The force of attraction between two charges separated by a distance in air is F. If the medium air is replaced by a dielectric medium of dielectric constant K, the force of attraction between the charges will become:

A pair of adjacent coils has a mutual inductance of 2.0 H. If the current in one coil changes from 0 to 25 A in 0.8 s, the change of flux linkage with the other coil is

Light of two different frequencies whose photons have energies 1 eV and 2.5 eV respectively, illuminate a metal of work function 0.5 eV. The ratio of the maximum KE of the emitted electrons will be :

Three resistances of 1 \(\Omega\), 2 \(\Omega\) and 3 \(\Omega\) are given. In order to obtain an equivalent resistance of 11/3 \(\Omega\) they are to be connected as

A magnetic substance has a susceptibility \( - 0.05 \) at 300 K. The magnetic susceptibility at 600 K is :

A parallel plate capacitor filled with oil of dielectric constant \( k = 3 \), has a capacitance \( C \). After removing the oil between the plates, the capacitance of the capacitor will become:

A radioactive nucleus M undergoes series of decays given below: M \(\xrightarrow{\beta^- decay}\) N \(\xrightarrow{\gamma decay}\) O \(\xrightarrow{\alpha decay}\) P. The mass number of M is 150 and Atomic No of M is 64. The Atomic number of P is

Which of the following is NOT a disaccharide?

Read the passage carefully and answer the Questions
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 :

If \(|\vec{a}|=a\), then the value of \(|\vec{a} \times \hat{i}|^2+|\vec{a} \times \hat{j}|^2+|\vec{a} \times \hat{k}|^2\) is :

Match List-I with List-II

List-I	List-II
(A) The equation of the line passing through the points \((-1,0,2)\) and \((3,4,6)\) is	(I) \(\vec{r}=(-\hat{i}+2 \hat{k})+\lambda(4 \hat{i}+4 \hat{j}+4 \hat{k})\)
(B) The vector equation of the line \(\frac{x-1}{2}=\frac{y+1}{3}=\frac{4-z}{5}\) is	(II) \(\vec{r}=(\hat{i}+3 \hat{j}+2 \hat{k})+\lambda(2 \hat{i}+\hat{j}+3 \hat{k})\)
(C) The equation of the line passing through \((1,3,2)\) and parallel to \(\frac{x+1}{2}=\frac{y-1}{1}=\frac{z+1}{3}\) is	(III) \(\vec{r}=(-\hat{i}+2 \hat{j}+3 \hat{k})+\lambda(2 \hat{i}+\hat{j}+4 \hat{k})\)
(D) The equation of the line along \(2 \hat{i}+\hat{j}+4 \hat{k}\) and passing through \((-1,2,3)\) is	(IV) \(\vec{r}=(\hat{i}-\hat{j}+4 \hat{k})+\lambda(2 \hat{i}+3 \hat{j}-5 \hat{k})\)

where \(\lambda\) is an arbitrary constant.
Choose the correct answer from the options given below:

Which of the following ethers cannot be prepared by bimolecular dehydration of alcohol?
(A) 2-Methoxy-2-methylpropane
(B) 2-Methoxy propane
(C) 1-Ргорохургopane
(D) 2-Ethoxy butane
Choose the correct answer from the options given below:

Three identical polaroid sheets \(P_1, P_2, P_3\) are oriented so that pass axis of \(P_2\) and \(P_3\) are inclined to \(P_1\) at 60° and 90° respectively. A monochromatic source of intensity \(I_0\) is used to pass through \(P_1, P_2, P_3\). Intensities after passing through \(P_1, P_2, P_3\) will be respectively :
(A) \(I_0, \frac{I_0}{2}, \frac{I_0}{8}\)
(B) \(\frac{I_0}{2}, \frac{I_0}{8}, \frac{I_0}{32}\)
(C) \(\frac{I_0}{2}, \frac{I_0}{8}, \frac{3 I_0}{32}\)
(D) \(I_0, \frac{I_0}{2}\), zero
Choose the correct answer from the options given below :