List of top Economics Questions on Logarithmic Differentiation

Given below are two statements, one is labelled as Assertion (A) and the other is labelled as Reason (R):
Assertion (A): The inverse of y = f(x) = ex exists for all x>0. 
Reason (R) : f(x) is differentiable and monotonic for all x>0. 
In the light of the above statements, choose the correct answer from the options given below: 
Given below are two statements, one is labelled as Assertion (A) and the other is labelled as Reason (R):
Assertion (A) : For a differential equation x + ax = b for a≠0 , F(x)=x=b-ax and the equilibrium is at \(\text{x}=\frac{b}{a}\). This a equilibrium is stable for a > 0. Reason (R) : The equilibrium is obtained for x=b-ax=0 or \(\text{x}=\frac{b}{a}\). Stability is obtained when F'(x) is <0. Here F'(x) = -a and so the equilibrium is stable if a> 0. 
In the light of the above statements, choose the correct answer from the options given below:
The solution of the difference equation \(x_t =\frac{1}{2} x_{t-1}+3\) is
Match List-I with List-II :
List-I
[Utility functions U(x1,x2)]		List-II
(MRSx1,x2)
(A)\(Cx^{a}_1x^{b}_2\)(I)\(\frac{-(x_2+1)}{(x_1+2)}\)
(B)\((x_1+2)(x_2+1)\)(II)\(-(\frac{x_1}{x_2})^{a-1}\)
(C)\(ax_1+b\sqrt{x_2}\)(III)\(\frac{-ax_2}{bx_1}\)
(D)\((x^{a}_1+x^{a}_2)^b\)(IV)\(-\frac{2a\sqrt{x_2}}{b}\)
Choose the correct answer from the options given below: