HSC Science (Electronics) 12th Standard Board Exam - Maharashtra State Board Important Questions

Show that for radioactive decay N(t) = `"N"_"O" "e"^{-λ"t"}`, where symbols have their usual meaning.

Obtain an expression for the half-lifetime of radioactive material. Hence state the relation between an average life and half life time of radioactive material.

A radioactive substance decays to (1/10)^th of its original value in 56 days. Calculate its decay constant. 

Determine the shortest wavelengths of Balmer and Pasch en series. Given the limit for the Lyman series is 912 Å.

The disintegration rate of a radio-active sample is 10¹⁰ per hour at 20 hours from the start. It reduces to 5 × 10⁹ per hour after 30 hours. Calculate the decay constant.

State unit and dimensions of Magnetic susceptibility.

What is binding energy of a hydrogen atom?

Calculate the wavelength of the first two lines in the Balmer series of hydrogen atoms.

The co-efficient of mutual induction between primary and secondary coil is 2H. Calculate induced e.m.f. if current of 4A is cut off in 2.5 x 10^-4 seconds

Electric field intensity in free space at a distance ‘r’ outside the charged conducting sphere of radius ‘R’ in terms of surface charge density ‘ a ’ is............................

(a)`sigma / in_0[R/r]^2`

(b)`in_0/sigma[R/r]^2`

(c)`R/r[sigma/in_0]^2`

(d)`R/sigma[r/in_0]^2`

A solenoid 3.142m long and 5.0 cm in diameter has two layers of windings of 500 turns each and carries a current of 5A. Calculate the magnetic induction at its centre along the axis.

The magnetic flux through a loop varies according to the relation Φ = 8t² + 6t + C, where ‘C’ is constant, 'Φ' is in milliweber and 't' is in second. What is the magnitude of induced e.m.f. in the loop at t = 2 seconds.

Two metal spheres having charge densities 5μC/m² and -2μC/m² with radii 2mm and  1mm respectively are kept in a hypothetical closed surface. Calculate total normal electric induction over the closed surface.

Obtain an expression for e.m.f. induced in a coil rotating with uniform angular velocity in a uniform magnetic field. Show graphically the variation of e.m.f. with time (t).

Resistance of a potentiometer wire is 0.1Ω/cm. A cell of e.m.f 1.5V is balanced at 300 cm on this potentiometer wire. Calculate the current and balancing length for another cell of e.m.f. 1.4V on the same potentiometer wire.

Discuss the composition of two S.H.M.s along the same path having same period. Find the resultant amplitude and intial phase.

Obtain an expression for average power dissipated in a purely resistive A.C. circult. 

If the radius of a sphere is doubled without changing the charge on it, then electric flux originating from the sphere is ______.

A coil of 100 turns, each of area 0.02m² is kept in a uniform field of induction 3.5 x10^-5 T. If the coil rotates with a speed of 6000 r.p.m. about an axis in the plane of the coil and perpendicular to the magnetic induction, calculate peak value of e.m.f. induced in the coil.

Six capacitors of capacities 5, 5. 5, 5, 10 and X μ F are connected as shown in the network in the diagram. 

Find :

1. The value of X if the network is balanced, and
2. The resultant capacitance between A and C.

An A.C. circuit consists of inductor of inductance 125 mH connected in parallel with a capacitor of capacity 50 μF. Determine the resonant frequency.