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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 – 18x2 + 96x y’ = 3x2 - 36x + 96 = 0 x2 - 12x + 32 = 0... 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) = 2x + 18x (xy = 6) f′ (x) = 2 − 18x2 f′ (x) = 0 for maximum or... 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 1 min. values Solution: (1) –37, –9 y = x5 – 5x4 + 5x3... 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 = 1. f (x) = x + (1 / x) f’ (x) = 1 - (1 / x2) = [x2 - 1] / x2... 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) sin2 x For minima or maxima, dy / dx = 0 e(2x^2 - 2x + 1) sin2 x... 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) = cos x + cos (√2x) is 2 at x = 0.... 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 to 1 4) Is equal to –1 Solution: (4)... 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 = –2 f (x) = x3 / 3 + (x2 / 2) - 2x + 1 f’ (x) = x2 + x - 2 f’ (x) = 0 (x... View Article

One maximum point of sin^p x cos^q x is

1) x = tan-1 √(p / q) 2) x = tan-1 (√q / p 3) x = tan-1 (p / q) 4) x = tan-1 (q / p) Solution: (1) x = tan-1 √(p / q) y = sinp x... 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)] / [1 + x] f (x) = 1 + 4 / (1 + x) + (5 + x) = (6 + x) + 4 / (1 +... 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 = 4 y = 4 - x 1 / x + 1 / y = (x + y) / xy f (x) = 4 / xy = (4 /... 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 + 36x – 20 f' (x) = 6x2 - 42x + 36 f' (x) = 0... 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. In AlCl3, Al shares electrons... 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... 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.... View Article

Does nitrobenzene show Tautomerism

Nitrobenzene does not show tautomerism. Compounds with alpha hydrogen only show tautomerism. Nitrobenzene does not have alpha hydrogen.... View Article

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.... View Article

Is polymerization reversible?

Polymerization is a reversible process. Depolymerization is the process to convert the polymers into a monomer or a mixture of monomers.... View Article

Is polymerization endothermic or exothermic

Generally, polymerization is an exothermic reaction. The polymerisation is the reaction in which the monomers combine to form polymers.... View Article

Is SiO2 a dielectric?

Silicon dioxide (SiO2) is an amorphous material used as a dielectric in capacitors.... View Article

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