BE Computer Engineering Semester 1 (FE First Year) - University of Mumbai Important Questions

Solve the following system of equation by Gauss Siedal Method,20x+y-2z=17
             3x+20y-z =-18
             2x-3y+20z=𝟐𝟓

Find the roots of the equation `x^4+x^3 -7x^2-x+5 = 0` which lies between 2 and 2.1 correct to 3 places of decimals using Regula Falsi method.

Evaluate : `lim_(x->0)((2x+1)/(x+1))^(1/x)`

Solve the following equation by Gauss Seidal method:

`10x_1+x_2+x_3=12`
`2x_1+10x_2+x_3-13`
`2x_1+2x_2+10x_3=14`

Obtain the root of 𝒙^𝟑−𝒙−𝟏=𝟎 by Regula Falsi Method
(Take three iteration).

Solve by Gauss Jacobi Iteration Method: 5x – y + z = 10, 2x + 4y = 12, x + y + 5z = -1. 

By using Regular falsi method solve 2x – 3sin x – 5 = 0.

Solve using Gauss Jacobi Iteration method 
2𝒙 + 12y + z – 4w = 13
13𝒙 + 5y - 3z + w = 18
2𝒙 + y – 3z + 9w = 31
3𝒙 - 4y + 10z + w = 29

What are crystal imperfections Mention any two significance of it .

Draw and explain the unit cell of sodium chloride (NaCl) crystal determine effective number of NaCl molecule per unit cell and co-ordination number.

 Explain analysis of crystal structure using Bragg’s X ray spectrometer

Calculate the critical radius ratio of an ionic crystal in ligancy-6 . what is the maximum size of cation in ligancy 6 configuration when size of anion is 2.02A°?

Draw the unit cell of HCP structure and work out the no. of atoms per unit cell.

What is the principle of solar cell? Write its advantages and disadvantages

Draw the following : (1,-1,3) ,(2,0,0) , [0,0,-1]
An electron is accelerated through 1200 volts and is reflected from a crystal. The second order reflection occurs when glancing angle is 60°. Calculate the inter planar spacing of the crystal.

Find the following parameter for DC(Diamond Cubic) structure:- 
⦁ No. of atoms per unit cell.
⦁ Co-ordination number.
⦁ Nearest atomic distance.
⦁ Atomic radius.
⦁ APF.

Why X-rays are used to study the crystal structure?

With neat diagram of unit cell, explain the structure of NaCl crystal and calculate the no .of ions per unit cell, co ordination no. and lattice constant. Calculate the packing factor of NaCl crystal assuming the radius of _Na+is 0.98 A° and radius of Cl is 1.81 A°. 

Define ligancy and critical radius ratio. Calculate critical radius ratio for ligancy 8. 

‘Crystal acts as three dimensional grating for X-rays’, explain.