Correct Answer: C. pituitary gland

Correct Answer: A. both feed on fishes

Correct Answer: A. increased real income

Correct Answer: D. Prospectus

Correct Answer: C. African countries

Explanation

(a)(i) \(f(x) = \frac{2x - 3}{(x^{2} - 1)(x + 2)}\)

f(x) is undefined at \((x^{2} - 1)(x + 2) = 0\).

Either \((x^{2} - 1) = \text{0 or (}x + 2) = 0\)

\((x + 2) = 0 \implies x = -2\)

\((x^{2} - 1) = 0 \implies x^{2} = 1 \)

\(x = \pm 1\)

At the points x = -1, 1 or 2, f(x) is undefined.

(ii) \(\frac{2x - 3}{(x^{2} - 1)(x + 2)} = \frac{A}{x + 1} + \frac{B}{x - 1} + \frac{C}{x + 2}\)

\(\frac{A}{x + 1} + \frac{B}{x - 1} + \frac{C}{x + 2} = \frac{A(x - 1)(x + 2) + B(x + 1)(x + 2) + C(x - 1)(x + 1)}{(x^{2} - 1)(x + 2)}\)

When x = -1,

\(-2A = 2(-1) - 3 \implies -2A = -5\)

\(A = \frac{5}{2}\)

When x = 1,

\(6B = 2(1) - 3 = -1\)

\(B = \frac{-1}{6}\)

When x = -2,

\(3C = 2(-2) - 3 = -7\)

\(C = \frac{-7}{3}\)

\(\frac{2x - 3}{(x^{2} - 1)(x + 2)} = \frac{5}{2(x + 1)} - \frac{1}{6(x - 1)} - \frac{7}{3(x + 2)}\)

(c) Equation of circle : \((x + 3)^{2} + (y - 1)^{2} = r^{2}\)

Circle passes through (3,1) :

\(\therefore (3 + 3)^{2} + (1 - 1)^{2} = r^{2}\)

\(6^{2} = r^{2} \implies r = 6\)

Equation becomes :

\((x + 3)^{2} + (y - 1)^{2} = 6^{2}\)

\(x^{2} + 6x + 9 + y^{2} - 2y + 1 - 36 = 0\)

\(x^{2} + 6x + y^{2} - 2y - 26 = 0\)

\(x^{2} + y^{2} + 6x - 2y - 26 = 0\)

Correct Answer: D. -3

Explanation

\(g(x) = \frac{x + 1}{x + 2}, x \neq 2\)

Let y = x, then \(g(y) = \frac{y + 1}{y + 2}\)

Let x = g(y), so that \(x = \frac{y + 1}{y + 2}\)

\(x(y + 2) = y + 1\)

\(xy + 2x = y + 1 \implies xy - y = 1 - 2x\)

\(y(x - 1) = 1 - 2x \implies y = \frac{1 - 2x}{x - 1}\)

\(y = g^{-1}(x) = \frac{1 - 2x}{x - 1}\)

\(g^{-1}(2) = \frac{1 - 2(2)}{2 - 1} = -3\)

Correct Answer: B. maintenance ration

Correct Answer: D. 0.80

Explanation

Masses of kerosene = 24.8 - 15.2

= 9.6

mass of H₂O = 27.2 - 15.2

= 12

R.d = \(\frac{9.6}{12}\) = 0.8

Correct Answer: A. maintain her chastity