# 12th Maths Paper Solutions Set 3 : CBSE Delhi Previous Year 2011

General Instructions:
i. All questions are compulsory.
ii. The question paper consists of 29 questions divided into three sections A, B and C. Section A comprises of 10 questions of one mark each, Section B comprises of 12 questions of four marks each, and Section C comprises of 7 questions of six marks each.
iii. All questions in section A are to be answered in one word, one sentence or as per the exact requirements of the question.
iv. There is no overall choice. However, internal choice has been provided in 4 questions of four marks each and 2 questions of six marks each. You have to attempt only one of the alternatives in all such questions.
v. Use of calculators is not permitted.
Q1 :

Write the value of We know that if which is the principal value branch of  Q2 :

Write the value of  Q3 :

State the reason for the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} not to be transitive.

It is known that a relation R in a set A is transitive if (a1, a2) âˆˆR and (a2, a3) âˆˆ R â‡’ (a1, a3) âˆˆ R &mnForE; a1, a2, a3âˆˆ A.

It can be observed that (1, 2), (2, 1) âˆˆ R, but (1,1) âˆ‰ R.

Thus, the relation R in the set {1, 2, 3} is not transitive.

Q4 :

For a 2 x 2 matrix, A = [aij] whose elements are given by , write the value of a12.

Q5 :

For what value of x, the matrix is singular?

Q6 :

Write A-1 for Q7 :

Write the value of Q8 :

For what value of ‘a’ the vectors are collinear?

Q9 :

Write the direction cosines of the vector Q10 :

Write the intercept cut off by the plane 2x + yz = 5 on x-axis.

Q11 :

Using properties of determinants, prove the following: Q12 :

Find the values of a and b such that the following function f (x) is a continuous function: Q13 :

Solve the following differential equation: Q14 :

If two vectors are such that then find the value of Q15 :

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 *.

Q16 :

Prove the following: OR Q17 : OR Q18 :

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.

Q19 : OR Q20 :

Solve the following differential equation: Q21 :

Find the angle between the following pair of lines: and check whether the lines are parallel or perpendicular.

Q22 :

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.

Q23 :

A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a six.

Find the probability that it is actually a six.

Q24 :

Show that of all the rectangles of given area, the square has the smallest perimeter.

Q25 :

Using matrix method, solve the following system of equations: OR

Using elementary transformations, find the inverse of the matrix Q26 :

Using integration find the area of the triangular region whose sides have equations y = 2x + 1, y = 3x + 1 and x = 4.

Q27 : OR Q28 :

Find the equation of the plane which contains the line of intersection of the planes and which is perpendicular to the plane 