List of practice Questions

Define \( T : \mathbb{R}^3 \to \mathbb{R}^3 \) by \[ T(x, y, z) = (x + z, 2x + 3y + 5z, 2y + 2z), \quad \text{for all } (x, y, z) \in \mathbb{R}^3 \] Then, which one of the following is TRUE?

For which one of the following choices of \( N(x, y) \), is the equation \[ (e^x \sin y - 2y \sin x) \, dx + N(x, y) \, dy = 0 \] an exact differential equation?

In the given outline map of India, locate the following places by the symbol \(\bigcirc\) with names. For correct mention of name and location \(\frac{1}{2} + \frac{1}{2}\) marks have been allotted. \begin{itemize} \item[(i)] The place where the session of Indian National Congress was held in 1927. \item[(ii)] The district where Jallianwala Bagh incident took place. \item[(iii)] The place where the programme of Non-Cooperation movement was accepted. \item[(iv)] The district where Chauri-Chaura incident took place. \item[(v)] The place where the Indigo farmers' movement took place. \end{itemize}

Show the following on the given outline map of India: \begin{itemize} \item[(i)] National Corbett Park by \(\square\) symbol with name. \item[(ii)] Any one of the sea-ports on the western coast of India by \(\Delta\) symbol with name. \item[(iii)] Shivalik ranges by \(\wedge\wedge\) symbol with name. \item[(iv)] The capital of Gujarat by \(\bigcirc\) symbol with name. \item[(v)] Any one main region of coal by \(C\) symbol with name. \end{itemize}

What is meant by Satyagraha? What were the views of Mahatma Gandhi about Satyagraha?

Explain the main reasons for the rise of Nationalism in India.

Which one of the following is a biotic resource?

Economic sector of agriculture is: