Define the determinant of a 2×2 matrix and explain its significance. Find the determinant of a matrix with elements 2, 3 in the first row and 4, 5 in the second row.
Fill in the blanks:
(a) Growers of woad in Europe saw __________
as a crop which would provide competition
to their earnings.
(b) The demand for indigo increased in late
eighteenth-century Britain because of
__________.
(c) The international demand for indigo was
affected by the discovery of __________.
(d) The Champaran movement was against
__________.
Define a square matrix and explain the concept of the transpose of a matrix. Show that the transpose of a symmetric matrix is itself.
Match the following:
ryot village
mahal peasant
nij cultivation on ryot’s lands
ryoti cultivation on planter’s own land
Explain the concept of inverse trigonometric functions. Solve for x if sine inverse of x plus cosine inverse of x equals pi over 2.
Define a one-one function and an onto function. Give an example of a function that is both one-one and onto.
Define enthalpy of formation. Using Hess’s law, explain how it is used to determine the enthalpy of reaction.
Explain Charles’s law and its significance. Describe an experiment to demonstrate Charles’s law.
Explain the concept of hybridization. Describe the hybridization of carbon in methane, ethene, and ethyne.
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