1. If the complement of a \(3x^\circ\) angle is \(6x^\circ\), then what is the value of \(x\)?
(a) 10 (b) 9 (c) 20 (d) 12
2. If \(\alpha\) and \(\beta\) are complementary angles, find the value of the expression: \[ (1 - \sin^2 \alpha)(1 - \cos^2 \alpha)(1 + \cot^2 \beta)(1 + \tan^2 \beta) \]
3. Write the value of the complement of the angle measuring 63°35'15".
4. 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
5. If sinA+sinB=2, then what is the value of cosA-cosB
(a) 0 (b) 1 (c) 2 (d) 3
6. 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) -\(\cfrac{1}{3}\)
7. In triangle ABC , what is the value of sin\(\cfrac{(B+C)}{2} \) ?
(a) sin\(\cfrac{A}{2}\) (b) sinA (c) cosA (d) cos \(\cfrac{A}{2}\)
8. 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
9. If \( 2 \cos \theta = 1 \), what is the value of \( \theta \) ?
(a) 10° (b) 15° (c) 60° (d) 30°
10. 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
11. If PQRS is a cyclic parellelogram, what is the value of \( \angle P \) ?
(a) 45° (b) 60° (c) 90° (d) 75°
12. 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
13. 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°
14. 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
15. If, tanθ=cot3θ, then the value of sin2θ be:
(a) \(\cfrac{1}{√2}\) (b) \(\cfrac{√3}{2}\) (c) \(\cfrac{1}{2}\) (d) 0
16. Find the value of: (sin43°cos47°+cos43°sin47°)
(a) 0 (b) 1 (c) sin4° (d) cos4°
17. if a: \(\cfrac{27}{64}=\cfrac{3}{4}\):a then the value of a be-
(a) \(\cfrac{81}{256}\) (b) 9 (c) \(\cfrac{9}{16}\) (d) \(\cfrac{16}{9}\)
18. 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°
19. 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
20. The value of (sin43°cos47° +cos43°sin47°) is:
21. If \(α\) and \(β\) are the roots of the equation \(3x^2 + 8x + 2 = 0\), find the value of \(\cfrac{1}{α} + \cfrac{1}{β}\).
(a) \(-\cfrac{3}{8}\) (b) \(\cfrac{2}{3}\) (c) -4 (d) 4
22. If the data arranged in ascending order, 8, 9, 12, 17, x+2, x+4, 30, 31, 34, 39 has a median of 24, then the value of x -
(a) 22 (b) 21 (c) 20 (d) 24
23. The value of (√125 – √5) is
(a) √120 (b) √80 (c) √100 (d) 5√5
24. 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°
25. 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) \(\cfrac{5}{3}\)
26. 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
27. If the roots of the quadratic equation \(ax^2+bx+c=0\) are real and unequal, the value of \(b^2-4ac\) will be:
(a) >0 (b) <0 (c) 0 (d) None of these
28. 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°
29. If sinθ + cosθ = √2 (where 0° < θ < 90°), then the value of θ is
(a) 30° (b) 45° (c) 60° (d) 90°
30. 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
