Two parallel conductors each carrying a current of 10 mA in opposite directions are placed at a distance 10 cm apart. The force per unit length between two conductors is

The core of electromagnets are made of ferromagnetic material like soft iron because the soft iron has-

The figure shows a long cylindrical straight wire of radius a carrying steady current (I). The current (I) is uniformly distributed across the cross-section of the wire. The ratio of the magnetic fields at points \(r=\frac{a}{3}\) and \(r=\frac{a}{2^{\prime}}\) respectively is: Here r is the distance of point from the axis of cylinder.

The following table gives the lenght, diameter and appiled potential difference of four copper wires, A, B, C, D, across their ends. Arrange the wires in correct order of the increasing electric field.

Wire	Length	Diameter	Potential difference
(A) Wire A	l	3d	V
(B) Wire B	2l	d	V
(C) Wire C	3l	2d	2V
(D) Wire D	3l	2d	V

Choose the correct answer from the options given below:

The work function of cesium is 2.27 eV. The cut off voltage which stops the emission of electron from cesium when irradiated with light of wavelength 400 nm is

Which of the following examples are based upon the total internal reflection of light?
(A) Optical fibre
(B) Twinkling of stars
(C) Mirage
(D) Sparkling of diamond
Choose the correct answer from the options given below:

The angle of minimum deviation of an equilateral prism is equal to its refracting angle. The refractive index of the material of the prism is :

The velocity and acceleration vectors of a particle moving in a magnetic field are given by : \(\vec{v}=3 \hat{i}+4 \hat{j}\) and \(\vec{a}=2 \hat{i}+\hat{j}\) respectively, Then :
(A) the magnetic field is along \(z\)-direction
(B) \(v=3\)
(C) the kinetic energy of the particle is constant
(D) the acceleration is in x-z plane
(E) the particle is moving in \(x-y\) plane

The diagonal elements of a skew symmetric matrix are all

If the objective function for an L.P.P. is \(z=3 x-4 y\) and the corner points for the bounded feasible region are \((0,0),(5,0),(6,5),(6,8),(4,10)\) and \((0,8)\), then the minimum value of \(z\) occurs at :

Read the passage and answer the following
Microbes are organisms that cannot be seen with the naked eye. They include bacteria, archaea, protists, viruses, prions, and fungi. They account for most of the diversity of life on earth. Far more microbes inhabit a single person's body than there are people on the entire planet. Microbes also dominate in terms of their ability to live and thrive in extreme environments, including clouds, deep-sea volcanoes, springs, ice caps, and animal intestines. Most animals, including humans, exhibit numerous associations with microbes. Our "human microbiome" includes our skin, hair, mouth, and gut.
Select the chemical substances which are produced by some microbes and they can kill or prevent growth of other microbes :

The degree of the differential equation \(\left(\frac{d^3 y}{d x^3}\right)^2+x\left(\frac{d^2 y}{d x^2}\right)^3+x^2\left(\frac{d y}{d x}\right)^4=x+y\) is:

Two metals, X and Y have work functions, 4 eV and 10 eV, respectively. The ratio of threshold wavelengths of metal X to metal Y is