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# Board Paper of Class 12-Humanities Term-II 2022 Math Delhi(Set 2) - Solutions

General Instructions:
1. This question paper contains three Sections - A, B and C.
2. Each section is compulsory.
3. Section - A has 6 short-answer type-I questions of 2 marks each.
4. Section - B has 4 short answer type-II questions of 3 marks each.
5. Section - C has 4 long-answer 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 $2\stackrel{^}{i}-\stackrel{^}{j}+\stackrel{^}{k}$ and parallel to the line joining the points . 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:
$\frac{dy}{dx}={e}^{x-y}+{x}^{2}{e}^{-y}$ VIEW SOLUTION

• Question 4
Events A and B are such that

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 , 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 x1, x2, x3, x4 such that 2P(X = x1) = 3P(X = x2) = P(X = x3) = 5P(X = x4).
Find the probability distribution of X. VIEW SOLUTION

• Question 7
Find:

OR

Find:
$\int \frac{2x}{\left({x}^{2}+1\right)\left({x}^{2}+2\right)}dx$ VIEW SOLUTION

• Question 8
Find the equation of the plane passing through the line of intersection of the planes   and passing through the point (–2, 3, 1). VIEW SOLUTION

• Question 9
Let . If  $\stackrel{^}{n}$ is a unit vector such that .

OR

If  are unit vectors inclined at an angle 30° to each other, then find the area of the parallelogram with  as adjacent sides. VIEW SOLUTION

• Question 10
Evaluate: $\underset{0}{\overset{\frac{\mathrm{\pi }}{2}}{\int }}\frac{1}{1+{\left(\mathrm{tan}x\right)}^{\frac{2}{3}}}\mathrm{d}x$ VIEW SOLUTION

• Question 11
Solve the following differential equation :
(y – sin2x)dx + tanx dy = 0

OR

Find the general solution of the differential equation:
(x3 + y3)dy = x2ydx VIEW SOLUTION

• Question 12
Find the area bounded by the curves y = |– 1| and y = 1, using integration. VIEW SOLUTION

• Question 13
In a factory, machine A produces 30% of total output, machine B produces 25% and the machine C produces the remaining output. The defective items produced by machines A, B and C are 1%, 1.2%, 2% respectively. An item is picked at random from a day's output and found to be defective. Find the probability that it was produced by machine B. VIEW SOLUTION

• Question 14
Two motorcycles A and B are running at the speed more than the allowed speed on the roads represented by the lines respectively. Based on the above information, answer the following questions:
(a) Find the shortest distance between the given lines.
(b) Find the point at which the motorcycles may collide. VIEW SOLUTION
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