List of top Applied Mathematics Questions asked in CBSE CLASS XII

If a random variable \( X \) has the probability distribution:
\[ P(X = x) = \begin{cases} k, & \text{if } x = 0 \\ 2k, & \text{if } x = 1 \text{ or } 2 \\ 0, & \text{otherwise} \end{cases} \] then the value of \( k \) is
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 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 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
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
The variations which occur due to change in climate, festivals or weather conditions are known as
The mean of $t$-distribution is
A pair of dice is thrown two times. If $X$ represents the number of doublets obtained, then the expectation of $X$ is
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 slope of the normal to the curve \( y = \frac{x - 3}{x - 4} \) at \( x = 6 \) is
If \( \left| \begin{array}{cc} 2x & 5 \\ 4 & x \end{array} \right| = \left| \begin{array}{cc} 3 & 5 \\ 4 & 6 \end{array} \right| \), then the value of \( x \) is:
The inverse of matrix \( A = \begin{bmatrix} 4 & -1 \\ 2 & 1 \end{bmatrix} \) is
If $A$ and $B$ are symmetric matrices of the same order, then $(AB' - BA')$ is a
If $a>b$ and $c<0$, then which of the following is true?
$-41 \mod 9$ 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.
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?
If \( R_1 \) is the feasible region, then what are the other two non-trivial constraints?
What are the two trivial constraints?
Determine the values of \( x \) and \( y \).
Find the inverse of matrix \( A \).
Write the system of linear equations, obtained in (i) above, in matrix form \( AX = B \).