Let \(\mathbf{a}, \mathbf{b}\) and \(\mathbf{c}\) be three vectors such that $\mathbf{a} \times \mathbf{b} = \mathbf{a} \times \mathbf{c} \text{ and } \mathbf{a} \times \mathbf{b} \neq 0 \text{ Show that } \mathbf{b} = \mathbf{c}$.
A carpenter needs to make a wooden cuboidal box, closed from all sides, which has a square base and fixed volume. Since he is short of the paint required to paint the box on completion, he wants the surface area to be minimum.
On the basis of the above information, answer the following questions :
Find \( \frac{dS}{dx} \).
Bittu and Chintu were partners in a firm sharing profit and losses in the ratio of 4:3. Their Balance Sheet as at 31st March, 2024 was as
On $1^{\text {st }}$ April, 2024, Diya was admitted in the firm for $\frac{1}{7}$ share in the profits on the following terms:
Prepare Revaluation Account and Partners' Capital Accounts.