Maths Week 6 Graded Assignments IIT Madras

Maths week 6 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. If $1 8^{x} - 1 2^{x} - (2 \times 8^{x}) = 0$ , then the value of $x$ is.

l n 3 - l n 2 l n 2

l n 12 - l n 8 l n 18

ln 2

ln 18

No, the answer is incorrect.
Score: 0

Accepted Answers:

l n 3 - l n 2 l n 2

2. Suppose three distinct persons $A$ , $B$ and $C$ are standing on the $X$ – axis of the $X Y$ – plane (as shown in the figure) and the distance between $B$ and $A$ is same as the distance between $C$ and $B$ . The coordinates of $A$ , $B$ and $C$ are (log $_{5} 3$ , 0), (log $_{5} (3^{x} - 2 9)$ ,0) and (log $_{5} (3^{x} - 4 9)$ , 0) respectively. What is the distance between $C$ and $B$ ?

No, the answer is incorrect.
Score: 0

Accepted Answers:

(Type: Range) 0.24,0.26

1 point

3. In a city, a rumour is spreading about the safety of corona vaccination. Suppose $N$ number of people live in the city and $f (t)$ is the number of people who $have not$ yet heard about the rumour after $t$ days. Suppose $f (t)$ is given by $f (t) = N e^{- k t}$ , where $k$ is a constant. If the population of the city is $1000$ , and suppose $40$ have heard the rumor after the first day. After how many days (approximately) half of the population would have heard the rumor?
Note: Enter the nearest integer value.

No, the answer is incorrect.
Score: 0

Accepted Answers:

(Type: Numeric) 17

1 point

Use the following information for the questions 4 and 5.

Consider the function $f (x) = 3 e ^{x} + 1 2 e ^{x}$ from $R$ to $R$ .

1 point

4. Which of the following is true about $f$ ?

f

is not a one to one function.

f

is a one to one function.

Range of

f

R

f

is a bijective function.

No, the answer is incorrect.
Score: 0

Accepted Answers:

f

is a one to one function.

1 point

5. The inverse of $f$ would be

ln (2 - 3 x 2 x)

ln (2 - 3 x x)

ln (2 - x x)

No, the answer is incorrect.
Score: 0

Accepted Answers:

ln (2 - 3 x x)

Use the following information for the questions 6 and 7.

The amount of gold (in kilograms) sold by a jeweler on the $m$ th day of 2019 is given by the function $f (m) = lo g_{10} (m + 1) - 2 1 lo g_{m + 1} (0.01)$ (where $m = 1$ corresponds to the $1$ st January, $2019$ , and $m = 365$ corresponds to the $31$ st December, $2019$ ).

1 point

6. If $m > n > 9$ , then choose the correct option(s).

f (m) > f (n)

f (m) < f (n)

f (m) = f (n)

f (m) \leq f (n)

No, the answer is incorrect.
Score: 0

Accepted Answers:

f (m) > f (n)

1 point

7. Choose the correct option(s).

The jeweler sold

540

kg gold in

2019

The jeweler sold at least

730

kg gold in

2019

The jeweler sold at least

2

kg gold daily throughout the year

2019

The jeweler sold at least

10

kg gold daily throughout the year

2019

No, the answer is incorrect.
Score: 0

Accepted Answers:

The jeweler sold at least

730

kg gold in

2019

The jeweler sold at least

2

kg gold daily throughout the year

2019

1 point

8. The stock market chart of a tourism company $(A)$ is shown roughly in the Figure below. This company was listed in February $(x = 2)$ and experiences a logarithmic fall after the COVID $- 19$ outbreak which is given by $y = - a l o g (x - h) + a$ . $x$ represents the number of months since the beginning of the year and $y$ represents the stock price in ₹(1000). During the $1 0^{t h}$ month the pharmacy company announced that the vaccine is made for the COVID $- 19$ . Thereafter, the stock price of the company $(A)$ is raised exponentially $y = 1 0^{b x} - b$ . Choose the correct set of options. (Note: $a$ is any positive real number, $b$ is a positive integer and $h$ is a constant.)

For logarithmic fall the value of

a = 1.5

and

h = 2

For exponential rise passing through

(10, 0)

the value of

b = 10

The stock price in

1 2^{t h}

month is ₹4000.

If the vaccine was not made and the stock price just followed the same logarithmic function through out, then the investor would have lost his/her entire investment on the

1 2^{t h}

month.

No, the answer is incorrect.
Score: 0

Accepted Answers:

For logarithmic fall the value of

a = 1.5

and

h = 2

For exponential rise passing through

(10, 0)

the value of

b = 10

If the vaccine was not made and the stock price just followed the same logarithmic function through out, then the investor would have lost his/her entire investment on the