The wavelength of light from the spectral emission line of sodium is 662 nm.
The kinetic energy at which an electron would have the same de-Broglie wavelength would be:
(Given: \( h = 6.62 \times 10^{-34} \text{ J s}, m_e = 9 \times 10^{-31} \text{ kg} \))

The voltage sensitivity of a voltmeter can be increased by :
(A) decreasing the resistance of the voltmeter
(B) increasing the resistance of the voltmeter
(C) decreasing the torsional constant of spring
(D) increasing the number of turns of the coil
(E) taking a strong permanent magnet
Choose the correct answer from the options given below :

The frequency of revolution of an electron revolving in a circular path in a magnetic field of \( 7.8 \times 10^{-4} \, \text{T} \) will be (Take \( e = -1.6 \times 10^{-19} \, \text{C} \), \( m_e = 9.1 \times 10^{-31} \, \text{kg} \), \( \pi = 22/7 \))

A short bar magnet of magnetic moment \( 5.25 \times 10^{-2} \text{ J/T} \) is placed with its axis perpendicular to Earth's magnetic field direction. The distance from the center of the magnet on its perpendicular bisector where the resultant field makes 45° with Earth's field will be : (Earth's magnetic field at that place is 0.42 G.)

The force between two small charged spheres having charges of \( 0.2 \, \mu\text{C} \) and \( 0.6 \, \mu\text{C} \) placed 0.6 m apart in air will be:

Three capacitors each of capacitance \( 3 \mu F \) are provided. These cannot be combined to provide the resultant capacitance of:

A wire of length \( L \) meters, carrying a current \( I \) ampere is bent in the form of a circle. The magnitude of its magnetic moment, in SI units, is:

Let \(A=\left[\begin{array}{ccc}1 & \cos \theta & 1 \\ -\cos \theta & 1 & \cos \theta \\ -1 & -\cos \theta & 1\end{array}\right], 0 \leq \theta \leq 2 \pi\), then :

Identify the incorrect statement(s) among the following:
(A) Two electric field lines of force never intersect.
(B) Two opposite charges, each of \( 10 \times 10^{-9} \, \text{C} \), separated by 5 mm. The magnitude of the dipole moment is \( 5 \times 10^{-11} \, \text{C-m} \).
(C) Electric field intensity due to a single charge varies as the square of the distance from the charge, whereas electric field intensity due to an electric dipole varies inversely as the cube of the distance of the point.
(D) Electric field intensity due to an electric dipole has spherical symmetry around it in space.
Choose the correct answer from the options given below:

If \(\int_0^1 \frac{a \sqrt{x} d x}{\left(x^{3 / 2}+1\right)}=1\), then \(a\) is equal to:

A line through the points \(A(3,4,1)\) and \(B(5,1,6)\) is drawn.
The coordinates of the points where the line through the points \(A \backslash \& B\) crosses the \(X Y\) plane is:

The least distance of distinct vision of a person is 50 cm. He wants to read a book placed at 25 cm. The focal length of the spectacles would be :

Observe the given figures and answer the question

Identify the statements which hold true for Miller's experiment:
(A) He created an electric discharge in a closed flask containing CH4, N2, NH3 and water vapour at 1200°°C
(B) He created electric discharge in a closed flask containing CH4, N2, NH3 and water vapour at 800°C
(C) He observed the formation of amino acids only
(D) He observed the formation of amino acids, sugars and fats
Choose the correct answer from the options given below: