Given that x, y and b are real numbers x < y, b > 0, then

(a)

xb < yb

(b)

xb > yb

(c)

xb ≤ yb

(d)

\(\frac { x }{ b } \ge \frac { y }{ b } \)

If \({ log }_{ \sqrt { x } }\) 0.25 = 4, then the value of x is

(a)

0.5

(b)

2.5

(c)

1.5

(d)

1.25

If a and b are the roots of the equation x²- kx + 16 = 0 and a²+ b² = 32, then the value of k is

(a)

10

(b)

-8

(c)

-8, 8

(d)

6

If a and b are the real roots of the equation x²- kx + c = 0, then the distance between the points (a, 0) and (b, 0) is

(a)

\(\sqrt { { k }^{ 2 }-4c } \)

(b)

\(\sqrt { { 4k }^{ 2 }-c } \)

(c)

\(\sqrt { 4c-{ k }^{ 2 } } \)

(d)

\(\sqrt { k-8c } \)

The value of log₃ 11.log₁₁ 13.log₁₃ 15.log₁₅ 27.log₂₇ 81 is

(a)

1

(b)

2

(c)

3

(d)

4

Evaluate \(\left( \left[ (256)^{ \frac { -1 }{ 2 } } \right] ^{ \frac { -1 }{ 4 } } \right) ^{ 3 }\)

Solve for x  \(\left| 3-\frac { 3 }{ 4 } x \right| \le \frac { 1 }{ 4 } \)

Factorize: x⁴ + 1

If x=\(\sqrt { 2 } +\sqrt { 3 } \)  find \(\frac { { x }^{ 2 }+1 }{ { x }^{ 2 }-2 } \)

Determine the region in the plane determined by the inequalities.
\(2x+3y\le 6,\ x+4y\le 4,\ x\ge 0,\ y\ge 0.\)

Solve the linear inequalities and exhibit the solution set graphically: x + y ≥ 3, 2x - y ≤ 5, -x + 2y ≤ 3. 

Evaluate \(\sqrt [ 3 ]{ {{{(45.4)}^{2}}\over{{(3.2)}^{2}}\times{(6.5)}^{2}} } \)

Resolve into partial fractions \(\frac { 9 }{ (x-1)(x+2)^{ 2 } } \)