Board Paper of Class 12Humanities TermII 2022 Math Delhi(Set 2)  Solutions
General Instructions:
Read the following instructions very carefully and strictly follow them:
1. This question paper contains three Sections  A, B and C.
2. Each section is compulsory.
3. Section  A has 6 shortanswer typeI questions of 2 marks each.
4. Section  B has 4 short answer typeII questions of 3 marks each.
5. Section  C has 4 longanswer type questions of 4 marks each.
6. There is an internal choice in some questions.
7. Question 14 is a case study based question with two subparts of 2 marks each.
Read the following instructions very carefully and strictly follow them:
1. This question paper contains three Sections  A, B and C.
2. Each section is compulsory.
3. Section  A has 6 shortanswer typeI questions of 2 marks each.
4. Section  B has 4 short answer typeII questions of 3 marks each.
5. Section  C has 4 longanswer type questions of 4 marks each.
6. There is an internal choice in some questions.
7. Question 14 is a case study based question with two subparts of 2 marks each.
 Question 1
Find the vector equation of a line passing through a point with position vector $2\hat{i}\hat{j}+\hat{k}$ and parallel to the line joining the points $\hat{i}+4\hat{j}+\hat{k}\mathrm{and}\hat{i}+2\hat{j}+2\hat{k}$. VIEW SOLUTION
 Question 2
Find: $\int \frac{dx}{\sqrt{4x{x}^{2}}}$ VIEW SOLUTION
 Question 3
Find the general solution of the following differential equation:
$\frac{dy}{dx}={e}^{xy}+{x}^{2}{e}^{y}$ VIEW SOLUTION
 Question 4
Events A and B are such that
$\mathrm{P}\left(\mathrm{A}\right)=\frac{1}{2},\mathrm{P}\left(\mathrm{B}\right)=\frac{7}{12}\mathrm{and}\mathrm{P}\left(\overline{\mathrm{A}}\cup \overline{\mathrm{B}}\right)=\frac{1}{4}$
Find whether the events A and B are independent or not.OR
A box ${\mathrm{B}}_{1}$ contains 1 white ball and 3 red balls. Another box ${\mathrm{B}}_{2}$ contains 2 white balls and 3 red balls. If one ball is drawn at random from each of the boxes ${\mathrm{B}}_{1}\mathrm{and}{\mathrm{B}}_{2}$, then find the probability that the two balls drawn are of the same colour. VIEW SOLUTION
 Question 5
Let X be a random variable which assumes values x_{1}, x_{2}, x_{3}, x_{4} such that 2P(X = x_{1}) = 3P(X = x_{2}) = P(X = x_{3}) = 5P(X = x_{4}).
Find the probability distribution of X. VIEW SOLUTION
 Question 6
If $\overrightarrow{a}=\hat{i}+\hat{j}+\hat{k},\overrightarrow{a}.\overrightarrow{b}=1$ and $\overrightarrow{a}\times \overrightarrow{b}=\hat{j}\u2013\hat{k},\mathrm{then}\mathrm{find}\left\overrightarrow{\mathit{b}}\right$ VIEW SOLUTION
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