Board Paper of Class 12Science 2014 Maths All India(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.
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
If $\mathrm{R}=\left[\left(x,y\right):x+2y=8\right]$ is a relation on N, write the range of R. VIEW SOLUTION
 Question 2
If ${\mathrm{tan}}^{1}\mathrm{x}+{\mathrm{tan}}^{1}\mathrm{y}=\frac{\pi}{4},\mathrm{xy}1,$ then write the value of $\mathrm{x}+\mathrm{y}+\mathrm{xy}$. VIEW SOLUTION
 Question 3
If A is a square matrix, such that ${\mathrm{A}}^{2}=\mathrm{A}$, then write the value of $7\mathrm{A}{\left(\mathrm{I}+\mathrm{A}\right)}^{3}$, where I is an identity matrix. VIEW SOLUTION
 Question 4
If $\left[\begin{array}{cc}\mathrm{x}\mathrm{y}& \mathrm{z}\\ 2\mathrm{x}\mathrm{y}& \mathrm{w}\end{array}\right]=\left[\begin{array}{cc}1& 4\\ 0& 5\end{array}\right]$, find the value of $\mathrm{x}+\mathrm{y}$. VIEW SOLUTION
 Question 5
If $\left[\begin{array}{cc}3\mathrm{x}& 7\\ 2& 4\end{array}\right]=\left[\begin{array}{cc}8& 7\\ 6& 4\end{array}\right]$, find the value of x. VIEW SOLUTION
 Question 6
If $\mathrm{f}\left(\mathrm{x}\right)={\int}_{0}^{x}\mathrm{t}\mathrm{sin}\mathrm{t}\mathrm{dt}$, then write the value of f ' (x). VIEW SOLUTION
 Question 7
$\underset{2}{\overset{4}{\int}}\frac{\mathrm{x}}{{\mathrm{x}}^{2}+1}\mathrm{dx}$ VIEW SOLUTION
 Question 8
Find the value of 'p' for which the vectors $3\hat{\mathrm{i}}+2\hat{\mathrm{j}}+9\hat{\mathrm{k}}$ and $\hat{\mathrm{i}}2\mathrm{p}\hat{\mathrm{j}}+3\hat{\mathrm{k}}$ are parallel. VIEW SOLUTION
 Question 9
Find $\overrightarrow{\mathrm{a}}\xb7(\overrightarrow{\mathrm{b}}\times \overrightarrow{\mathrm{c}}),\mathrm{if}\overrightarrow{\mathrm{a}}=2\hat{\mathrm{i}}+\hat{\mathrm{j}}+3\hat{\mathrm{k}},\overrightarrow{\mathrm{b}}=\hat{\mathrm{i}}+2\hat{\mathrm{j}}+\hat{\mathrm{k}}\mathrm{and}\overrightarrow{\mathrm{c}}=3\hat{\mathrm{i}}+\hat{\mathrm{j}}+2\hat{\mathrm{k}}.$ VIEW SOLUTION
 Question 10
If the Cartesian equations of a line are $\frac{3x}{5}=\frac{y+4}{7}=\frac{2z6}{4}$, write the vector equation for the line. VIEW SOLUTION
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