A charged particle with charge 0.01 C rotates on a circular path of radius 0.5 m , with velocity \(0.2 m / s\). What is the value of \(B\) at the center of the circle ?

The variation of resistivity of a metallic conductor with temperature is given correctly by which of the following relations?
(Where \( \rho_T \) is the resistivity at a temperature T and \( \rho_0 \) is the resistivity at a reference temperature \( T_0 \), \( \alpha \) is the temperature coefficient of resistivity, \( T > T_0 \))

There are four media in which light is traveling. The speed of light in each medium along with relative permeability of the medium are given as below. Arrange the relative permittivity of each of the medium in increasing order.
(A) Medium I: \( v_1 = 2 \times 10^8 \, \text{m/s}, \mu_r = 1 \)
(B) Medium II: \( v_{II} = 1.5 \times 10^8 \, \text{m/s}, \mu_r = 1 \)
(C) Medium III: \( v_{III} = 3 \times 10^8 \, \text{m/s}, \mu_r = 1 \)
(D) Medium IV: \( v_{IV} = 2 \times 10^8 \, \text{m/s}, \mu_r = 2 \)

What type of wavefront will emerge from a (i) distant light source and (ii) point source?

Ferromagnetic material core used for transformer must have

The force between two small charged spheres having charges of \( 0.2 \, \mu\text{C} \) and \( 0.6 \, \mu\text{C} \) placed 0.6 m apart in air will be:

Two slits are made 0.8 mm apart and the screen is placed 1.5 m away. What should be the width of each slit to obtain 8 maxima of the double slit pattern within the central maximum of the single slit pattern?

Which one of the following compounds undergoes predominantly SN2 reaction with aqueous NaOH in polar aprotic solvent:

The nitration of chlorobenzene gives major product as :

For the linear programming problem (LPP) :
Maximize \(Z=x+1.5 y\), subject to constraints, \(x+2 y \leq 40,2 x+y \leq 40, x+y \leq 25, x \geq 0, y \geq 0\).
Which of the following is NOT correct?

"The rate constant of a first order reaction follows the equation 
 \(log\ k = 8.0 - \frac{5000}{T}\)
 The activation energy \((E_a)\) for the reaction is:
 (Given \(R = 8.3\ JK^{-1}\ mol^{-1}\))"

Read the following paragraph and answer the given questions.
Cancer detection is based on biopsy and histopathological studies. Techniques like radiography (use of X-rays), CT (computed tomography) and MRI (magnetic resonance imaging) are very useful to detect cancers of the internal organs. Do you know why mother's milk is considered very essential for the new-born infant? The yellowish fluid colostrum secreted by mother during the initial days of lactation has abundant antibodies (IgA) to protect the infant. Different species of Plasmodium (P. vivax, P. malaria and P. falciparum) are responsible for different types of malaria. Of these, malignant malaria caused by Plasmodium falciparum is the most serious one and can even be fatal. The exaggerated response of the immune system to certain antigens present in the environment is called allergy. The use of drugs like anti-histamine, adrenalin and steroids quickly reduce the symptoms of allergy. Drugs like barbiturates, amphetamines, benzodiazepines, and other similar drugs, that are normally used as medicines to help patients cope with mental illnesses like depression and insomnia, are often abused. Morphine is a very effective sedative and painkiller, and is very useful in patients who have undergone surgery.
Which one of the following is not used for detection of cancer?

The figure shows a Wheatstone bridge circuit arrangement with a galvanometer G of resistance 5 \( \Omega \) to detect the presence of current. The ratio of heat dissipated across four resistors, \( R_1, R_2, R_3 \) and \( R_4 \) respectively, is :