of
where 
Answer:
3. Name the square matrix
in which 
Answer:
Scalar matrix
4. If
and 
then evaluate A B.Answer:
Given that
5. Evaluate the determinant
.Answer:
6. Integrate the function
Answer:
Put
7. Evaluate
Answer:
8. If
then evaluate 
Answer:
9. Find the angle between the vectors
and 
Answer:
Formula
10. A line has direction-ratios 2,-1,-2. Find its direction-cosines.
Answer:
SECTION - B
11. In a set
of all straight lines lying in a single plane, a relation R is defined by 
). Prove that 
is an equivalence relation.Answer:
Or
Find the identity element for the binary operation
defined by 
in the set of integers.Answer:
12. Prove that
where 
Answer:
13. Prove that
Answer:
14. Examine the function
for its continuity at the point 
Answer:
Or
Prove that a function differentiable at some point is continuous at that point.
Answer:
15. In the interval
find 
of mean value theorem for the function 
Answer:
16. The radius of a circle is changing uniformly at the rate of 3 cm/sec. Find the rate of change of its area when its radius is 10 cm
Answer:
17. Integrate the function
with respect to 
.Answer:
17. Integrate the function
with respect to .Answer:
or
Evaluate
Answer:
18. Find the general solution of the differential equation
Answer:
19. Find the particular solution of the differential equation
given that 
when
Answer:
20. Find the area of parallelogram whose adjacent sides are given by the vectors
and 
Answer:
21. Find the equation of a plane passing through the intersection of the planes
and 
and the point 
Answer:
22. A family has two children. If it is known that at least one of the children is a girl, then find the probability that both of the children are girls.
Answer:
Or
Prove that if E and F are two independent events, then E and F1 are also independent.
Answer:
SECTION - C
23. with the help of elementary operations, find the inverse of the following matrix –
Answer:
24. Find the equations of tangent and normal to the curve
at the point where 
Answer:
Or
Prove that the rectangle of maximum area, inscribed in a circle, is a square.
Answer:
25. Evaluate
Answer:
26. Find the area bounded by curve
and the line 
Answer:
27. Find the shortest distance between the lines
and 
Answer:
28. A bag contains 4 red and 4 black balls, and another bag contains 2 red and 6 black balls. A ball is drawn at random from one of the bags and that ball is red. Find the probability that the ball is drawn from the first bag.
Answer:
Or
Find the probability distribution of the number of doublets obtained on tossing a pair of dice three times.
Answer:
29. Solve the following linear programming problem graphically -
maximize Z =4x+y
Subject to the constraints
Answer: