A system has two charges, \( q_A = 5 \times 10^{-7} \, \text{C} \) and \( q_B = -5 \times 10^{-7} \, \text{C} \), located at points \( A : (0, 0, -10 \, \text{cm}) \) and \( B : (0, 0, +10 \, \text{cm}) \), respectively. Which of the following are true?
(A) The electric field of dipole at point (0, 0, -15 cm) is \( 1.73 \times 10^6 \, \text{NC}^{-1} \)
(B) Electric field intensity is zero at origin (0, 0, 0)
(C) dipole moment \( (p) = 5 \times 10^{-8} \, \text{C-m} \)
(D) direction of the dipole moment is along the negative z- axis
Choose the correct answer from the options given below:

Arrange the following series of emission lines in the spectrum of hydrogen atom in sequence according to their increasing wavelengths:
(A) Paschen series
(B) Lyman series
(C) Balmer series
Choose the correct answer from the options given below:

Three parallel plates (each of area A) are separated by distances \( d_1 \) and \( d_2 \) respectively. The in-between spaces are filled with dielectrics of relative permittivity \( \epsilon_1 \) and \( \epsilon_2 \). The permittivity of free space is \( \epsilon_0 \). The capacitance of the combination is:

Two parallel plate capacitors of capacitances \(2 \, \mu\text{F}\) and \(3 \, \mu\text{F}\) are joined in series and connected to a battery of V volts. The values of potential across the two capacitors \(V_1\) and \(V_2\) and energy stored in them \(U_1\) and \(U_2\) are related as :

When the light of frequency \(2 \nu_0\) (where \(\nu_0\) is the threshold frequency) is incident on a photosensitive material, the maximum velocity of electrons emitted is \(v_1\). When the frequency of the incident radiation is increased to \(3 \nu_0\), the maximum velocity of emitted electrons from the same material is \(v_2\). The ratio of \(v_1\) to \(v_2\) will then be :

A conducting wire of length 0.1 m and mass \( 3 \times 10^{-3} \text{ kg} \), carrying a current of 5 A is suspended freely in a horizontal direction in a uniform magnetic field. The magnitude of magnetic field perpendicular to the length of conductor is:

A 20 m long horizontal wire extends from North-East to South-West. It is falling down with a speed of \(4 \mathrm{~m} / \mathrm{s}\) horizontally. The horizontal components of the earth's magnetic field is \(0.4 \times 10^{-4}\) T. Find the value of induced current in the wire if the resistance of wire is \(2 \Omega\) is :

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Molar conductivity \(\Lambda_m^0\)of a solution at a given concentration (c) is the conductance of volume, V of solution, containing one mole of electrolyte kept between the two electrodes with area of cross-section A and at a distance of unit length. It increases with the decrease in concentration and when the concentration approaches zero, the molar conductivity is called limiting molar conductivity \(\Lambda_m^0\) . For a strong electrolyte, \(\Lambda_m\) increases linearly with dilution and is given by \(\Lambda_m=\Lambda_m^0-A c^{1 / 2}\). The value of the constant A for a given solvent depends on the type of electrolyte along with temperature. According to Kohlrausch law, they value of \(\Lambda_m^0\) for an electrolyte is \(\Lambda_m^0=\nu_{+} \lambda_{+}^0+\nu_{-} \lambda_{-}^0\), where \(\nu_{+}\)and \(\nu_{-}\) are the number of cations and anions, respectively, per molecule of the electrolyte and \(\lambda_{+}^0\) and \(\lambda_{-}^0\) are limiting molar conductivities of cation and anion, respectively. Kohlrausch law finds many applications, like determining the solubility of a sparingly soluble salt, determining the degree of dissociation \(\left(\Lambda_m / \Lambda_m^0\right)\), and the dissociation constant of a weak electrolyte.
If the molar conductance values of Ca²⁺ and Cl^- at infinite dilution are, respectively, 118.8 × 10^-4 ohm^-1 m² mol^-1 and 77.33 × 10^-4 ohm^-1 m² mol^-1, then the molar conductance of CaCl₂ at infinite dilution will be :

The function \(f(x)=\left\{\begin{array}{ll}\frac{\sin 2 x}{x}+\cos x & , \text { if } x \neq 0 \\ K & , \text { if } x=0\end{array}\right.\) is continuous at \(x = 0\) then the value of K is:

Let \(f: R \rightarrow R\) be defined as \(f(x)=3 x+4\). Choose the correct answer.

The focal length of a convex lens in air and in a liquid medium are 20 cm and 80 cm, respectively. If the absolute refractive index of lens is 1.5, then the refractive index of liquid is :

A radiation of energy E is normally incident on a perfectly reflecting surface. The momentum transferred to the surface will be: (Given: speed of light c)

A charged particle moves along a circular path in a uniform magnetic field of 0.04 T with a velocity of \( 2 \times 10^5 \text{ m/s} \). The charge to mass ratio of the particle is \( 5 \times 10^7 \text{ C/kg} \). The radius of the circular path of the charged particle is: