JEE Advanced 2021 — Set 1

The smallest division on the main scale of a Vernier calipers is 0.1 cm. Ten divisions of the Vernier scale correspond to nine divisions of the main scale. The figure below on the left shows the reading of this calipers with no gap between its two jaws. The figure on the right shows the reading with a solid sphere held between the jaws. The correct diameter of the sphere is

An ideal gas undergoes a four step cycle as shown in the 𝑃−𝑉 diagram below. During this cycle, heat is absorbed by the gas in

An extended object is placed at point O, 10 cm in front of a convex lens L1 and a concave lens L2 is placed 10 cm behind it, as shown in the figure. The radii of curvature of all the curved surfaces in both the lenses are 20 cm. The refractive index of both the lenses is 1.5. The total magnification of this lens system is

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

The value of 𝑡 is ___ .

The value of 𝑥 is ___ . Question Stem for Question Nos. 7 and 8 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 𝑞1 µC. Then S is switched to position Q. After a long time, the charge on the capacitor is 𝑞2 µC. SECTION 2 • This section contains THREE (03) question stems. • There are TWO (02) questions corresponding to each question stem. • The answer to each question is a NUMERICAL VALUE. • For each question, enter the correct numerical value corresponding to the answer in the designated place using the mouse and the on-screen virtual numeric keypad. • If the numerical value has more than two decimal places, truncate/round-off the value to TWO decimal places. • Answer to each question will be evaluated according to the following marking scheme: Full Marks : +2 If ONLY the correct numerical value is entered at the designated place; Zero Marks : 0 In all other cases.

The magnitude of 𝑞1 is ___ .

The magnitude of 𝑞2 is ___ . Question Stem for Question Nos. 9 and 10 Question Stem Two point charges −𝑄 and +𝑄/√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.

The value of 𝑅 is ___ meter.

The value of 𝑏 is ___ meter.