JEE Main 2016 Question Paper (03-Apr-2016)

Question 1

A particle performs simple harmonic motion with amplitude $ A $. Its speed is tripled at the instant that it is at a distance $ \frac{2A}{3} $ from the equilibrium position. The new amplitude of the motion is:

Accepted Answer

$\frac{7\mathrm{A}}{3}$

Answer

$ \mathrm{A} \sqrt{3} $

Answer

$\frac{\mathrm{A}}{3}\sqrt{41}$

Answer

$3\,\mathrm{A}$

Question 2

For a common emitter configuration, if $\alpha$ and $\beta$ have their usual meanings, the correct relationship between $\alpha$ and $\beta$ is:

Accepted Answer

$ \mathrm{\alpha} = \frac{\mathrm{\beta}}{1 + \mathrm{\beta}} $

Answer

$ \alpha = \frac{\beta_2}{1 + \beta_2} $

Answer

$ \frac{1}{\alpha} = \frac{1}{\beta} - 1 $

Answer

$ \mathrm{\alpha} = \frac{\mathrm{\beta}}{1 - \mathrm{\beta}} $

Question 3

A student measures the time period of $100$ oscillations of a simple pendulum four times. The data set is $90 \mathrm{s}$, $91 \mathrm{s}$, $95 \mathrm{s}$, and $92 \mathrm{s}$. If the minimum division in the measuring clock is $1 \mathrm{s}$, then the reported mean time should be:

Accepted Answer

$92 \pm 2 \ \mathrm{s}$

Answer

$92 \pm 1.8\,\mathrm{s}$

Answer

$92 \pm 3\,\mathrm{s}$

Answer

$92 \pm 5.0\,\mathrm{s}$

Question 4

If $a$, $b$, $c$, $d$ are inputs to a gate and $\mathrm{x}$ is its output, then, as per the following time graph, the gate is:

Accepted Answer

OR

Answer

NAND

Answer

NOT

Answer

AND

Question 5

A particle of mass $ m $ is moving along the side of a square of side $ a $, with a uniform speed $ \upsilon $ in the x-y plane as shown in the figure: Which of the following statements is false for the angular momentum $ \overrightarrow{L} $ about the origin?

Accepted Answer

$\overrightarrow{\mathrm{L}} = \frac{m \upsilon}{\sqrt{2}} R \widehat{\mathrm{k}}$ when the particle is moving from D to A.

Answer

$\overrightarrow{\mathrm{L}} = m \upsilon \left[ \frac{R}{\sqrt{2}} + a \right] \widehat{\mathrm{k}}$ when the particle is moving from B to C.

Answer

$ \overrightarrow{\mathrm{L}} = -\frac{m v}{\sqrt{2}} R \widehat{k} $ when the particle is moving from A to B.

Answer

$\overrightarrow{\mathrm{L}} = m \upsilon \left[ \frac{R}{\sqrt{2}} + a \right] \widehat{\mathrm{k}}$ when the particle is moving from C to D.