Maths 1 Quiz 2: 13 March 2022, Set QPE1 (January 2022 term)

Which of the following statements are correct?

Stock price $(y)$ (in ₹) for a motor cycle company $(A)$ is predicted by the equation

$y = -7\log_2(x + a) + 35,$

where $x$ represents the number of months since January of the year 2022 (note: for January, consider $x = 0$) and $a \in \mathbb{N}$. If the stock price of the company goes to zero in November of the year 2022, following the same trend, then find the value of $a$.

NOTE: Enter your answer to the nearest integer.

Ravi borrowed ₹3,000 and ₹12,000 from his friends Vinay and Bhumi respectively. Vinay lent the money at 7 percent simple interest per annum for 4 years and Bhumi lent the money at 10 percent compound interest per annum for $x$ years. The compound interest which Bhumi received after $x$ years is thrice the value of the simple interest which Vinay received after 4 years. What is the value of $x$?

[Note: Simple interest $= \frac{PTR}{100}$ and Compound Interest $= P(1 + \frac{R}{100})^T - P$, where $P$ is the principle amount, $T$ is time (in years) and $R$ is the interest rate per annum, i.e., if $x\%$ is the interest rate per annum then $R = x$]

NOTE: Enter your answer to the nearest integer.

If the limit exists at x = 0 for the given function f(x), then what will be the value of p?
NOTE: Enter your answer to the nearest integer.

NOTE: Enter your answer to the nearest integer.

If f is differentiable everywhere, then find the value of r.
NOTE: Enter your answer to the nearest integer.

What is the value of f(0)?
NOTE: Enter your answer to the nearest integer.

What is the value of f′(1)?
NOTE: Enter your answer to the nearest integer.

Use the following information and answer the given subquestions.

Consider a sequence $\{a_n\}$ defined as

$a_n = \begin{cases} \frac{3n - \lfloor \frac{n}{2} \rfloor}{7+n} & \text{when } n \text{ is odd} \\ \frac{5n^2 - 4n + 1}{6n + 2n^2} & \text{when } n \text{ is even} \end{cases}$

where $\lfloor x \rfloor$ is the greatest integer that is less than or equal to a real number $x$.

Which of the following statements are correct?

Use the following information and answer the given subquestions.

Consider a sequence $\{a_n\}$ defined as

$a_n = \begin{cases} \frac{3n - \lfloor \frac{n}{2} \rfloor}{7+n} & \text{when } n \text{ is odd} \\ \frac{5n^2 - 4n + 1}{6n + 2n^2} & \text{when } n \text{ is even} \end{cases}$

where $\lfloor x \rfloor$ is the greatest integer that is less than or equal to a real number $x$.

Find the limit of the sequence {4an}.
NOTE: Enter your answer to the nearest integer.

Use the following information and answer the given subquestions.

Consider a sequence $\{a_n\}$ defined as

$a_n = \begin{cases} \frac{3n - \lfloor \frac{n}{2} \rfloor}{7+n} & \text{when } n \text{ is odd} \\ \frac{5n^2 - 4n + 1}{6n + 2n^2} & \text{when } n \text{ is even} \end{cases}$

where $\lfloor x \rfloor$ is the greatest integer that is less than or equal to a real number $x$.

NOTE: Enter your answer to the nearest integer.