A 1.0 m long metallic rod is rotated with an angular frequency of \( 500 \, \text{rad s}^{-1} \) with one end hinged at the center and the other end at the circumference of a circular metallic ring of radius 1 m about an axis passing through the center and perpendicular to the plane of the ring. A constant and uniform magnetic field of 0.6 T parallel to the axis exists everywhere. The emf developed between the center and the ring is

Which of the following are not electromagnetic waves?
A. Gamma rays
B. Cathode rays
C. X-rays
D. \(\beta\)-rays
E. Radio waves
Choose the correct answer from the options given below:

The focal length of a lens depends on

An a.c. source of 200 V is connected through a diode 'D' to a capacitor as shown in figure. Find the maximum potential difference across the capacitor :

Identify the incorrect statement(s) among the following:
when a dielectric medium is introduced between the plates of a charged capacitor:
(A) If a plate of dielectric constant k, thickness t is placed between the plates of a charged capacitor of area A and distance d, then the new capacitance will be \( \frac{A\varepsilon_0}{d - t(1 - 1/k)} \)
(B) The electric field between plates of the charged capacitor when the dielectric is introduced will be \( E = (E_0 - E_p) \)
(C) Dielectric constant of the dielectric placed between plates of charged capacitor will be \( k = \frac{E_0}{E_0 - E_p} \)
(D) Dielectric strength of the dielectric is the maximum value of the electric field which may be applied before its breakdown.
Choose the correct answer from the options given below :

A change of current from 6.0 A to 3.0 A in 300 ms in a coil produces an induced emf of 0.5 V in the neighboring coil. The mutual inductance between the two coils would be

How much energy will be carried out by electromagnetic radiation of wavelength \( 3 \times 10^{-6} \text{ m} \)?

\(\int \frac{\sin 2 x d x}{\sqrt{9-\cos ^4 x}}\) equals

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.
The drug, which is very effective sedative and painkiller and useful for patients who have undergone surgery is -

The unit of Productivity in terms of energy is :

Which of the following techniques are commonly used for early detection
of cancer?
(A) Biopsy and histopathological studies
(B) Radiography (x-rays)
(C) MRI (Magnetic Resonance Imaging)
(D) Electrocardiogram (ECG)
Choose the correct answer from the options given below:

When the electronic configuration of a transition metal element \(X\) in +3 oxidation state is \([ Ar ] 3 d^5\), what is its atomic number?

A photo cathode is illuminated by a very small bright source placed 1 m away. When the same source of light is placed 0.5 m away, the number of electrons emitted by the photo cathode would become