A \( 25 \, \mu\text{F} \) capacitor, a 0.10 H inductor and a \( 25 \, \Omega \) resistor are connected in series with an ac source of emf \( \epsilon = 310 \sin 314t \). What is the frequency of AC source ?

A p-type semiconductor can be obtained by adding

The binding energy per nucleon for \( ^{56}Fe \) is

A common emitter amplifier has a current gain 75. The collector resistance is 4 \( k\Omega \) and the input resistance is 500 \( \Omega \). The voltage gain of amplifier is:

An infinite plane sheet of charge density \(10^{-8} \text{ C m}^{-2}\) is held in air. In this situation, the distance between two equipotential surfaces, whose potential difference is 10 V, will be (Given: Permittivity of vacuum\(\epsilon_0 \approx 8.85 \times 10^{-12} F / m\))

A very long solenoid has 800 turns per unit length. A current of 1.6 A flows through it. Then the magnetic induction in the middle of the solenoid on its axis is approximately :
(1) \( 16 \times 10^{-4} \text{ T} \)
(2) \( 8 \times 10^{-4} \text{ T} \)
(3) \( 32 \times 10^{-4} \text{ T} \)
(4) \( 4 \times 10^{-4} \text{ T} \)

A capacitor is charged through a potential difference of 200 V, when 0.1 C charge is stored in it. When it is discharged, the energy it will release would be :

Read the following passage carefully and answer the given questions.
Cancerous cells just continue to divide giving rise to masses of cells called tumors. Benign tumors normally remain confined to their original location and do not spread to other parts of the body and cause little damage. The malignant tumors, on the other hand are a mass of proliferating cells called neoplastic or tumor cells. Transformation of normal cells into cancerous neoplastic cells may be induced by physical, chemical or biological agents. Ionising radiations like X-rays and gamma rays and non-ionizing radiations like UV cause cancer. Cancer-causing viruses are called oncogenic viruses which have viral oncogenes. The substances to which an immune response is produced are called allergens. The antibodies produced to these are of IgE type. Common examples of allergens are mites in dust, pollens, animal dander, etc. The primary lymphoid organs are bone marrow and thymus. The secondary lymphoid organs provide the sites for interaction of lymphocytes with the antigen, which then proliferate to become effector cells.
Cancer cells divide without any control due to:

Consider the line \(\frac{x-2}{2}=\frac{2 y-5}{-3}, z=-1\).
Then which of the following is/are true?
(A) It has Direction ratios \((2,-3,-1)\)
(B) It has Direction cosines \(\left(\frac{4}{5},-\frac{3}{5},-\frac{1}{5}\right)\)
(C) It has Direction ratios \(\left(2,-\frac{3}{2}, 0\right)\)
(D) It has Direction cosines \(\left(\frac{4}{5},-\frac{3}{5}, 0\right)\)
Choose the correct answer from the options given below :

\(\int \frac{d x}{\left(1+5 \sin ^2 x\right)}\) is equal to

Read the following statements carefully and identify the correct statements.
(A) Most interference and diffraction effects exist even for longitudinal waves like sound in air
(B) Optical fibers work on the phenomenon of total internal reflection
(C) Optical density and mass density are the same
(D) Polarisation phenomena are specific to transverse waves like light waves
Choose the correct answer from the options given below:

Magnetic moment values for \(\left[ Fe \left( H _2 O \right)_6\right]^{3+}\) and \(\left[ Fe ( CN )_6\right]^{3-}\) are .....

In a time series, the variations which occur due to general tendency of the data to increase or decrease over a long term are known as :