List of top Applied Mathematics Questions on Absolute maxima and Absolute minima

At 6 % p.a., compounded quarterly, find the present value of a perpetuity of ₹ 600 payable at the end of each quarter.

Given that the scores of a set of candidates on an IQ test are normally distributed, if the IQ test has a mean of 100 and a standard deviation of 10, determine the probability that a candidate who takes the test will score between 90 and 110.
[Given \( P(Z<1) = 0.8413 \) and \( P(Z<-1) = 0.1587 \)]

Assertion (A): The function \( f(x) = x^2 - x + 1 \) is strictly increasing on \((-1, 1)\). Reason (R): If \( f(x) \) is continuous on \([a, b]\) and derivable on \((a, b)\), then \( f(x) \) is strictly increasing on \([a, b]\) if \( f'(x)>0 \) for all \( x \in (a, b) \).

A mobile phone costs ₹ 12,000 and its scrap value after a useful life of 3 years is ₹ 3,000. Then, the book value of the mobile phone at the end of 2 years is:

The function \( f(x) = x^2 - x + 1 \) is:

If \( x>y \) and \( z<0 \), then:

In number theory, it is often important to find factors of an integer \( N \). The number \( N \) has two trivial factors, namely 1 and \( N \). Any other factor, if it exists, is called a non-trivial factor of \( N \). Naresh has plotted a graph of some constraints (linear inequations) with points \( A(0, 50) \), \( B(20, 40) \), \( C(50, 100) \), \( D(0, 200) \), and \( E(100, 0) \). This graph is constructed using three non-trivial constraints and two trivial constraints. One of the non-trivial constraints is \( x + 2y \geq 100 \).

Based on the above information, answer the following questions:

On her birthday, Prema decides to donate some money to children of an orphanage home.

If there are 8 children less, everyone gets ₹ 10 more. However, if there are 16 children more, everyone gets ₹ 10 less. Let the number of children in the orphanage home be \( x \) and the amount to be donated to each child be \( y \).

Based on the above information, answer the following questions:

Let \( X \) denote the number of hours a Class 12 student studies during a randomly selected school day. The probability that \( X \) can take the values \( x_i \), for an unknown constant \( k \):

\[ P(X = x_i) = \begin{cases} 0.1, & {if } x_i = 0, \\ kx_i, & {if } x_i = 1 { or } 2, \\ k(5 - x_i), & {if } x_i = 3 { or } 4. \end{cases} \]

Find the effective rate which is equivalent to a normal rate of 10% p.a. compounded:

Given:

\[ (1.05)^2 = 1.1025, \quad (1.025)^4 = 1.1038. \]

A recent accounting graduate opened a new business and installed a computer system that costs ₹ 45,200. The computer system will be depreciated linearly over 3 years and will have a scrap value of ₹ 0.