List of practice Questions

Prove the following identities, where the angles involved are acute angles for which the expressions are defined:\(\text{(sin A + cosec A)² + (cos A + sec A)² = 7 + tan² A + cot² A}\)
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:\(\frac{\text{(sinθ - 2sin³θ)}}{\text{(2cos³θ - cosθ)}} = \text{tan θ}\)

While cooking, if the bottom of the vessel is getting blackened on the outside, it means that

Butanone is a four-carbon compound with the functional group

Ethane, with the molecular formula C2H6 has

Prove the following identities, where the angles involved are acute angles for which the expressions are defined:\(\sqrt{\frac{\text{1 + sin A}}{\text{1 - sin A }}}= \text{sec A+ tan A}\)
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:\(\frac{(\text{cos A - sin A + 1})}{\text{(cos A + sin A + 1)}} = \text{cosec A + cot A}\), using the identity cosec2 A = 1 + cot2 A.
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:\(\frac{(1 + \text{sec A})}{\text{sec A}} = \frac{\text{sin² A}}{(\text{1 - cos A})}\) [Hint: Simplify LHS and RHS separately]
Prove the following identities, where the angles involved are acute angles for which the expressions are defined: \(\frac{\text{tan θ}}{(\text{1 - cot θ})} + \frac{\text{cot θ}}{(\text{1 - tan θ})} = 1 + \text{secθ cosecθ}\) [Hint: Write the expression in terms of \(\text{sin θ}\) and \(\text{cos θ}\)]
Prove the following identities, where the angles involved are acute angles for which the expressions are defined: \(\frac{\text{cos A}}{(1 + \text{sin A})} + \frac{(1 +\text{ sin A})}{\text{cos A }}=\text{ 2 sec A}\)
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:\( (\text{cosec θ}-\text{cot θ})²=\frac{(1-\text{cos θ})}{(1 +\text{cos θ})}\)
Choose the correct option. Justify your choice. \(\frac{(1 + \text{tan}^2 A)}{(1 +\text{ cot}^ 2 A)}\)
Choose the correct option. Justify your choice. (sec A + tan A) (1 - sin A)
What is biological magnification? Will the levels of this magnification be different at different levels of the ecosystem?
Will the impact of removing all the organisms in a trophic level be different for different trophic levels? Can the organisms of any trophic level be removed without causing any damage to the ecosystem?
Choose the correct option. Justify your choice. \((1+\text{tan θ+sec θ}) (1+\text{cot θ - cosec θ}) =\)
What will happen if we kill all the organisms in one trophic level?
Which of the following are environment-friendly practices?
Which of the following constitute a food-chain?
Which of the following groups contain only biodegradable items?

Give two important uses of washing soda and baking soda.

What is a neutralization reaction? Give two examples.

Plaster of Paris should be stored in a moisture-proof container. Explain why?

A milkman adds a very small amount of baking soda to fresh milk.
(a) Why does he shift the pH of the fresh milk from 6 to slightly alkaline?
(b) Why does this milk take a long time to set as curd?

Fresh milk has a pH of 6. How do you think the pH will change as it turns into curd? Explain your answer.