If x is real, then greatest and least values of [x2 – x + 1] / [x2 + x + 1] are
1) 3, – 1 / 2 2) 3, 1 / 3 3) – 3, 1 / 3 4) None of... View Article
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x / [1 + x tan x] is maxima at
1) x = sin x 2) x = cos x 3) x = π / 3 4) x = tan... View Article
The maximum value of sin x (1 + cos x) will be at the
1) x = π / 2 2) x = π / 6 3) x = π / 3 4) x... View Article
The maximum and minimum values of x3 – 18x2 + 96x in the interval (0, 9) are
1) 160, 0 2) 60, 0 3) 160, 128 4) 120, 28 Solution: (3) 160, 128 y = x3 –... View Article
The minimum value of 2x + 3y, where xy = 6 is
1) 12 2) 9 3) 8 4) 6 Solution: (1) 12 f (x) = 2x + 3y f (x) =... View Article
What are the minimum and maximum values of the function x5 – 5x4 + 5x3 – 10
1) –37, –9 2) 10, 0 3) It has 2 min. and 1 max.values 4) It has 2 max. and... View Article
Let x and y be two variables such that x > 0 and xy = 1. Then the minimum value of x + y is
1) 2 2) 3 3) 4 4) 0 Solution: (1) 2 Let f (x) = x + y, where xy... View Article
The minimum value of e(2x2 – 2x + 1) sin2 x is
1) e 2) 1 / e 3) 1 4) 0 Solution: (3) 1 y = e(2x^2 – 2x + 1)... View Article
The number of values of x where the function f (x) = cos x + cos (√2x) attains its maximum is
1) 0 2) 1 3) 2 4) Infinite Solution: (2) 1 The maximum value of the function f (x) =... View Article
If f (x) = [x2 – 1] / [x2 + 1], for every real number x, then the minimum value of f
1) Does not exist because f is unbounded 2) Is not attained even though f is bounded 3) Is equal... View Article
The points of local maxima for the function f (x) = x3 / 3 + (x2 / 2) – 2x + 1 are
1) x = –2 2) x = 1 3) x = 2 4) x = –1 Solution: (1) x =... View Article
One maximum point of sinp x cosq x is
1) x = tan-1 √(p / q) 2) x = tan-1 (√q / p 3) x = tan-1 (p /... View Article
The minimum value of [(5 + x) (2 + x)] / [1 + x] for non-negative real x is
1) 12 2) 1 3) 9 4) 8 Solution: (3) 9 f (x) = [(5 + x) (2 + x)]... View Article
The sum of two non – zero numbers is 4. The minimum value of the sum of their reciprocals is
1) 3 / 4 2) 6 / 5 3) 1 4) None of these Solution: (3) 1 x + y... View Article
The minimum value of the function y = 2x3 – 21x2 + 36x – 20 is
1) –128 2) –126 3) –120 4) None of these Solution: (1) –128 f (x) = 2x3 – 21x2 +... View Article
Which is more covalent NaCl or AlCl3?
AlCL3 is more covalent than NaCl. In NaCl, Na will donate one electron to Cl therefore forming an ionic bonding.... View Article
Are keto enol tautomers constitutional isomers
Keto-enol tautomers are constitutional isomers that are interconvertible. The keto-enol tautomers are usually distinguished by the different location of the... View Article
Does benzophenone show Tautomerism
Benzophenone does not show tautomerism because it does not have the alpha hydrogen. Compounds with alpha hydrogen only show tautomerism.
Does nitrobenzene show Tautomerism
Nitrobenzene does not show tautomerism. Compounds with alpha hydrogen only show tautomerism. Nitrobenzene does not have alpha hydrogen.
Does acetone show tautomerism?
Acetone exhibits the keto-enol tautomerism. The “keto” structure (CH3)2C= O is in equilibrium with the enol (CH3)C(OH)=(CH2) structure.
