List of top Economics Questions on Logarithmic Differentiation asked in CUET (PG)

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) = e^x 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: