1. Find the value of: (sin43°cos47°+cos43°sin47°)

(a) 0 (b) 1 (c) sin4° (d) cos4°

2. In a circle with center \( O \), \( AB \) and \( CD \) are two equal-length chords. \( E \) is the midpoint of \( CD \), and \( \angle AOB = 70^\circ \). The value of angle \( \angle COE \) is:

(a) 70° (b) 110° (c) 35° (d) 55°

3. The value of 1 radian is:

(a) In between 40° and 50° (b) less than 40° (c) In between 50° and 60° (d) greater than 60°

4. The minimum value of \( \cos^2\theta + \sec^2\theta \) is:

(a) -2 (b) 1 (c) 2 (d) -1

5. The expression \(x^4 - 2x^2 + k\) will be a perfect square when the value of \(k\) is:

(a) \(\cfrac{1}{4}\) (b) 0 (c) \(\cfrac{1}{2}\) (d) 1

6. If \(4^x = 8^3\), then the value of \(x\) is:

(a) \(\frac{3}{2}\) (b) \(\frac{9}{2}\) (c) 3 (d) 9

7. If \(20^{-x} = \dfrac{1}{7}\), then the value of \((20)^{2x}\) is:

(a) \(\frac{1}{49}\) (b) 7 (c) 49 (d) 1

8. If \(4 \times 5^x = 500\), then the value of \(x^x\) is:

(a) 8 (b) 1 (c) 64 (d) 27

9. If the point \((x, 4)\) is at a distance of 5 units from the origin, then the value of \(x\) is:

(a) \(\pm 4\) (b) \(\pm 5\) (c) \(\pm 3\) (d) None of the above

10. If \(\log_{\sqrt{x}} 0.25 = 4\), then the value of \(x\) is:

(a) 0.5 (b) 0.25 (c) 4 (d) 16

11. If \(\log_{10} (7x - 5) = 2\), then the value of \(x\) is:

(a) 10 (b) 12 (c) 15 (d) 18

12. If the roots of the quadratic equation \(5x^2+13x+k=0\) are reciprocals of each other, then the value of \(k\) is:

(a) 3 (b) 4 (c) 5 (d) -5

13. The English translation is: "If \(x^2 = \sin^2 30° + 4\cot^2 45° - \sec^2 60°\), determine the value of \(x\)."