$\sum_{k=1}^5 \frac{1^3+2^3+\ldots+k^3}{1+3+5+\ldots+(2k-1)}$ is equal to (in $.5$)

Which set of compounds in the following pair of ionic compounds has the higher lattice energy?
$(i) \, KCl$ or $MgO$ $(ii) \, LiF$ or $LiBr$ $(iii) \, Mg_3N_2$ or $NaCl$

$A$ Young's double slit experiment uses a monochromatic source. The shape of the interference fringes formed on a screen is

If $a, b, c$ and $d$ are real numbers such that $a^2+b^2+c^2+d^2=1$ and $A=\left[\begin{array}{cc}a+i b & c+i d \\ -c+i d & a-i b\end{array}\right]$,then $A^{-1}$ is equal to

Which layer of the uterus undergoes cyclical changes during the menstrual cycle?

Given in the figure are two blocks $A$ and $B$ of weight $20 \, N$ and $100 \, N$,respectively. These are being pressed against a wall by a force $F$ such that the system does not slide as shown. If the coefficient of friction between the blocks is $0.1$ and between block $B$ and the wall is $0.15$,the frictional force applied by the wall on block $B$ is ........ $N$.