If speed $(V)$,acceleration $(A)$,and force $(F)$ are considered as fundamental units,the dimension of Young's modulus will be

The force $F$ is given by the equation $F = at + bt^2$,where $t$ is time. What are the dimensions of $a$ and $b$?

In a system,the unit of mass is $A \,kg$,length is $B \,m$,and time is $C \,s$. Then,the value of $10 \,N$ in this system is:

If energy is given by $U = \frac{A\sqrt{x}}{x^2 + B}$,then the dimensions of $AB$ are:

If $E$ and $E_0$ denote energies at time $t$ and $t_0$ respectively,and $L$ and $L_0$ denote distances from some point at $t$ and $t_0$ respectively,then which of the following equations can be declared to be incorrect on dimensional grounds?
$(A) E = \frac{2 E_0 L}{L_0}$
$(B) E = E_0 e^{-\frac{2 L}{L_0}}$
$(C) E = 2 L e^{-\frac{L}{E_0}}$
$(D) E = 2 \left( \frac{E_0}{L_0} \right) e^{-\frac{L}{L_0}}$

In the expression $A=B+\frac{C}{D+E}$,the dimensions of physical quantities $B$ and $C$ are $[L^{1} M^{0} T^{-1}]$ and $[L^{1} M^{0} T^{0}]$ respectively. The dimensions of quantities $A, D$ and $E$ are