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Maths Week 5 Graded Assignments IIT Madras

Maths week 5 graded assignment Complete  Solutions Are Discussed In This Blog We Hope This Might Help You All In Matching Answers . Or For Some Others Reasons Not Able To Complete Graded Assignments 

1. A graph is shown in the below figure,  symbol signifies that the straight line does not touch the point and the  symbol signifies that the line touches the point. Choose the correct option(s)


2. For �=��,where  is a positive integer and �∈�, which of the following statements are true?

3. If 4�−�= -2, then the value of (16�2�+27�96�) is

4. Half-life of an element is the time required for half of a given sample of radioactive element to change to another element.The rate of change of concentration is calculated by the formula �(�)=��(12)(��) where  is the half-life of the material, �� is the initial concentration of the radioactive element in the given sample, �(�) is the concentration of the radioactive element in the sample after time . If Radium has a half-life of 2000 years and the initial concentration of Radium in a sample was 100%, then calculate the percentage of Radium in that sample after 4000 years.

5. If �(�)=(1−�)12 and �(�)=(1−�2), then find the domain of the composite function �∘�.
6. Find the domain of the inverse function of �=�3+1.

7. If �(�)=�3, then choose the points where the graphs of the functions �(�) and �−1(�) intersect each other?

8.In a survey, the population growth in an area can be predicted according to the equation �(�)=��(1+�100)� where  is the percentage growth rate of population per year and  is the time since the initial population count �� was taken. If in 2016, the population of Adyar was 40000.0 and the population growth rate is 2% per year, then what will be the approximate population of Adyar in 2021?( �=0 corresponds to the year 2016, �=1 corresponds to the year 2017 and so on..)

1 point
9. An ant moves along the curve whose equation is �(�)=�2+1 in the restricted domain [0,∞). Let a mirror be placed along the line �=�. If the reflection of the ant with respect to the mirror moves along the curve �(�), then which of the following options is(are) correct?
1 point
10. Suppose a textile shop provides two different types of offers during a festival season. The first offer(�1) is “shop for more than 14,999 and pay only 9,999″. The second offer(�2) is “avail 30% discount on the total payable amount”. If Shalini wants to buy two dresses each of which costs more than 8,000 and she is given the choice to avail both offers simultaneously, then which of the following options is(are) correct?

1 point
11. If �(�)=�2 and ℎ(�)=�−1, then which of the following options is(are) incorrect?

1 point
12. Let �(�),   �(�),  �(�) and  �(�) be the functions defined on . Refer Figure 3 (A and B) and choose the correct option(s) from the following.

                                                                                  Figure 3

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