A.\(\dfrac{{{e^2} - 1}}{e}\).
B.\(\dfrac{{{e^2} - 1}}{{2020e}}\). 
C.\(0\).  
D.\(\dfrac{{{e^2} - 1}}{{2019e}}\).

A.\((P):x + 2y + 3z - 8 = 0\). 
B.\((P):\dfrac{x}{1} + \dfrac{y}{2} + \dfrac{z}{1} = 1\).
C.\((P):x + y + z - 4 = 0\). 
D.\((P):x + 2y + z - 6 = 0\).

A.\({d_1}:\,\,\dfrac{{x + 7}}{2} = \dfrac{y}{2} = \dfrac{{z + 12}}{1}\)
B.\({d_2}:\,\,\dfrac{{x - 1}}{2} = \dfrac{{y - 2}}{2} = \dfrac{{z - 4}}{1}\)
C.\({d_3}:\dfrac{x}{2} = \dfrac{y}{2} = \dfrac{z}{1}\)
D.\({d_4}:\,\,\dfrac{{x - 5}}{2} = \dfrac{{y - 3}}{2} = \dfrac{{z - 12}}{1}\)

A.\(2015\).
B.\(2018\). 
C.\(2019\). 
D.\(2014\).

A.5   
B.3    
C.7    
D.9

A.\(\dfrac{{10\pi {a^3}}}{9}\)
B.\(\dfrac{{5\pi {a^3}}}{2}\)
C.\(\dfrac{{\pi {a^3}}}{3}\)
D.\(\dfrac{{10\pi {a^3}}}{7}\)

A.\(\dfrac{{16\sqrt {11} }}{3}\)  
B.\(\dfrac{{5\sqrt {11} }}{3}\)   
C.\(\dfrac{{64\sqrt {11} }}{3}\)   
D.\(\dfrac{{32\sqrt {11} }}{3}\)

A.\(P = \sqrt {ab} \)
B.\(P = \dfrac{1}{{\sqrt[4]{{ab}}}}\)
C.\(P = \sqrt[4]{{ab}}\)
D.\(P =  - \sqrt[4]{{ab}}\)

A.\(\dfrac{{x - 1}}{1} = \dfrac{{y - 2}}{3} = \dfrac{{z + 2}}{1}\)   
B.\(\dfrac{x}{{ - 1}} = \dfrac{{y - 1}}{{ - 1}} = \dfrac{{z - 3}}{5}\)
C.\(\dfrac{{x + 1}}{1} = \dfrac{{y + 2}}{3} = \dfrac{{z - 2}}{1}\)   
D.\(\dfrac{{x + 1}}{1} = \dfrac{{y + 1}}{2} = \dfrac{{z - 5}}{{ - 2}}\)

A.\(672\)  
B.\(483\)   
C.\(3.\left( {{2^{21}} - 1} \right)\)   
D.\({3^{21}} - 1\)