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

Explain with the help of chemical reactions “ Setting and Hardening “ of cement .

Write a short note on decay of concrete .

What are carbon nanotubes? Explain different types of carbon  nanotubes?

Witte the CVD method for preparation of carbon nanotubes.

Write the applications of Fullerenes.

Discuss fullerenes. Give its applications. 

Explain CVD method for production of CNTs.

What are carbon nanotubes. what are its types. Discuss the laser method for its production. 

Write a brief note on CNTs.

Write a note on fullerene.

Differentiate between SWNT and MWNT .

Explain laser ablation method for production of CNT’s

Prove that 𝒕𝒂𝒏𝒉−𝟏(𝒔𝒊𝒏 𝜽) = 𝒄𝒐𝒔𝒉−𝟏(𝒔𝒆𝒄 𝜽) 

If `cos alpha cos beta=x/2, sinalpha sinbeta=y/2`, prove that:

`sec(alpha -ibeta)+sec(alpha-ibeta)=(4x)/(x^2-y^2)`

Prove that the matrix `1/sqrt3`  `[[ 1,1+i1],[1-i,-1]]` is unitary. 

If `z =log(e^x+e^y) "show that rt" - s^2 = 0  "where r"= (del^2z)/(delx^2),t=(del^2z)/(dely^2)"s"=(del^2z)/(delx dely)`

If Z=tan^1 (x/y), where` x=2t, y=1-t^2, "prove that" d_z/d_t=2/(1+t^2).` 

Find the nth derivative of cos 5x.cos 3x.cos x. 

Evaluate : `Lim_(x→0) (x)^(1/(1-x))`

If x = uv, y `=(u+v)/(u-v).`find `(del(u,v))/(del(x,y))`.