Board Paper of Class 12Commerce 2011 Maths Abroad(SET 2)  Solutions
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.
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
What are the direction cosines of a line that makes equal angles with the coordinate axes? VIEW SOLUTION
 Question 2
If $\overrightarrow{\mathrm{a}}\xb7\overrightarrow{\mathrm{a}}=0\mathrm{and}\overrightarrow{\mathrm{a}}\xb7\overrightarrow{\mathrm{b}}=0$, then what can be concluded about the vector $\overrightarrow{\mathrm{b}}$? VIEW SOLUTION
 Question 3
Write the position vector of the midpoint of the vector joining the points P(2, 3, 4) and Q(4, 1, −2). VIEW SOLUTION
 Question 4
Evaluate :
$\underset{1}{\overset{\sqrt{3}}{\int}}\frac{\mathrm{dx}}{1+{\mathrm{x}}^{2}}$ VIEW SOLUTION
 Question 5
If $\left\begin{array}{cc}\mathrm{x}& \mathrm{x}\\ 1& \mathrm{x}\end{array}\right=\left\begin{array}{cc}3& 4\\ 1& 2\end{array}\right$, write the positive value of x. VIEW SOLUTION
 Question 6
Write the order of the product matrix:
$\left[\begin{array}{c}1\\ 2\\ 3\end{array}\right]\left[\begin{array}{ccc}2& 3& 4\end{array}\right]$ VIEW SOLUTION
 Question 7
Write the values of x − y + z from the following equation:
$\left[\begin{array}{ccccc}x& +& y& +& z\\ & x& +& z& \\ & y& +& z& \end{array}\right]=\left[\begin{array}{c}9\\ 5\\ 7\end{array}\right]$ VIEW SOLUTION
 Question 8
Write the principal value of tan^{−1}(−1). VIEW SOLUTION
 Question 9
Write fog if f : R → R and g : R → R are given by
f(x) = x and g(x) = 5x − 2. VIEW SOLUTION
 Question 10
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