List of top Applied Mathematics Questions

Assertion (A): The area of the region bounded by the line $y - 1 = x$, the $x$-axis and the ordinates $x = -1$ and $x = 1$ is 2 square units.
Reason (R): The area of the region bounded by the curve $y = f(x)$, the $x$-axis and the ordinates $x = a$ and $x = b$ is given by \[ \int_{a}^{b} f(x)\, dx. \]
A boat goes 3.5 km upstream and then returns. Total time taken is 1 hour and 12 minutes. If the speed of the current is 1 km/h, then find the speed of the boat in still water.
If the cost function and revenue function of $x$ items are respectively given as $C(x) = 100 + 0.015x^2$, $R(x) = 3x$, then the value of $x$ for maximum profit is
The test statistic $t$ for testing the significance of differences between the means of two independent samples is given by
The demand function of a monopolist is given by $p = 30 + 5x - 3x^2$, where $x$ is quantity and $p$ is price. The marginal revenue when 2 units are sold is
The effective rate of interest equivalent to a nominal rate of 4% compounded semi-annually, is
The CAGR of an investment, whose starting value is ₹ 5,000 and it grows to ₹ 25,000 in 4 years, is: [Given $(5)^{0.25} = 1.4953$]
The rate of change of population $P(t)$ with respect to time $(t)$, where $\alpha$, $\beta$ are the constant birth and death rates, respectively, is
The variations which occur due to change in climate, festivals or weather conditions are known as
A pair of dice is thrown two times. If $X$ represents the number of doublets obtained, then the expectation of $X$ is
The present value of a sequence of payments of ₹ 100 made at the end of every year and continuing forever, if the money is worth 5% compounded annually, is
The mean of $t$-distribution is
In a LPP, the maximum value of $z = 3x + 4y$ subject to the constraints $x + y \leq 40$, $x + 2y \leq 60$, $x, y \geq 0$ is
$-41 \mod 9$ is
If $A$ and $B$ are symmetric matrices of the same order, then $(AB' - BA')$ is a
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?
\[ \text{{Given: }} (1.03)^{16} = 1.6047 \]
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 \( \sqrt{5} = 2.24 \), \( t_{19}(0.05) = 1.729 \)]
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 value of \[ \Delta = \begin{vmatrix} 42 & 2 & 5 \\ 79 & 7 & 9 \\ 29 & 5 & 3 \end{vmatrix} \] is:

Fit a straight-line trend by the method of least squares for the following data:

\[ \begin{array}{|c|c|c|c|c|c|c|c|} \hline \textbf{Year} & 2004 & 2005 & 2006 & 2007 & 2008 & 2009 & 2010 \\ \hline \textbf{Profit (₹ 000)} & 114 & 130 & 126 & 144 & 138 & 156 & 164 \\ \hline \end{array} \]
Tabulate the trend values of the years and compute the expected sales trend for the year 2002.
Determine the equation of the straight-line trend.

When observed over a long period of time, a time series data can predict trends that can forecast increase, decrease, or stagnation of a variable under consideration. The table below shows the sale of an item in a district during 1996–2001:

\[ \begin{array}{|c|c|c|c|c|c|c|} \hline \textbf{Year} & 1996 & 1997 & 1998 & 1999 & 2000 & 2001 \\ \hline \textbf{Sales (in lakh ₹)} & 6.5 & 5.3 & 4.3 & 6.1 & 5.6 & 7.8 \\ \hline \end{array} \]
If \( R_1 \) is the feasible region, then find the maximum value of the objective function \( z = 5x + 2y \).
If \( R_2 \) is the feasible region, then what are the other two non-trivial constraints?