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If the time interval $\Delta t \to 0$ for an object in circular motion, the average acceleration becomes the instantaneous acceleration. In this scenario, the instantaneous acceleration is directed:

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Explanation

The NCERT states, 'In Fig. 3.18(c), $\Delta t \to 0$ and the average acceleration becomes the instantaneous acceleration. It is directed towards the centre*.' The footnote clarifies, 'In the limit $\Delta t \to 0$, $\Delta r$ becomes perpendicular to r. In this limit $\Delta v \to 0$ and is consequently also perpendicular to V. Therefore, the acceleration is directed towards the centre, at each point of the circular path.' Since the velocity vector is tangential, the acceleration (towards the center) is perpendicular to the velocity.

Consider a car on a level road taking a circular turn. If $v$ is the speed, $R$ is the radius, and $\mu_s$ is the coefficient of static friction, the condition for the car not to slip is:

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Explanation

The NCERT text mentions that for a car on a level road, $f_s \le \mu_s N$. Since $N = mg$ and $f_s = mv^2/R$, we have $mv^2/R \le \mu_s mg$. This simplifies to $v^2/R \le \mu_s g$, or $v^2 \le \mu_s R g$. This is the condition for not slipping.

For a rigid body rotating about a fixed axis, which of the following quantities is the same for all particles of the body?

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Explanation

The NCERT text states, 'We observe that at any given instant the relation $v = \omega r$ applies to all particles of the rigid body. ... We use the same angular velocity $\omega$ for all the particles. We therefore, refer to $\omega$ as the angular velocity of the whole body.'

When an object moves in uniform circular motion, what can be said about its average speed compared to the magnitude of its average velocity over a given time interval?

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Explanation

The 'POINTS TO PONDER' section states, 'The average speed of an object is greater than or equal to the magnitude of the average velocity over a given time interval. The two are equal only if the path length is equal to the magnitude of displacement.' In circular motion, unless the time interval is zero, path length is generally greater than displacement, so average speed is greater or equal.

After the biosynthetic stage in biotechnological processes, the product undergoes a series of steps to be made ready for marketing. These steps are collectively known as:

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Explanation

As per the NCERT text, 'After completion of the biosynthetic stage, the product has to be subjected through a series of processes before it is ready for marketing as a finished product. The processes include separation and purification, which are collectively referred to as Downstream Processing.'

Which of the following processes are inherently part of Downstream Processing?

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Explanation

The NCERT text explicitly states that 'The processes include separation and purification, which are collectively referred to as Downstream Processing.'

The primary objective of Downstream Processing is to:

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Explanation

The NCERT states, 'After completion of the biosynthetic stage, the product has to be subjected through a series of processes before it is ready for marketing as a finished active product.' This indicates the primary objective.

Which of the following would NOT be directly involved in the 'downstream processing technologies' as mentioned in the context of biotechnology's critical research areas?

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Explanation

Genetic modification of the organism (option 4) falls under providing the best catalyst (an improved organism) or creating the specific gene product, which is an upstream or biosynthetic step. Downstream processing specifically deals with purifying the protein/organic compound after it has been produced.

A biotechnological product, after being produced in a bioreactor, must undergo a critical series of steps before reaching the market. These steps are referred to as:

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Explanation

The entirety of steps from separation and purification to final preparation for marketing is termed Downstream Processing. Formulation and packaging are part of making it ready, but Downstream Processing encompasses more, including separation and purification.

In the context of biotechnology, what is the ultimate stage mentioned after purification of a gene product and before marketing?

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Explanation

The summary mentions, 'expression of the foreign gene, purification of the gene product, i.e., the functional protein and finally making a suitable formulation for marketing.' This 'making a suitable formulation' is part of downstream processing, coming after purification and before marketing.

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