In active voice, the subject 'my mother' performs the action of baking the cake, thus it becomes 'My mother baked the cake.'

Capacitance (C) is directly proportional to the area of the plates (A) and the dielectric constant (ε) and inversely proportional to the distance (d) between the plates.

The capacitance (C) of a parallel plate capacitor is given by the formula C = ε₀A/d, where A is the area of the plates and d is the separation between them.

The capacitance of a spherical capacitor depends on both the radius of the inner sphere and the outer sphere.

The correct word is 'quick' as it implies the mouse was fast enough to escape.

A cat lives in a house just as a fish lives in a tank.

The relationship is predatory; a cat hunts a mouse just as a dog is associated with a bone.

The most logical option is 'mat' as it is a common place for a cat to sit.

The word 'excited' describes the children's feelings about the circus.

Circumference = 2πr => r = circumference / (2π) = 31.4 / (2 * 3.14) = 5 cm

The conclusion assumes that the current funding is inadequate to provide quality education, which is necessary for improving student performance.

The correct form is 'The committee has made its decision.' 'Committee' is a collective noun and is treated as singular.

The context indicates that participants were looking forward to the event, so 'disappointment' is the most fitting response.

The phrase 'eagerly anticipating' suggests that the participants were looking forward to the event, making 'disappointment' the correct choice.

Postponing an eagerly anticipated event would likely lead to disappointment rather than applause or enthusiasm.

The word 'thorough' indicates a careful and comprehensive analysis, which is essential for sound decision-making.

The context suggests a negative reaction, making 'outrage' the correct choice.

The context indicates a negative reaction, making 'outrage' the most fitting choice.

The term 'unanimous' indicates that the decision was agreed upon by all members, which fits the context of a hard-won consensus.

The word 'unanimous' indicates that all members agreed, which is consistent with the context of a consensus.

A decision reached after extensive discussions suggests it was unanimous, not arbitrary or divisive.

The word 'unanimous' indicates that the decision was made collectively, with all members in agreement.

'Ahimsa' is a fundamental principle in Indian philosophy that advocates for non-violence and respect for all living beings.

The term 'Artificial Intelligence' was coined in the 1950s during a conference at Dartmouth College.

The Congress of Vienna (1815) established the idea of buffer states in Europe to prevent any one power from becoming too dominant.

The agricultural revolution increased the carrying capacity of land, allowing for larger populations to be sustained.

Climate refugees are people who are forced to leave their homes due to sudden or gradual changes in their environment, particularly natural disasters exacerbated by climate change.

A youthful population can lead to a demographic dividend, where the working-age population is larger than the non-working-age population, potentially boosting economic growth.

'Dharma' in Indian culture refers to moral and ethical duties that guide individuals in their conduct and responsibilities.

The concept of 'Ecological Footprint' was popularized in the 1990s, providing a measure of human demand on the Earth's ecosystems and resources.