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Instructions

For the following questions answer them individually

Question 21

Question 22

Question 23

## A heavy nucleus Q of half-life 20 minutes undergoes alpha-decay with probability of 60% and beta-decay with probability of 40%. Initially, the number of Q nuclei is 1000. The number of alpha-decays of Q in the first one hour is

Instructions

Question Stem
A projectile is thrown from a point O on the ground at an angle $$45^\circ$$ from the vertical and with a speed $$5\sqrt{2}$$ m/s. The projectile at the highest point of its trajectory splits into two equal parts. One part falls vertically down to the ground, 0.5 s after the splitting. The other part, 𝑡 seconds after the splitting, falls to the ground at a distance 𝑥 meters from the point O. The acceleration due to gravity $$g = 10 m/s^2$$.

Question 24

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Question 25

## The value of 𝑥 is ___.

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Question Stem
In the circuit shown below, the switch S is connected to position P for a long time so that the charge on the capacitor becomes $$q_1 \mu C$$. Then S is switched to position Q. After a long time, the charge on the capacitor is $$q_2 \mu C$$.

Question 26

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Question 27

## The magnitude of $$q_2$$ is ___ .

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Question Stem
Two point charges $$−Q$$ and $$+ \frac{Q}{\sqrt{3}}$$ are placed in the xy-plane at the origin (0, 0) and a point (2, 0), respectively, as shown in the figure. This results in an equipotential circle of radius 𝑅 and potential 𝑉=0 in the xy-plane with its center at (b, 0). All lengths are measured in meters.

Question 28

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Question 29

## The value of b is ___ meter.

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Instructions

For the following questions answer them individually

Question 30