Two particles x and y having equal charge, after being accelerated through the same potential difference, enter a region of a uniform magnetic field. They describe circular paths of radii \( R_1 \) and \( R_2 \), respectively. The ratio of the mass of x to that of y is:

A coil of 400 turns of effective area \(0.05 \text{ m}^2\) is kept perpendicular to a magnetic field of \(5 \times 10^{-3} \text{ T}\). When the plane of coil is rotated by \(90^\circ\) around any of its co-planar axis in 0.2 s in magnetic field, the emf induced in the coil is

A cell of emf E and internal resistance r gives current of 0.5 A with external resistance of 12 \(\Omega\) and a current of 0.25 A with an external resistance 25 \(\Omega\). What is the value of internal resistance?

When a capacitor is subjected to a D.C. source it takes small time internal to get fully charged up. During this small time interval there is no passage of charge through dielectric, yet we use a term - displacement current. This term is used because :

The linear magnifications of the object in the conjugate positions of a convex lens are 4 and 2, respectively. The distance between the conjugate positions is 40 cm . This convex lens of glass \((u=1.5)\) is immersed in water \((u=1.33)\). The new focal length of convex lens in water is :

What are the respective numbers of \( \alpha \) and \( \beta \) particles emitted respectively in the following radioactive decay?
\( {}^{200}_{90}X \rightarrow {}^{168}_{80}Y \)

The total energy of the electron in a hydrogen atom is \( -1.51 \text{ eV} \).
A. Its Kinetic energy is \( -1.51 \text{ eV} \)
B. Its potential energy is \( -3.02 \text{ eV} \)
C. electron is in second excited state
D. The ground state energy of hydrogen atom is 13.6 eV
Choose the correct answer from the options given below:

Read the passage carefully and answer
The crystal field theory (CFT) is an electrostatic model which considers the metal-ligand bond to be ionic arising purely from electrostatic interactions between the metal ion and the ligand. Ligands are treated as point charges in case of anions or dipoles in case of neutral molecules. The five d orbitals in an isolated gaseous metal atom/ion have same energy, i.e., they are degenerate. This degeneracy is maintained if a spherically symmetrical field of negative charges surrounds the metal atom/ion. However, when this negative field is due to ligands (either anions or the negative ends of dipolar molecules like NH3 and H2O) in a complex, it becomes asymmetrical and the degeneracy of the d orbitals is lifted. It results in splitting of the d orbitals. The pattern of splitting depends upon the nature of the crystal field.
The hybridisation and magnetism of the complexes \(\left[\mathrm{Co}\left(\mathrm{C}_2 \mathrm{O}_4\right)_3\right]^{3-}\) and \(\left[\mathrm{Mn}(\mathrm{CN})_6\right]^{3-}\) respectively is:

The points on the curve \(9 y^2=x^3\) where normal to the curve makes equal intercepts with the axes is/are:

Which of the following is NOT a property of charges?

The constancy of the binding energy per nucleons in the range \( 30 < A < 170 \), where A is the mass number shows that :

An LCR series circuit, with \( L = \frac{2}{\pi} \text{ H} \), \( R = 100 \text{ } \Omega \) and \( C = \frac{100}{\pi} \text{ } \mu\text{F} \) is connected across a source of 200 V, 50 Hz as shown. The peak potential difference between A and B is:

The area of the smaller region enclosed by the ellipse \(\frac{x^2}{16}+\frac{y^2}{9}=1\) and the ne straight straight line \(\frac{x}{4}+\frac{y}{3}=1\) is \(a \pi+b\). The value of a + b is: