Class 12th

A beam of protons with speed 4 * 10⁵ ms⁻¹ enters a uniform magnetic field of 0.3 T at an angle of 60° to the magnetic field. The pitch of the resulting helical path of protons is close to: (Mass of the proton = 1.67 * 10⁻²⁷ kg, charge of the proton = 1.69 * 10⁻¹⁹ C)

An amplitude modulated wave is represented by the expression vₘ = 5(1 + 0.6cos 6280t)sin(211 * 10⁴t) volts. The minimum and maximum amplitudes modulated wave are respectively

A 5µF capacitor is charged fully by a 220 V supply. It is then disconnected from the supply and is connected in series to another uncharged 2.5µF capacitor. If the energy change during the charge redistribution is X/100 J then value of X to the nearest integer is:

When radiation of wavelength λ is used to illuminate a metallic surface, the stopping potential is V. When the same surface is illuminated with radiation of wavelength 3λ, the stopping potential is V/4. If the threshold wavelength for the metallic surface is nλ then value of n will be:

A circular coil of radius 10 cm is placed in a uniform magnetic field of 3.0 * 10⁻⁵ T with its plane perpendicular to the field initially. It is rotated at constant angular speed about an axis along the diameter of coil and perpendicular to magnetic field so that it undergoes half of rotation in 0.2 s. The maximum value of EMF induced (in V) in the coil will be close to the integer.

A spherical mirror is obtained as shown in the figure from a hollow glass sphere. if an object is positioned infront of the mirror, what will be the nature and magnification of the image of the object? (Figure drawn as schematic and not to scale)

Consider four conducting materials copper, tungsten, mercury and aluminum with resistivity ρc, ρt, ρm and ρa respectively. Then

Interference fringes are observed on a screen by illuminating two thin slits 1 mm apart with a light source (λ = 632.8 nm). The distance between the screen and the slits is 100 cm. If a bright fringe is observed on a screen at distance of 1.27 mm from the central bright fringe, then the path difference between the waves, which are reaching this point from the slits is close to:

The integral ∫₀² x-1|-x|dx is equal to [numerical value].1|-x|dx is equal to.

The major product in the following reaction is :