Mathematics Tes...

Two slits, 4 mm apart, are illuminated by light of wavelength 6000 A. What will be the fringe width on a screen placed 2 m from the slits?

A coil of inductive reactance $31\Omega$has a resistance of $8\Omega$.It is placed in series with a condenser of capacitive reactance $25\Omega$.The combination is connected to an ac source of 110 V. The power factor of the circuit is :

In an N-P-N transistor as common emitter amplifier 10¹⁰ electrons enter the emitter in 10^-6 s. If 2% of the electrons are lost in the base. Then Calculate the current transfer ratio and current amplification factor.

Work done by the system in closed path ABCA, as shown in figure is :

Estimate the speed of sound in air at standard temperature and pressure. The mass of 1 mole of air is 29.0 × 10^-3 kg.

Prism angle & refractive index for a prism are 60^o & 1.414. Angle of minimum deviation will be :

An electron gun G emits electron of energy 2 kev travelling in the (+)ve x-direction. The electron are required to hit the spot S where GS = 0.1m & the line GS makes an angle of ${60}^0$with the x-axis, as shown in the fig. A uniform magnetic field $\underset{B}{\to }$parallel to GS exists in the region outsides to electron gun. Find the minimum value of B needed to make the electron hit S.

A body executes S.H.M. of period 20 seconds. Its velocity is 5 cm s^-1, 2 seconds after it has passed the mean position. Find amplitude of the bob :

A uniform rod of mass m and length ℓ is rotating with constant angular velocity ω about an axis which passes through its one end and perpendicular to the length of rod. The area of cross section of the rod is A and its Young's modulus is Y. Neglect gravity. The strain at the mid point of the rod is :

Two masses m₁ and m₂ are connected by a string of length l. They are held in a horizontal plane at a height H above two heavy plates A and B made of different material placed on the floor. Initially distance between two masses is a < l. When the masses are released under gravity they make collision with A and B co - efficient of restitution 0.8 and 0.4 respectively. The time after the collision when the string becomes tight is :