# Board Paper of Class 12-Humanities Term-II 2022 Applied Math Delhi(Set 4) - Solutions

Read the following instructions very carefully and strictly follow them:

1. This question paper contains

2.

3.

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6. There is an internal choice in some questions.

7. Question 14 is a case study based question with

**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**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
Evaluate: $\underset{0}{\overset{1}{\int}}\frac{x{e}^{x}}{{\left(x+1\right)}^{2}}dx$
**OR**

Solve the following differential equation : $\frac{dy}{dx}={e}^{x+y}+{x}^{2}{e}^{y}$ VIEW SOLUTION

- Question 2
Find the present value of a perpetuity of ₹18,000 payable at the end of 6 months, if the money is worth 8% p.a. compounded semi-annually. VIEW SOLUTION

- Question 3
Find the effective rate which is equivalent to nominal rate of 10% p.a. compounded monthly.

[Given that : (1.00833)^{12 }= 1.1047]**OR**

Abhay bought a mobile phone for ₹30,000. The mobile phone is estimated to have a scrap value of ₹3,000 after a span of 3 years. Using the linear depreciation method, find the book value of the mobile phone at the end of 2 years. VIEW SOLUTION

- Question 4
Consider the following hypothesis:

H_{0}: μ = 35

H_{1}: μ ≠ 35

A sample of 81 items is taken whose mean is 37∙5 and the standard deviation is 5. Test the hypothesis at 5% level of significance.

[Given: Critical value of Z for a two-tailed test at 5% level of significance is 1∙96] VIEW SOLUTION

- Question 5
The following table shows the annual rainfall (in mm) recorded for Cherrapunji, Meghalaya:
**Year****Rainfall**

(in mm)20011∙220021∙92003220041∙420052∙120061∙320071∙820081∙120091∙3

Determine the trend of rainfall by 3-year moving average.

- Question 6
Maximize
*z*= 3*x*+ 4*y*, if possible,

Subject to the constraints:

*x*–*y*≤ –1

–*x*+*y*≤ 0

*x*,*y*≥ 0 VIEW SOLUTION

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