The de-Broglie wavelength associated with a ball of mass \( m = 150 \, g \) traveling at \( v = 30.0 \, m/s \) would be

An electromagnet has stored 540 J of magnetic energy when a current of 6 A exists in its coil. What is the value of average emf induced, if the current is reduced to zero in 0.54s?

What will be the minimum length of antenna required to transmit a radio signal of frequency 10 MHz ?

A radioactive source is freshly prepared. It is found that it emits radiation of intensity which is 128 times the premissible safe level. The half life of this sample is 3 hours. Find the minimum time after which it would be possible to work safely with this radioactive source.

There are two metallic spheres A and B having radii equal to R and 2R respectively. A charge Q is distributed on these two spheres such that the two spheres have equal surface charge densities. The ratio of charge on A to charge on B is :

Which of the following are explained in Rutherford's model of an atom?
(A) An atom consists of a core called nucleus.
(B) The nucleus occupies a very small space as compared to the size of atom.
(C) The stability of an atom.
(D) The electrons revolve around the nucleus in various orbits.
Choose the correct answer from the options given below:

The self-inductance of an inductance coil having 100 turns is 20 mH. The total flux through the coil for a current of 40 mA is :

In terms of Bohr radius \( a_0 \), the radius of the 2nd Bohr orbit ofHydrogen is:

The equation of the normal to the curve \(y=\frac{x-7}{(x-2)(x-3)}\) at (7,0) is:

Read the following paragraph carefully and answer the given questions.
Certain types of leukocytes (WBC) of our body like polymorpho-nuclear leukocytes (PMNL-neutrophils) and monocytes and natural killer (type of lymphocytes) in the blood as well as macrophages in tissues can phagocytose and destroy microbes. For determining the cause of allergy, the patient is exposed to or injected with very small doses of possible allergens, and the reactions studied. The use of drugs like anti-histamine, adrenalin and steroids quickly reduce the symptoms of allergy. Heroin, commonly called smack is chemically diacetylmorphine which is a white, odourless, bitter crystalline compound. This is obtained by acetylation of morphine. 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. 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.
Which one of the following drugs can not quickly reduce the symptoms of allergy?

In a series LCR circuit, \( C = 80 \, \mu\text{F} \), \( L = 5.0 \, \text{H} \) and \( R = 40 \, \Omega \) are connected to a variable frequency source of 240 V. The angular frequency of the source which drives the circuit at resonance will be:

If A is a square matrix and I is the identify matrix of same order such that \(A ^2= I\), then \(3( A - I )^3+3( A + I )^3-15 A\) is equal to

In the process of extraction, gold combines with cyanide in the presence of oxygen and water to make a complex.
The formula of the complex is