1. 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
2. The volume ratio of a sphere and the circumscribed cube of the sphere is
(a) π:2 (b) π:3 (c) π:4 (d) π:6
3. If the ratio of the capital investments of A, B, and C is \(\cfrac{1}{2} : \cfrac{1}{3} : \cfrac{1}{4}\) and the total profit is ₹520, then C's share of the profit will be
(a) ₹120 (b) ₹160 (c) ₹180 (d) ₹140
4. Pallavi invests ₹500 for 9 months, and Rajiya invests ₹600 for 5 months in a business. The profit will be distributed between them in the ratio –
(a) 3:2 (b) 5:6 (c) 6:5 (d) 9:5
5. If the ratio of the radii of two vertical solid circular cylinders is 2:3, and the ratio of their heights is 5:3, then the ratio of their curved surface areas will be –
(a) 2:5 (b) 8:7 (c) 10:9 (d) 16:9
6. 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
7. If the volumes of two cones are in the ratio 1:4 and the ratio of the diameters of their bases is 4:5, find the ratio of their heights
(a) 1:5 (b) 5:4 (c) 5:16 (d) 25:64
8. If \(∑f_i d_i = 400\), \(∑f_i = 50\), and \(a =\) assumed mean \(= 52\), then the value of the combined mean is –
(a) 52 (b) 60 (c) 80 (d) 55
9. If the ratio of the principal and the total amount is 10:11, what is the annual interest rate?
(a) 10% (b) 11% (c) \(10\cfrac{1}{11}\)% (d) 12%
10. A straight line parallel to side BC of \(\triangle\)ABC intersects AB and AC at points P and Q, respectively. If AQ = 2AP, then what is the ratio PB:QC?
(a) 1:2 (b) 2:1 (c) 1:1 (d) None of these
11. If a hemisphere and a cone have equal base areas and equal heights, then what will be the ratio of their volumes?
(a) 1:3 (b) 2:3 (c) 3:2 (d) 3:1
12. In a partnership business, Ratan, Suresh, and Ramesh invested in the ratio \(\frac{1}{6} : \frac{1}{5} : \frac{1}{4}\). If the profit at the end of the year is ₹3700, what is Ramesh's share of the profit?
(a) ₹ 1400 (b) ₹ 1200 (c) ₹ 1500 (d) ₹ 1600
13. The volume of a right rectangular prism is 960 cubic centimeters. If the ratio of its length, width, and height is 6:5:4, what is the total surface area of the prism?
(a) 590 square cm (b) 592 square cm (c) 295 square cm (d) 596 square cm
14. A's amount is \(\cfrac{3}{4}\) of B's amount, and B's amount is \(1\cfrac{1}{5}\) times C's amount. What is the ratio of A's amount to C's amount?
(a) 19:20 (b) 10:9 (c) 9:10 (d) 20:19
15. The ratio of monthly income of K and Kh is 3 : 8, and the ratio of monthly income of Kh and G is 4 : 9. What will be the ratio of monthly income of K and G?
(a) 2:3 (b) 1:6 (c) 1:4 (d) 3:2
16. The ratio of the base radii of two right circular cones is 2 : 3, and the ratio of their heights is 3 : 2. Then the ratio of their volumes is —
(a) 3:2 (b) 9:4 (c) 4:9 (d) 2:3
17. What is the ratio of the speeds of the hour hand, minute hand, and second hand of a clock?
(a) 1:12:60 (b) 1:60:720 (c) 1:12:720 (d) None of the above
18. A, B, and C started a joint business. A's invested amount is 3 times that of B, and C invested \(\frac{2}{3}\) of what B invested. What will be the ratio of the capital contributions of A, B, and C?
(a) 6:2:3 (b) 2:6:3 (c) 3:6:2 (d) 6:3:2
19. What is the ratio of the volumes of a right circular cylinder and a cone having the same radius and height?
(a) 1:3 (b) 3:2 (c) 3:1 (d) 2:3
20. If the diameters of two cones are equal and the ratio of their slant heights is 5:7, then what is the ratio of their curved surface areas?
(a) 25:7 (b) 25:49 (c) 5:49 (d) 5:7
21. If the length, breadth, and height of a right rectangular prism are in the ratio 3:2:1 and its total surface area is 88 square centimeters, then what is its volume?
(a) 120 cubic cm (b) 64 cubic cm (c) 48 cubic cm (d) 24 cubic cm
22. If the volumes of two cones are in the ratio 2:3 and the ratio of their base radii is 1:2, then what is the ratio of their heights?
(a) 3:8 (b) 8:3 (c) 3:4 (d) 4:3
23. If the combined average of 5, 15, 22, x, y, 25, and z is 14, then which of the following is correct?
(a) x+y+z=42 (b) x+y+z=31 (c) x+y=z (d) x+y=2z
24. If \(\sum f_iu_i = 10\), class width = 20, \(\sum f_i = 40 + k\), the combined mean is 54, and the assumed mean is 50, then what is the value of \(k\)?
25. If \(\sum{f_ix_i} = 216\), \(\sum{f_i} = 16\), and the combined mean is \(13.5 + p\), then what is the value of \(p\)?
(a) 0 (b) 1 (c) 0.1 (d) 0.01
26. If the combined mean of \(n\) quantities is \(\bar{x}\), and the sum of the first \((n-1)\) quantities is \(k\), then the \(n\)th quantity will be —
(a) \(k+n\) (b) \(\bar{x}+k\) (c) \(\bar{x}-k\) (d) \(n\bar{x}-k\)
27. If the combined average of the expressions ???? − 3 , ???? − 1 , 7 , ???? , 2 ???? − 1 , and 3 ???? − 5 is 3.5, then what will be the median of these expressions?
(a) 3.5 (b) 4.5 (c) 5 (d) 5.5
28. If the mode and the combined mean of a statistical distribution are ₹12.30 and ₹18.48 respectively, then the median of the distribution will be —
(a) ₹ 16 (b) ₹ 17 (c) ₹ 16.42 (d) ₹ 17.42
29. If the ratio of A to B is 2:3 and the ratio of B to C is 4:3, then what is the ratio A:B:C?
(a) 8:12:15 (b) 6:9:8 (c) 8:12:9 (d) 8:16:9
30. In a partnership business, the capital ratio between A and B is 2:3, and the capital ratio between B and C is 6:5. If A's profit share is ₹400, what will be C's profit share?
(a) ₹ 500 (b) ₹ 600 (c) ₹ 700 (d) ₹ 800
