Identify the correct statements among the following:
(A) The gravitational force is much stronger than the Coulomb force.
(B) The nuclear force between two nucleons falls rapidly to zero as their distance is more than a few femtometers.
(C) The nuclear force depends on the electric charge.
(D) The nuclear force is much stronger than the coulomb force.
Choose the correct answer from the options given below:

A plane electromagnetic wave travels in vacuum along y-direction. At the same instant, the direction of Electric and magnetic fields are:

Which of the following equation is not correct for \( \beta \)-decay?

A storage battery of emf 8.0 V and internal resistance 0.5 \(\Omega\) is being charged by a 60 V dc supply using a series resistor of 12.5 \(\Omega\). The terminal potential difference between the terminals of the battery during charging is

A printed page is kept pressed by a glass cube-shaped paper-weight of edge 3.0 cm. The refractive index of the glass is \( \mu = 1.5 \).
By what amount will the printed letters appear to be shifted when viewed from the top?

A closely wound coil of 50 turns and radius 15 cm carries a current of 3 A. The magnetic moment of the coil is:

In the decay chain given below the sequential order in which the radioactive radiations are emitted will be :
\(^{A}_{Z}X \to ^{A}_{Z+1}Y \to ^{A-4}_{Z-1}P^* \to ^{A-4}_{Z-1}P\)

The matrix \(A=\left[\begin{array}{lll}0 & 0 & 5 \\ 0 & 5 & 0 \\ 0 & 0 & 5\end{array}\right]\) is a:

Read the following paragraph and answer the given questions.
Bio-fertilisers are organisms that enrich the nutrient quality of the soil like cyanobacteria, while there are organisms that help to control plant diseases and pests. The very familiar beetle, the ladybird and dragonflies are useful to get rid of aphids and mosquitoes, respectively. An example of microbial biocontrol agents that can be introduced to control butterfly caterpillars is certain bacteria, which are available in sachets in the form of dry spores. These spores are mixed with water and sprayed onto vulnerable plants. Trichoderma species that are very common in the root ecosystem, are very effective biocontrol agents of several plant pathogens.Baculoviruses attack insects and other arthropods. Usage of these viruses is desirable when an ecological sensitive area is being treated.
Find the odd one out of the given organisms?

Consider an LPP: Maximise \(Z=50 x+15 y\) subjected to constraints
\(\begin{array}{l}x+y \leq 60 \\5 x+y \leq 100 \\x, y \geq 0\end{array}\)
If the maximum value of \(Z\) occurs at \(x=a\) and \(y=\beta\), then the value of \(a+\beta\) is :

A diverging lens of glass (\( \mu = 1.5 \)) has both surfaces of the same radius of curvature (R). On immersion in a medium of refractive index (\( \mu = 1.8 \)), it will behave as:

Given below are two statements :
Statement (I) : In a ground wave communication system, low frequency signal (< 2 MHz) can be transmitted.
Statement (II) : If frequency is high then it will induce electrical signal on the surface of the earth and so attenuation takes place.
In the light of the above statements, choose the most appropriate answer from the options given below :

If \(\cos^2 y + \sin(xy) = \lambda\), then \(\frac{dy}{dx} =\)