1. The roots of the equation \(ax^2+bx+c=0\) will be equal in magnitude but opposite in sign if-
(a) \(c=0, a≠0\) (b) \(b=0, a≠0\) (c) \(c=0, a=0\) (d) \(b=0, a=0\)
2. If ABCD is a cyclic quadrilateral and \(\angle\)A=120°, what is the measure of \(\angle\)C ?
(a) \(\cfrac{π}{3}\) (b) \(\cfrac{π}{6}\) (c) \(\cfrac{π}{2}\) (d) \(\cfrac{2π}{3}\)
3. If the roots of the equation \( ax^2+bx+c=0 \,(a\ne 0) \) are real and equal, then
(a) \(c=\cfrac{-b}{2a}\) (b) \(c=\cfrac{b}{2a}\) (c) \(c= \cfrac{-b^2}{4a}\) (d) \(c = \cfrac{b^2}{4a}\)
4. If sinA+sinB=2, then what is the value of cosA-cosB
(a) 0 (b) 1 (c) 2 (d) 3
5. If 2a=3b=4c, then what is 2a:5b:7c ?
(a) 2:3:4 (b) 4:15:28 (c) 12:20:21 (d) None of these
6. The median of the data set 6,10,5,4,9,11,20,186,10,5,4,9,11,20,18
(a) 9 (b) 10 (c) 9.25 (d) 9.5
7. 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) -\(\cfrac{1}{3}\)
8. In triangle ABC , what is the value of sin\(\cfrac{(B+C)}{2} \) ?
(a) sin\(\cfrac{A}{2}\) (b) sinA (c) cosA (d) cos \(\cfrac{A}{2}\)
9. The median of the data set 6,7,8,8,9,15,10,15,20,19,25,24,216,7,8,8,9,15,10,15,20,19,25,24,21 is:
(a) 10 (b) 15 (c) 9 (d) 19
10. 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
11. If \( 2 \cos \theta = 1 \), what is the value of \( \theta \) ?
(a) 10° (b) 15° (c) 60° (d) 30°
12. If the ratio of the radii of two perpendicular solid cones is 2:3 and the ratio of their heights is 5:3, what is the ratio of their volumes ?
(a) 27:20 (b) 20:27 (c) 4:9 (d) 9:4
13. If the average of \( x_1, x_2, x_3, \dots, x_n \) is \( \bar{x} \), then what is the average of \( ax_1, ax_2, ax_3, \dots, ax_n \) ?
(a) \(\bar{x}\) (b) \(a\bar{x}\) (c) \(n\bar{x}\) (d) None of these
14. 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
15. 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
16. The median of 10, 14, 8, 16, 20, 15, 9 is
(a) 20 (b) 16 (c) 15 (d) 14
17. At an annual interest rate of 5%, for how many years will the interest on 300 rupees amount to 120 rupees?
(a) 4 (b) 8 (c) 12 (d) 12\(\frac{1}{2}\)
18. The total surface area of a cube is 216 square centimeters. Find the volume of the cube.
19. The median of the numbers 67, 62, 70, 68, 90, 84, 94, 98:
(a) 77 (b) 70 (c) 68 (d) 84
20. 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
21. If, tanθ=cot3θ, then the value of sin2θ be:
(a) \(\cfrac{1}{√2}\) (b) \(\cfrac{√3}{2}\) (c) \(\cfrac{1}{2}\) (d) 0
22. The ratio of the volumes of two cubes is 4:125. What is the ratio of the surface areas of the two cubes?
(a) 2:5 (b) 4:25 (c) 4:5 (d) 2:25
23. If \(2a = 3b = 4c\), then \(a : b : c\) will be.
(a) 2:3:4 (b) 6:4:3 (c) 4:3:2 (d) 3:4:6
24. In a circle with center O, a tangent PT is drawn from an external point P to the circle, with T being the point of tangency. If PT = 12 cm and OP = 13 cm, the diameter of the circle will be:
(a) 5 cm (b) 8 cm (c) 6 cm (d) 10 cm
25. If \(\cfrac{1}{20}\) of a principal is the annual interest, the simple interest rate will be:
(a) 4% (b) 5% (c) 10% (d) 8%
26. 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) \(\cfrac{16}{9}\)
27. The current price of a machine is rupees 2P, and if its price decreases by 2r% each year, then after 2n years, the price of the machine will be:
(a) \(P\left(1-\cfrac{r}{100}\right)^n\) (b) \(2P\left(1-\cfrac{r}{50}\right)^n\) (c) \(P\left(1-\cfrac{r}{50}\right)^{2n}\) (d) \(2P\left(1-\cfrac{r}{50}\right)^{2n}\)
28. A principal amount doubles in 20 years at a certain simple interest rate. At the same rate of simple interest, the time required for the principal to become three times will be:
(a) 30 Years (b) 35 Years (c) 40 Years (d) 45 Years
29. 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
30. In the cyclic quadrilateral ABCD, if \(\angle\)A = 120°, then the measure of \(\angle\)C in a circular sense.
(a) \(\cfrac{π}{2}\) (b) \(\cfrac{π}{3}\) (c) \(\cfrac{π}{6}\) (d) \(\cfrac{π}{4}\)
