Let f (x) be a quadratic expression which is positive for all real x. If g(x) = f (x) + f ¢ (x) + f ¢¢ (x), then for any real x

=

For such questions, we should know different the condition of limit to exist.

then sinx =

If then x=

If 2 = x then x =

I : +
II : = 0
Which of the above statements is correct?

The solubility product of a salt having general formula in water is . The concentration of ions in the aqueous solution of the salt is:

the-dissociation of weak electrolyte (weak acid) is expressed in terms of Ostwald dilution law stronger is the acid, weaker is its conjugate base_ The dissociation constants of an acid () and its conjugate base ( ) are related by the given relation: -

At (Ionic product of water)
Phosphoric acid isa weak acid. It is used in fertilizer, food, detergent and toothpaste. Structure of phosphoric acid is:

Aqueous solution of phosphoric acid with a density oflg mL^-1 containing 0.05% by weight of phosphoric acid is used to impart tart taste to many soft drinks. Phosphate ion is an inteife ring radical in qualitative analysis. It should be removed for analysis beyond third group of qualitative analysis
the basicity of phosphoric acid is:

The product of the concentrations of the -ions of an electrolyte raised to power of their coefficients in the balanced chemical equation in the solution at any concentration. Its value is not constant and varies with change in concentration. Ionic product of the saturated solution is called solubility product
i) When ' the solution is just saturated and no precipitation takes place
ii) When the solution is unsaturated, and precipitation will not take place
iii) When ' the solution is supersaturated, and precipitation takes place
Which of the following is most soluble?

An acid-base titration consists of the controlled addition of a dissolved base to a dissolved acid (or the reverse). Acid-base react rapidly to neutralize each other. At the equivalence point, enough titrant, the solution being added, has gone into make the chemical amounts of the acid and base' exactly equal. The pH of a titration changes every time a drop of titrant is added, but the rate of this change varies enormously. A titration curve, graph of pH tis a function of the volume of titrant, displays in detail how the pH changes over the course of an acid-base titration. Significantly, the pH changes most rapidly near the equivalence point. The exact shape of a titration curve depends on the and acid and base
Which of the titrations could it represent?

An acid-base titration consists of the controlled addition of a dissolved base to a dissolved acid (or the reverse). Acid-base react rapidly to neutralize each other. At the equivalence point, enough titrant, the solution being added, has gone into make the chemical amounts of the acid and base' exactly equal. The pH of a titration changes every time a drop of titrant is added, but the rate of this change varies enormously. A titration curve, graph of pH tis a function of the volume of titrant, displays in detail how the pH changes over the course of an acid-base titration. Significantly, the pH changes most rapidly near the equivalence point. The exact shape of a titration curve depends on the and acid and base
The following figure represents titration curve of HCl against NaOH. The pH at equivalence point will be:

When a salt reacts with water to form acidic or basic solution, the process is called hydrolysis. The pH of salt solution can be calculated using the following relations

(for salt of weak acid and strong base.)

(for salt of weak base and strong acid.)

(for salt of weak acid and weak base.)
where, 'C' represents the concentration of salt.
When a weak acid or a weak base is not completely neutralized by strong base or strong acid respectively, then formation of buffer takes place. The pH of buffer solution can be calculated using the following relation


When 50 mL of 0.1 M NaOH is added to 50 mL of 0.05 M solution. The pH of the solution is: