A uniformly charged conducting sphere of radius 1.3 m has a surface charge density of \( 70 \, \mu\text{C m}^{-2} \). What is the total electric flux leaving the surface of the sphere ?

The expression of the magnetic energy stored in a solenoid in terms of magnetic field B, cross-sectional area A and length l of the solenoid, is:

The current in a resistive series circuit is 7.0 A. On adding a resistance of 1.6 \( \Omega \) in the same circuit in series, the current drops to 5.0 A. The original resistance of the circuit is :

Identify the correct statements.
(A) Neutrons penetrate the nucleus more readily as compared to protons.
(B) It is easier to release an orbital electron, but quite difficult to release a nucleon.
(C) Nuclear density is not the same for all nuclei.
(D) The radius of the nucleus is directly proportional to the cube root of the mass number.
Choose the correct answer from the options given below:

There are two thin parallel charged sheets having surface charge density \( \sigma \) placed at a small distance apart. Which of the following statements are correct?
(A) If both the sheets are positively charged, then the electric field between them is \( \sigma/\epsilon_0 \)
(B) If both the sheets are negatively charged, then the electric field between them is \( \sigma/\epsilon_0 \)
(C) If the left sheet is positively charged and the right sheet is negatively charged the field between them is \( \sigma/\epsilon_0 \)
(D) If the right sheet is positively charged and the left sheet is negatively charged then the field between them is \( \sigma/\epsilon_0 \)
Choose the correct answer from the options given below:

Two cells with internal resistances \( r_1 \) and \( r_2 \) are connected across the load resistance R as shown in the figure. The values of \( r_1, r_2 \) and R are (1/2) \( \Omega \), (1/3) \( \Omega \) and (9/5) \( \Omega \), respectively. The current through R is:

The frequency of a photon whose energy is 66.3 eV would be
(Given \( h = 6.63 \times 10^{-34} \text{ Js} \))

The desirable properties of core of a transformer are

Out of the following half cells, which two half cell combination gives the largest \(E_{\text{cell}}\text{}\) value?
(I) \(A^{3-} \rightarrow A^{2-} + e^-\text{}\) \(E^{\circ} = +1.5\text{V}\)
(II) \(B^{+} + e^- \rightarrow B\) \(E^{\circ} = -0.5\text{V}\)
(III) \(C^{2+} + e^- \rightarrow C^{+}\) \(E^{\circ} = +0.5\text{V}\)
(IV) \(D \rightarrow D^{2+} + 2e^-\text{}\) \(E^{\circ} = -1.5\text{V}\)
Choose the correct answer from the options given below:

An LCR series circuit with L = 100 mH, C = 100 \( \mu \)F, R = 10 \( \Omega \) is connected to an AC source of emf 220 V. The resonant frequency of the circuit will be nearly

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.
Heroin, commonly called smack is chemically ______ which is a white, odourless, bitter crystalline compound.

Arrange the following electrodes in decreasing order of the strength of the respective ions as reducing agent.
(A) \(Cu ^{2+}+2 e^{-} \rightarrow Cu ( s ) \quad E^{\circ}=0.34 V\)
(B) \(Sn ^{2+}+2 e^{-} \rightarrow Sn (s) \quad E^{\circ}=-0.14 V\)
(C) \(AgBr (s)+e^{-} \rightarrow Ag (s)+ Br ^{-} \quad E^{\circ}=0.10 V\)
(D) \(Pb ^{2+}+2 e^{-} \rightarrow Pb (s) \quad E^{\circ}=-0.13 V\)
Choose the correct answer from the options given below:

The area enclosed between \(y^2=4 x, x=1, x=4\) in first quadrant is :