Board Paper of Class 12Commerce 2011 Maths (SET 1)  Solutions
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.
 Question 1
State the reason for the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} not to be transitive.
VIEW SOLUTION
 Question 2
Write the value of
VIEW SOLUTION
 Question 3
For a 2 × 2 matrix, A = [a_{ij}] whose elements are given by , write the value of a_{12}.
VIEW SOLUTION
 Question 4
For what value of x, the matrix is singular?
VIEW SOLUTION
 Question 5
Write A^{−1} for
VIEW SOLUTION
 Question 6
Write the value of
VIEW SOLUTION
 Question 7
Write the value of
VIEW SOLUTION
 Question 8
For what value of ‘a’ the vectors and are collinear?
VIEW SOLUTION
 Question 9
Write the direction cosines of the vector
VIEW SOLUTION
 Question 10
Write the intercept cut off by the plane 2x + y − z = 5 on xaxis.
VIEW SOLUTION
 Question 11
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 *.
VIEW SOLUTION
 Question 12
 Question 13
Using properties of determinants, prove that
VIEW SOLUTION
 Question 14
 Question 15
 Question 16
Sand is pouring from a pipe at the rate of 12 cm^{3}/s. The falling sand forms a cone on the ground in such a way that the height of the cone is always onesixth 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 x^{2} + y^{2} − 2x − 3 = 0 at which the tangents are parallel to xaxis.
VIEW SOLUTION
 Question 17
 Question 18
Solve the following differential equation:
e^{x} tan y dx + (1 − e^{x}) sec^{2}y dy = 0
VIEW SOLUTION
 Question 19
Solve the following differential equation:
VIEW SOLUTION
 Question 20
Find a unit vector perpendicular to each of the vector and where
VIEW SOLUTION
 Question 21
Find the angle between the following pair of lines:
and check whether the lines are parallel or perpendicular.
VIEW SOLUTION
 Question 22
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.
VIEW SOLUTION
 Question 23
Using matrix method, solve the following system of equations:
OR
Using elementary transformations, find the inverse of the matrix
VIEW SOLUTION
 Question 24
Show that of all the rectangles inscribed in a given fixed circle, the square has the maximum area.
VIEW SOLUTION
 Question 25
Using integration find the area of the triangular region whose sides have equations y = 2x + 1, y = 3x + 1 and x = 4.
VIEW SOLUTION
 Question 26
 Question 27
Find the equation of the plane which contains the line of intersection of the planes and which is perpendicular to the plane
VIEW SOLUTION
 Question 28
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.
VIEW SOLUTION
 Question 29
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.
VIEW SOLUTION

Board Paper of Class 12Commerce 2019 Math Delhi(Set 1)  Solutions

Board Paper of Class 12Commerce 2019 Math Delhi(Set 2)  Solutions

Board Paper of Class 12Commerce 2019 Math Delhi(Set 3)  Solutions

Board Paper of Class 12Commerce 2019 Math Abroad(Set 3)  Solutions

Board Paper of Class 12Commerce 2018 Maths (SET 1)  Solutions

Board Paper of Class 12Commerce 2018 Maths (SET 2)  Solutions

Board Paper of Class 12Commerce 2018 Maths (SET 3)  Solutions

Board Paper of Class 12Commerce 2018 Maths  Solutions

Board Paper of Class 12Commerce 2018 Maths  Solutions

Board Paper of Class 12Commerce 2017 Maths (SET 1)  Solutions

Board Paper of Class 12Commerce 2017 Maths (SET 2)  Solutions

Board Paper of Class 12Commerce 2017 Maths (SET 3)  Solutions

Board Paper of Class 12Commerce 2017 Maths (SET 1)  Solutions

Board Paper of Class 12Commerce 2017 Maths (SET 3)  Solutions

Board Paper of Class 12Commerce 2017 Maths (SET 3)  Solutions

Board Paper of Class 12Commerce 2016 Maths (SET 1)  Solutions

Board Paper of Class 12Commerce 2016 Maths (SET 2)  Solutions

Board Paper of Class 12Commerce 2016 Maths (SET 3)  Solutions

Board Paper of Class 12Commerce 2016 Maths (SET 2)  Solutions

Board Paper of Class 12Commerce 2016 Maths (SET 2)  Solutions

Board Paper of Class 12Commerce 2015 Maths (SET 1)  Solutions

Board Paper of Class 12Commerce 2015 Maths (SET 2)  Solutions

Board Paper of Class 12Commerce 2015 Maths (SET 3)  Solutions

Board Paper of Class 12Commerce 2015 Maths (SET 2)  Solutions

Board Paper of Class 12Commerce 2015 Maths (SET 2)  Solutions

Board Paper of Class 12Commerce 2014 Maths (SET 1)  Solutions

Board Paper of Class 12Commerce 2014 Maths (SET 1)  Solutions

Board Paper of Class 12Commerce 2014 Maths (SET 2)  Solutions

Board Paper of Class 12Commerce 2014 Maths (SET 1)  Solutions

Board Paper of Class 12Commerce 2014 Maths (SET 3)  Solutions

Board Paper of Class 12Commerce 2013 Maths (SET 1)  Solutions

Board Paper of Class 12Commerce 2013 Maths (SET 2)  Solutions

Board Paper of Class 12Commerce 2013 Maths (SET 3)  Solutions

Board Paper of Class 12Commerce 2013 Maths (SET 1)  Solutions

Board Paper of Class 12Commerce 2013 Maths (SET 2)  Solutions

Board Paper of Class 12Commerce 2012 Maths (SET 2)  Solutions

Board Paper of Class 12Commerce 2012 Maths (SET 3)  Solutions

Board Paper of Class 12Commerce 2012 Maths (SET 3)  Solutions

Board Paper of Class 12Commerce 2011 Maths (SET 2)  Solutions

Board Paper of Class 12Commerce 2011 Maths (SET 3)  Solutions

Board Paper of Class 12Commerce 2010 Maths (SET 2)  Solutions

Board Paper of Class 12Commerce 2010 Maths (SET 2)  Solutions

Board Paper of Class 12Commerce 2008 Maths (SET 1)  Solutions

Board Paper of Class 12Commerce 2007 Maths (SET 1)  Solutions

Board Paper of Class 12Commerce 2006 Maths (SET 1)  Solutions

Board Paper of Class 12Commerce 2005 Maths (SET 1)  Solutions

Board Paper of Class 12Commerce 2005 Maths (SET 1)  Solutions

Board Paper of Class 12Commerce 2004 Maths (SET 1)  Solutions

Board Paper of Class 12Commerce 2004 Maths (SET 1)  Solutions