JEE Main 2017 Question Paper (02-Apr-2017)

Question 1

A radioactive nucleus $A$ with a half-life $T$ decays into a nucleus $B$. At $t=0$, there is no nucleus $B$. At some time $t$, the ratio of the number of $B$ to that of $A$ is $0.3$. Then, $t$ is given by: $ t = \frac{T}{\ln 2} \ln \left( \frac{1 + 0.3}{1 - 0.3} \right) $ (Consider $\log_e(x) = \log(x)$)

Accepted Answer

$ t = T \frac{\log 1.3}{\log 2} $

Answer

$ t = \frac{T}{\log(1.3)} $

Answer

$ t = \frac{T}{2} \frac{\log 2}{\log 1.3} $

Answer

$ t = T \log\left(1.3\right) $

Question 2

The following observations were taken for determining surface tension $T$ of water by capillary method:
diameter of capillary, $D = 1.25 \times 10^{-2} \mathrm{m}$
rise of water, $h = 1.45 \times 10^{-2} \mathrm{m}$
Using $g = 9.80 \quad \mathrm{m} \, \mathrm{s}^{-2}$ and the simplified relation \[ T = \frac{r h g}{2} \times 10^{3} \mathrm{N} \, \mathrm{m}^{-1} \] the possible error in surface tension is closest to:

Accepted Answer

$1.5\%$

Answer

$10\%$

Answer

$0.15\%$

Answer

$2.4\%$

Question 3

An electron beam is accelerated by a potential difference $V$ to hit a metallic target to produce $X$-rays. It produces continuous as well as characteristic $X$-rays. If ${\lambda}_{min}$ is the smallest possible wavelength of $X$-ray in the spectrum, the variation of $\log\left({\lambda}_{min}\right)$ with $\log\left(V\right)$ is correctly represented in :

Accepted Answer

""

Answer

Answer

Answer

Question 4

The moment of inertia of a uniform cylinder of length $l$ and radius $R$ about its perpendicular bisector is $I$. What is the ratio $\frac{l}{R}$ such that the moment of inertia is minimum?

Accepted Answer

$\sqrt{\frac{3}{2}}$

Answer

$\frac{3}{\sqrt{2}}$

Answer

$\frac{\sqrt{3}}{2}$

Answer

$1$

Question 5

A slender uniform rod of mass $M$ and length $l$ is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle $\theta$ with the vertical is:

Accepted Answer

$ \frac{3g}{2l} \sin \theta $

Answer

$ \frac{2g}{3l} \cos \theta $

Answer

$ \frac{2g}{3l} \sin \theta $

Answer

$ \frac{3g}{2l} \cos 	heta $