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 3 is the logarithm of 343, then the base is

(a)

5

(b)

7

(c)

6

(d)

9

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)

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

If  \(\frac { 1-2x }{ 3+2x-{ x }^{ 2 } } =\frac { A }{ 3-x } +\frac { B }{ x+1 } \), then the value of A + B is

(a)

\(\frac { -1 }{ 2 } \)

(b)

\(\frac { -2 }{ 3 } \)

(c)

\(\frac { 1 }{ 2 }\)

(d)

\(\frac { 2 }{ 3 } \)

If - 3x + 17 < -13 then ___________

(a)

x ∈ (10, ∞)

(b)

x ∈ [10, ∞)

(c)

x ∈ (-∞, 10]

(d)

x ∈ [10, 10)

The number of real solution of |2x - x²- 3| = 1 is ___________

(a)

0

(b)

2

(c)

3

(d)

4

(x²-2x+2)(x²+2x+2) are the factors of the polynomial ___________

(a)

(x²-2x)²

(b)

x⁴-4

(c)

x⁴+4

(d)

(x²-2x+2)²

If \(\alpha\) and \(\beta\) are the roots of 2x² + 4x + 5 = 0 the equation where roots are 2\(\alpha\) and 2\(\beta\) is ___________

(a)

4x²+ 4x + 5 = 0

(b)

2x² + 4x + 50 = 0

(c)

x² + 4x + 5 = 0

(d)

x²+ 4x + 10 = 0

The condition that the equation ax² + bx + c = 0 may have one root is the double the other is ___________

(a)

2b² = 9ac

(b)

b² = ac

(c)

b² = 4ac

(d)

9b² = 2ac

If P(x) = x³ + 3x² + 2x + 1, then the remainder on dividing p(x) by (x - 1) is ___________

(a)

7

(b)

0

(c)

6

(d)

1