#### 1.Table: M2W1G1 gives functions in Column A with their types in column B and their graphs in Column C.

Choose the options which represent the correct matching of a given function with its type and its graph.

### Yes, the answer is correct.

Score: 1

### Accepted Answers:

*1 point*

#### 2, Suppose $f(x)$ is a strictly increasing function and $g(x)$ is a strictly decreasing function. If the curves represented by $f(x)$ and $g(x)$ intersect at $x=x_{0}$, then choose the set of correct options.

### No, the answer is incorrect.

Score: 0

### Accepted Answers:

### 3. Suppose $a_{n}=3n+412n_{2}−n+184n_{2}+3$. Find the value of $n→∞lima_{n}$ (correct upto 2 decimal places).

### No, the answer is incorrect.

Score: 0

### Accepted Answers:

(Type: Range) 66.60,66.70

*1 point*

#### 4. In the graphs given below, how many of the curves have a (unique) tangent at the origin (i.e., (0, 0))?

### No, the answer is incorrect.

Score: 0

### Accepted Answers:

(Type: Numeric) 2

*0 points*

- $x→0limxlog(1+x)=1$
- $x→0limxe_{x}−1=1$
- $n→∞limn(n!2πn)_{n1}=e$
- $n→∞limnn!n=e$

### No, the answer is incorrect.

Score: 0

### Accepted Answers:

(Type: Numeric) 7

*1 point*

#### 6.Find the limit of the sequence given by $a_{n}=n_{2}3+5+7+…+(2n−1)$, (where $n∈N∖{0}$).

### No, the answer is incorrect.

Score: 0

### Accepted Answers:

(Type: Numeric) 1

*1 point*

#### 7. Find the value of $5x→16_{+}lim⌊x⌋−3x→2_{−}lim⌊x⌋$, where $⌊x⌋$ denotes the greatest integer less than or equal to $x$.

### No, the answer is incorrect.

Score: 0

### Accepted Answers:

(Type: Numeric) 77

*1 point*

8. Suppose a company runs three algorithms to estimate its future growth. Suppose the error in the estimation depends on the available number $(n)$ of data as follows:

- Error in estimation by Algorithm 1: $a_{n}=6n_{2}+1n_{2}+5n$.
- Error in estimation by Algorithm 2: $b_{n}=81+(−1)_{n}n1$
- Error in estimation by Algorithm 3: $c_{n}=7e_{n}e_{n}+4$

where $n∈N∖{0}$.Suppose the company has a large amount of data in hand (we can assume $n$ tends to $∞$). Using the information given above, answer the questions below.

*1 point*

Which of the following statements is (are) correct?

### No, the answer is incorrect.

Score: 0

### Accepted Answers:

*1 point*

#### 9. Suppose a new algorithm is designed to predict the growth of the company in future and the error in estimation by the new algorithm is given by $a_{n}−b_{n}$, where $a_{n}$ and $b_{n}$ are the same as defined earlier. Choose the set of correct options.

### Yes, the answer is correct.

Score: 1

### Accepted Answers:

#### 10.Suppose the company modified the error in estimation by Algorithm 3 as $c_{n}=ne_{(12n1)}−n$.

What will be the new error in estimation by Algorithm 3? (Correct upto 3 decimal places)

### No, the answer is incorrect.

Score: 0

### Accepted Answers:

(Type: Numeric) 0.083

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