What is the rate of depreciation?
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Top Questions on Absolute maxima and Absolute minima
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:
- CBSE CLASS XII - 2024
- Applied Mathematics
- Absolute maxima and Absolute minima
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:
- CBSE CLASS XII - 2024
- Applied Mathematics
- Absolute maxima and Absolute minima
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 \( k \):
\[ P(X = x_i) = \begin{cases} 0.1, & {if } x_i = 0, \\ kx_i, & {if } x_i = 1 { or } 2, \\ k(5 - x_i), & {if } x_i = 3 { or } 4. \end{cases} \]- CBSE CLASS XII - 2024
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- Absolute maxima and Absolute minima
- Find the intervals in which the following function \( f(x) \) is strictly increasing or strictly decreasing: \[ f(x) = 20 - 9x + 6x^2 - x^3. \]
- CBSE CLASS XII - 2024
- Applied Mathematics
- Absolute maxima and Absolute minima
- Semi-annually.
- CBSE CLASS XII - 2024
- Applied Mathematics
- Absolute maxima and Absolute minima
Questions Asked in CBSE CLASS XII exam
Fit a straight-line trend by the method of least squares for the following data:
\[ \begin{array}{|c|c|c|c|c|c|c|c|} \hline \textbf{Year} & 2004 & 2005 & 2006 & 2007 & 2008 & 2009 & 2010 \\ \hline \textbf{Profit (₹ 000)} & 114 & 130 & 126 & 144 & 138 & 156 & 164 \\ \hline \end{array} \]- CBSE CLASS XII - 2024
- Area of the region bounded
- Tabulate the trend values of the years and compute the expected sales trend for the year 2002.
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- System of Linear Equations
- Determine the equation of the straight-line trend.
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- Miscellaneous
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:
\[ \begin{array}{|c|c|c|c|c|c|c|} \hline \textbf{Year} & 1996 & 1997 & 1998 & 1999 & 2000 & 2001 \\ \hline \textbf{Sales (in lakh ₹)} & 6.5 & 5.3 & 4.3 & 6.1 & 5.6 & 7.8 \\ \hline \end{array} \]- CBSE CLASS XII - 2024
- Probability Distribution
- If \( R_1 \) is the feasible region, then find the maximum value of the objective function \( z = 5x + 2y \).
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