JEE Advanced 2016 · Paper 2

An accident in a nuclear laboratory resulted in deposition of a certain amount of radioactive material of half-life 18 days inside the laboratory. Tests revealed that the radiation was 64 times more than the permissible level required for safe operation of the laboratory. What is the minimum number of days after which the laboratory can be considered safe for use?

1. A64
2. B90
3. C108
4. D120

In an experiment to determine the acceleration due to gravity g, the formula used for the time period of a periodic motion is T = 2π√[7(R − r)/5g]. The values of R and r are measured to be (60 ± 1) mm and (10 ± 1) mm, respectively. In five successive measurements, the time period is found to be 0.52 s, 0.56 s, 0.57 s, 0.54 s and 0.59 s. The least count of the watch used for the measurement of time period is 0.01 s. Which of the following statement(s) is(are) true?

1. AThe error in the measurement of r is 10%
2. BThe error in the measurement of T is 3.57%
3. CThe error in the measurement of T is 2%
4. DThe error in the determined value of g is 11%

Consider two identical galvanometers and two identical resistors with resistance R. If the internal resistance of the galvanometers R꜀ < R/2, which of the following statement(s) about any one of the galvanometers is(are) true?

1. AThe maximum voltage range is obtained when all the components are connected in series
2. BThe maximum voltage range is obtained when the two resistors and one galvanometer are connected in series, and the second galvanometer is connected in parallel to the first galvanometer
3. CThe maximum current range is obtained when all the components are connected in parallel
4. DThe maximum current range is obtained when the two galvanometers are connected in series and the combination is connected in parallel with both the resistors

A block with mass M is connected by a massless spring with stiffness constant k to a rigid wall and moves without friction on a horizontal surface. The block oscillates with small amplitude A about an equilibrium position x₀. Consider two cases:

1. (i)
   when the block is at x₀; and
2. (ii)
   when the block is at x = x₀ + A. In both the cases, a particle with mass m (< M) is softly placed on the block after which they stick to each other. Which of the following statement(s) is(are) true about the motion after the mass m is placed on the mass M?