1. If the numerical value of the volume and the surface area of a sphere are equal, what is the numerical value of the radius of the sphere?

(a) 3 (b) 5 (c) 7 (d) 4

2. If sinA+sinB=2, then what is the value of cosA-cosB

(a) 0 (b) 1 (c) 2 (d) 3

3. For the equation \(5x^2+9x+3=0\) , if the roots are \(α\) and \(β\), then what is the value of \(\cfrac{1}{α}+\cfrac{1}{β}\) ?

(a) 3 (b) -3 (c) \(\cfrac{1}{3}\) (d) -\(\cfrac{1}{3}\)

4. In triangle ABC , what is the value of sin⁡\(\cfrac{(B+C)}{2} \) ?

(a) sin⁡\(\cfrac{A}{2}\) (b) sinA (c) cosA (d) cos⁡ \(\cfrac{A}{2}\)

5. For the equation \( 3x^2 + 8x + 2 = 0 \), if the roots are \( \alpha \) and \( \beta \), then what is the value of \( \frac{1}{\alpha} + \frac{1}{\beta} \)?"

(a) -\(\cfrac{3}{8}\) (b) \(\cfrac{2}{3}\) (c) -4 (d) 4

6. If \( 2 \cos \theta = 1 \), what is the value of \( \theta \) ?

(a) 10° (b) 15° (c) 60° (d) 30°

7. If \( 2\sqrt{6} \) is a rationalizing factor of \( \sqrt{2x} \), what is the value of \( x \) ?

(a) 2 (b) 3 (c) 6 (d) √6

8. If PQRS is a cyclic parellelogram, what is the value of \( \angle P \) ?

(a) 45° (b) 60° (c) 90° (d) 75°

9. If the number of vertices, faces, and edges of a cuboid are \( p \), \( q \), and \( r \) respectively, what is the value of \( \frac{3(p + r)}{2q} \) ?

(a) 10 (b) 12 (c) 5 (d) 6

10. 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°

11. For the quadratic equation \(x^2 - bkx + 5 = 0\), if one of the roots is 5, then the value of \(k\) will be.

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

12. 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°

13. If the mode of the numbers 64, 60, 48, x, 43, 48, 43, 34 is 43. Then the value of \((x+3)\) is.

(a) 44 (b) 45 (c) 46 (d) 48

14. The value of (sin43°cos47° +cos43°sin47°) is:

(a) 0 (b) 1 (c) sin4° (d) cos4°

15. The value of (√125 – √5) is

(a) √120 (b) √80 (c) √100 (d) 5√5

16. In a circle centered at O, the chords AB and CD have equal lengths. If \(\angle\)AOB = 60°, then the value of \(\angle\)COD is -

(a) 60° (b) 30° (c) 120° (d) 90°

17. If A + B = 90° and tanA = \(\cfrac{3}{4}\), then the value of cotB is -

(a) \(\cfrac{3}{4}\) (b) \(\cfrac{4}{3}\) (c) \(\cfrac{3}{5}\) (d) \(\cfrac{5}{3}\)

18. If 16, 15, 17, 16, 15, x, 19, 17, 14 have a mode of 15, then the value of x is-

(a) 15 (b) 16 (c) 17 (d) 19

19. PQRS is a cyclic trapezium. PQ is a diameter of the circle, and PO || SR. If \(\angle\)QRS = 110°, then the value of \(\angle\)QSR is -

(a) 20° (b) 25° (c) 30° (d) 40°

20. If sinθ + cosθ = √2 (where 0° < θ < 90°), then the value of θ is

(a) 30° (b) 45° (c) 60° (d) 90°

21. If \(u_i = \cfrac{x_i - 35}{10}\), \(∑f_i u_i = 30\), and \(∑f_i = 60\), then the value of \(\bar{x}\) is –

(a) 40 (b) 20 (c) 80 (d) None of these

22. If \(O\) is the circumcenter of the equilateral triangle \(ABC\), the value of \(\angle BOC\) will be -

(a) 100° (b) 120° (c) 140° (d) 60°

23. If \(S\) is the curved surface area and \(V\) is the volume of a sphere, the value of \(\cfrac{S^3}{V^2}\) is –

(a) 4π (b) 12π (c) 36π (d) 72π

24. ABC is a triangle. Find the value of \(\sin\left(\cfrac{B+C}{2}\right)\)

(a) sin⁡\(\cfrac{A}{2}\) (b) cos⁡\(\cfrac{A}{2}\) (c) sinA (d) cosA

25. If the product of the roots of the equation \(3x^2 - 5x + b = 0\) is \(4\), the value of \(b\) will be –

(a) \(\cfrac{5}{3}\) (b) \(\cfrac{3}{5}\) (c) 12 (d) -12

26. If \(\cfrac{p}{q} = \cfrac{5}{7}\) and \(p - q = -2\), then the value of \(p + q\) is –

(a) 12 (b) 13 (c) 14 (d) 15

27. If \(\theta\) is a positive acute angle and \( \sin \theta - \cos \theta = 0 \), then the value of \(\cot 2\theta\) is –

(a) \(\cfrac{1}{√3}\) (b) 1 (c) √3 (d) 0

28. If \(∑f_i(x_i - a) = 400\), \(∑f_i = 50\), and \(a\) (assumed mean) = 52, then the value of the combined mean \(\bar{x}\) is –

(a) 52 (b) 60 (c) 80 (d) 90

29. If the equation \(3x^2 - 6x + p = 0\) has real and equal roots, then the value of \(p\) is –

(a) \(\cfrac{5}{3}\) (b) -\(\cfrac{1}{3}\) (c) -3 (d) 3

30. In a circle with center \(O\), \(\bar{AB}\) is a diameter. On the opposite side of the circumference from the diameter \(\bar{AB}\), there are two points \(C\) and \(D\) such that \(\angle AOC = 130°\) and \(\angle BDC = x°\). Find the value of \(x\).

(a) 25° (b) 50° (c) 60° (d) 65°