State the reason for the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} not to be transitive.
Answer :
It is known that a relation R in a set A is transitive if (a1, a2) ∈R and (a2, a3) ∈ R ⇒ (a1, a3) ∈ R &mnForE; a1, a2, a3∈ A.
It can be observed that (1, 2), (2, 1) ∈ R, but (1, 1) ∉ R.
Thus, the relation R in the set {1, 2, 3} is not transitive.
Write the value of 
Answer :
Thus, the value of the given expression is 1.
For a 2 x
2 matrix, A = [aij] whose elements are given by
, write
the value of a12.
Answer :
Any element in the ith row
and jth column is 
For a12, the value of i = 1 and j = 2.
Thus, the value of a12 is
.
For what value of x, the matrix 
is
singular?
Answer :
For what value of ‘a’ the vectors 
and
are
collinear?
Answer :
Write the direction cosines of the vector 
Answer :
Write the intercept cut off by the plane 2x + y − z = 5 on x-axis.
Answer :
Consider the binary operation * on the set {1, 2, 3, 4, 5} defined by a * b = min. {a, b}. Write the operation table of the operation *.
Answer :
Prove the following:
OR
Find the value of 
Answer :
Using properties of determinants, prove that
Answer :
Find the value of ‘a’ for which the function f defined as
is
continuous at x = 0
Answer :
Differentiate
.
OR
If x = a (θ
- sinθ), y = a (1 + cosθ), find
.
Answer :
Sand is pouring from a pipe at the rate of 12 cm3/s. The falling sand forms a cone on the ground in such a way that the height of the cone is always one-sixth of the radius of the base. How fast is the height of the sand cone increasing when the height is 4 cm?
OR
Find the points on the curve x2 + y2 − 2x− 3 = 0 at which the tangents are parallel to x-axis.
Answer :
Solve the following differential equation:
extan y dx + (1 − ex) sec2y dy = 0
Answer :
Solve the following differential equation:
Answer :
Find a unit vector perpendicular to each of the vector and
where
Answer :
Find the angle between the following pair of lines:
and
check whether the lines are parallel or perpendicular.
Answer :
Probabilities of solving a specific problem independently by
A and B are 
and
respectively. If both try to solve the problem independently,
find the probability that (i) the problem is solved (ii) exactly
one of them solves the problem.
Answer :
Using matrix method, solve the following system of equations:
OR
Using elementary transformations, find the inverse of the matrix
Answer :
Show that of all the rectangles inscribed in a given fixed circle, the square has the maximum area.
Answer :
Using integration find the area of the triangular region whose sides have equations y = 2x + 1, y = 3x + 1 and x = 4.
Answer :
Find the equation of the plane which contains the line of
intersection of the planes 
and
which is perpendicular to the plane 
Answer :
A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftsman”™s time in its making while a cricket bat takes 3 hours of machine time and 1 hour of craftsman”™s time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman”™s time.
If the profit on a racket and on a bat is Rs 20 and Rs 10 respectively, find the number of tennis rackets and cricket bats that the factory must manufacture to earn the maximum profit. Make it as an L.P.P. and solve graphically.
Answer :
Suppose 5% of men and 0.25% of women have grey hair. A grey haired person is selected at random. What is the probability of this person being male? Assume that there are equal number of males and females.
Answer :
12th Maths Paper Solutions Set 1 : CBSE All India Previous Year 2013 will be available online in PDF book soon. The solutions are absolutely Free. Soon you will be able to download the solutions.
