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Tanaya N.

Student at BITS Pilani, Tutor for 10 years

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Chemistry

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Question:

pKa of a weak acid (HA) and pKb of a weak base (BOH) are 3.2 and 3.4, respectively. Find the pH of their salt (AB) solution.

Tanaya N.

Answer:

pKa (HA) = 3.2 pKb (BOH) = 3.4 As given salt is of weak acid and weak base pH = 7 + pKa/2 - pKb/2 = 7 + 1 1 (3.2) – (3.4) 2 2 = 6.9

Calculus

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Question:

Find the area enclosed by the curve y = f (x) defined parametrically as x = (1- t^2)/(1+ t^2) and y = 2t/(1+ t^2)

Tanaya N.

Answer:

Clearly, t can be any real number Let t = tan θ then we get x = cos 2θ and y = sin2θ giving the curve f(x) = y, a circle with radius = 1 unit area = pi * r^2 = pi * 1^2 = pi

Algebra

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Question:

x = a^3 + b^3 + c^3 y= a+b+c find value of x in terms of abc if y = 0

Tanaya N.

Answer:

a^3 + b^3 + c^3 - 3abc = (a+b+c)(a^2 +b^2 +c^2 -ab -bc -ca) using the above exapnsion we get x = 3abc

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