List of top Applied Mathematics Questions

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.

The mean weekly sales of a 4-wheeler was 50 units per agency in 20 agencies. After an advertising campaign, the mean weekly sales increased to 55 units per agency with a standard deviation of 10 units. Test whether the advertising campaign was successful.
[Given \( \sqrt{5} = 2.24 \), \( t_{19}(0.05) = 1.729 \)]
Evaluate \( \int_{0}^{2} x^2 \, dx \) and hence show the region on the graph whose area it represents.
Find the differential equation of all circles in the first quadrant which touch both the coordinate axes.
Evaluate \( \int_{0}^{1} \frac{e^{-x}}{1 + e^x} \, dx \).

A man bought an item for ₹ 12,000. At the end of the year, he decided to sell it for ₹ 15,000. If the inflation rate was 6%, find the nominal and real rate of return.

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

Find the solution to the following linear programming problem (if it exists) graphically: 

Maximize \( Z = x + y \) 
Subject to the constraints \[ x - y \leq -1, \quad -x + y \leq 0, \quad x, y \geq 0. \]

Using Cramer's rule, solve the following system of equations: \[ 2x_1 + 3x_2 = 5 \] \[ 11x_1 - 5x_2 = 6 \]
Given matrix equation: \[ \begin{bmatrix} x - y & 2x + z \\ 2x - y & 3z + w \end{bmatrix} = \begin{bmatrix} -1 & 5 \\ 0 & 13 \end{bmatrix} \] Find the values of \( x, y, z, \) and \( w \).
If \[ A = \begin{bmatrix} 1 & 0 \\ -1 & 7 \end{bmatrix} \] find the value of \( k \) such that \[ A^2 - 8A + kI = 0. \]
In a binomial distribution, \( n = 200 \) and \( p = 0.04 \). Taking Poisson distribution as an approximation to the binomial distribution:
Assertion (A): Mean of Poisson distribution = 8.
Reason (R): \( P(X = 4) = \frac{512}{3e^8} \).
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 \( x \in (a, b) \).

Questions number 19 and 20 are Assertion and Reason-based questions. Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C), and (D) as given below.

(A) Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of the Assertion (A).
(B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
(C) Assertion (A) is true, but Reason (R) is false.
(D) Assertion (A) is false, but Reason (R) is true.

In an LPP, if the objective function \( Z = ax + by \) has the same maximum value on two corner points of the feasible region, then the number of points at which the maximum value of \( Z \) occurs is:
The graph of the inequation \( 2x + 3y>6 \) is the:
What sum of money should be deposited at the end of every 6 months to accumulate ₹ 50,000 in 8 years, if money is worth 6% p.a. compounded semi-annually?
\[ \text{{Given: }} (1.03)^{16} = 1.6047 \]

Using flat rate method, the EMI to repay a loan of ₹ 20,000 in \( 2 \frac{1}{2} \) years at an interest rate of 8% p.a. is:

For the given values 23, 32, 40, 47, 58, 38, 42; the 5-yearly moving averages are:
What time will it be after 1275 hours, if the present time is 9:00 p.m.?
A fair coin is tossed twice and outcomes are noted. If the random variable \( X \) represents the number of heads that appeared in the experiment, then the mathematical expectation of \( X \) is:
The order and degree of the differential equation \[ y \, dx + x \, \log{\left(\frac{y}{x}\right)} \, dy - 2x \, dy = 0 \] are respectively:
The function \( f(x) = x^2 - x + 1 \) is:
The value of \[ \Delta = \begin{vmatrix} 42 & 2 & 5 \\ 79 & 7 & 9 \\ 29 & 5 & 3 \end{vmatrix} \] is:
Amrita buys a car for which she makes a down payment of ₹ 2,50,000 and the balance is to be paid in 2 years by monthly installments of ₹ 25,448 each. If the financer charges interest at the rate of 20\% p.a., find the actual price of the car.
[Given \( \left(\frac{61}{60}\right)^{-24} = 0.67253 \)]