Board Paper of Class 12Science 2014 Maths (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
Let * be a binary operation, on the set of all nonzero real numbers, given by $a*b=\frac{ab}{5}$for all a, b ∈ R – {0}. Find the value of x, given that 2 * (x * 5) = 10. VIEW SOLUTION
 Question 2
If $\mathrm{sin}\left({\mathrm{sin}}^{1}\frac{1}{5}+{\mathrm{cos}}^{1}x\right)=1,$ then find the value of x. VIEW SOLUTION
 Question 3
If $2\left[\begin{array}{cc}3& 4\\ 5& x\end{array}\right]+\left\begin{array}{cc}1& y\\ 0& 1\end{array}\right=\left[\begin{array}{cc}7& 0\\ 10& 5\end{array}\right],\mathrm{find}(xy).$ VIEW SOLUTION
 Question 4
Solve the following matrix equation for x: $\left[x1\right]\left[\begin{array}{cc}1& 0\\ 2& 0\end{array}\right]=\mathrm{O}.$ VIEW SOLUTION
 Question 5
If $\left\begin{array}{cc}2x& 5\\ 8& x\end{array}\right=\left\begin{array}{cc}6& 2\\ 7& 3\end{array}\right$, write the value of x. VIEW SOLUTION
 Question 6
Write the antiderivative of $\left(3\sqrt{x}+\frac{1}{\sqrt{x}}\right).$ VIEW SOLUTION
 Question 7
Evaluate : ${\int}_{0}^{3}\frac{\mathrm{d}x}{9+{x}^{2}}$ VIEW SOLUTION
 Question 8
Find the projection of the vector $\hat{\mathrm{i}}+3\hat{\mathrm{j}}+7\hat{\mathrm{k}}$ on the vector $2\hat{\mathrm{i}}3\hat{\mathrm{j}}+6\hat{\mathrm{k}}$. VIEW SOLUTION
 Question 9
If $\overrightarrow{\mathrm{a}}\mathrm{and}\overrightarrow{\mathrm{b}}$ are two unit vectors such that $\overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}}$ is also a unit vector, then find the angle between $\overrightarrow{\mathrm{a}}\mathrm{and}\overrightarrow{\mathrm{b}}$. VIEW SOLUTION
 Question 10
Write the vector equation of the plane, passing through the point (a, b, c) and parallel to the plane $\overrightarrow{\mathrm{r}}\xb7\left(\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}\right)=2$. VIEW SOLUTION
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