Board Paper of Class 12Commerce 2014 Maths Abroad(SET 1)  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. You may ask for logarithmic tables, if required.
 Question 1
Let R = {(a, a^{3}) : a is a prime number less than 5} be a relation. Find the range of R. VIEW SOLUTION
 Question 2
Write the value of ${\mathrm{cos}}^{1}\left(\frac{1}{2}\right)+2{\mathrm{sin}}^{1}\left(\frac{1}{2}\right)$. VIEW SOLUTION
 Question 3
Use elementary column operations ${\mathrm{C}}_{2}\to {\mathrm{C}}_{2}2{\mathrm{C}}_{1}$ in the matrix equation $\left(\begin{array}{cc}4& 2\\ 3& 3\end{array}\right)=\left(\begin{array}{cc}1& 2\\ 0& 3\end{array}\right)\left(\begin{array}{cc}2& 0\\ 1& 1\end{array}\right)$. VIEW SOLUTION
 Question 4
If $\left(\begin{array}{cc}\mathrm{a}+4& 3\mathrm{b}\\ 8& 6\end{array}\right)=\left(\begin{array}{cc}2\mathrm{a}+2& \mathrm{b}+2\\ 8& \mathrm{a}8\mathrm{b}\end{array}\right),$write the value of a − 2b. VIEW SOLUTION
 Question 5
If A is a 3 × 3 matrix, $\left\mathrm{A}\right\ne 0\mathrm{and}\left3\mathrm{A}\right=\mathrm{k}\left\mathrm{A}\right$, then write the value of k. VIEW SOLUTION
 Question 6
Evaluate :
$\int \frac{\mathrm{dx}}{{\mathrm{sin}}^{2}\mathrm{x}{\mathrm{cos}}^{2}\mathrm{x}}$ VIEW SOLUTION
 Question 7
Evaluate :
$\underset{0}{\overset{\frac{\pi}{4}}{\int}}\mathrm{tan}\mathrm{x}\mathrm{dx}$ VIEW SOLUTION
 Question 8
Write the projection of vector $\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}$ along the vector $\hat{\mathrm{j}}$. VIEW SOLUTION
 Question 9
Find a vector in the direction of vector $2\hat{\mathrm{i}}3\hat{\mathrm{j}}+6\hat{\mathrm{k}}$ which has magnitude 21 units. VIEW SOLUTION
 Question 10
Find the angle between the lines $\overrightarrow{r}=2\hat{i}5\hat{j}+\hat{k}+\lambda \left(3\hat{i}+2\hat{j}+6\hat{k}\right)\mathrm{and}\overrightarrow{r}=7\hat{i}6\hat{k}+\mu \left(\hat{i}+2\hat{j}+2\hat{k}\right)$. VIEW SOLUTION
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