#### 1. If $18_{x}−12_{x}−(2×8_{x})=0$, then the value of $x$ is.

### No, the answer is incorrect.

Score: 0

### Accepted Answers:

#### 2. Suppose three distinct persons $A$, $B$ and $C$ are standing on the $X$– axis of the $XY$– 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$_{5}(3_{x}−29)$,0) and (log$_{5}(3_{x}−49)$, 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 $f(t)=Ne_{−kt}$, 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 $f(x)=3e_{x}+12e_{x}$ from $R$ to $R$.

*1 point*

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

### No, the answer is incorrect.

Score: 0

### Accepted Answers:

*1 point*

#### 5. The inverse of $f$ would be

### No, the answer is incorrect.

Score: 0

### Accepted Answers:

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 $f(m)=g_{10}(m+1)−21g_{m+1}(0.01)$ (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).

### No, the answer is incorrect.

Score: 0

### Accepted Answers:

*1 point*

### 7. Choose the correct option(s).

### No, the answer is incorrect.

Score: 0

### Accepted Answers:

*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 $y=−alog(x−h)+a$. $x$ represents the number of months since the beginning of the year and $y$ represents the stock price in ₹(1000). During the $10_{th}$ 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 $y=10_{bx}−b$. Choose the correct set of options. (Note: $a$ is any positive real number,$b$ is a positive integer and $h$ is a constant.)

### No, the answer is incorrect.

Score: 0

### Accepted Answers:

#### 9. If $m_{log_{3}2}+2_{log_{3}m}=$ 16, then what is the value of $m$ ?

### No, the answer is incorrect.

Score: 0

### Accepted Answers:

(Type: Numeric) 27

*1 point*

*1 point*

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