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- Question
- The Sum of two number is 1215 and their H.C.F is 81, how many pairs of such number can be formed? Find them?
Options- A. 1
- B. 2
- C. 3
- D. 4
- Correct Answer
- 4
ExplanationLet the number be 81a and 81b where a and b are two numbers prime to each other.
? 81a + 81b = 1215
? a + b = 1215/81 = 15
Now, find two numbers, whose sum is 15, the possible pairs are (14, 1) , (13, 2), (12, 3), (11, 4), (10, 5), (9, 6 ), (8, 7) of these the only pairs of numbers that are prime to each other are (14, 1) , (13, 2), (11, 4), and (8, 7).
Hence, the required number are
(14 x 81, 1 x 81), (13 x 81, 2 x 81), (11 x 81, 4 x 81), (8 x 81, 7 x 81)
or (1134, 81), (1053, 162), (891, 324), (648, 567)
So, there are four such pairs . - 1. The sum of how many terms of the series 6 + 12 + 18 + 24 + ... is 1800?
Options- A. 16
- B. 24
- C. 20
- D. 18
- E. 22 Discuss
- 2. [(0.05) 2 + (0.41) 2 +(0.073) 2] / [(0.005) 2 + (0.041) 2 + (0.0073) 2] =?
Options- A. 0.1
- B. 10
- C. 100
- D. 1000 Discuss
- 3. A, B and C start at the same time in the same direction to run around a circular stadium. A completes a round in 252 seconds, B in 308 seconds and c in 198 seconds, all starting at the same point. After what time will they again at the starting point?
Options- A. 26 minutes and 18 seconds
- B. 42 minutes and 36 seconds
- C. 45 minutes
- D. 46 minutes and 12 seconds Discuss
- 4. (.356 x .365 - 2 x .365 x .106 + .106 x .106) / (.632 x .632 + 2 x .632 x .368 +.368 x .368) =?
Options- A. .25
- B. .0765
- C. .345
- D. 0.625 Discuss
- 5.
(469 + 174)2 - (469 - 174)2 =? (469 x 174)
Options- A. 2
- B. 4
- C. 295
- D. 643 Discuss
- 6. (3.65 x 3.65 + 2.35 x 2.35 - 2 x 2.35 x 3.65) / 1.69 =?
Options- A. 1.69
- B. 2.35
- C. 3.65
- D. 1 Discuss
- 7.
❨ xb ❩ (b + c - a) . ❨ xc ❩ (c + a - b) . ❨ xa ❩ (a + b - c) =? xc xa xb
Options- A. xabc
- B. 1
- C. xab + bc + ca
- D. xa + b + c Discuss
- 8. [{(0.1) 2 - (0.01) 2} / {0.0001 + 1 }] is equal to?
Options- A. 100
- B. 101
- C. 1010
- D. 1101 Discuss
- 9.
(243)n/5 x 32n + 1 =? 9n x 3n - 1
Options- A. 1
- B. 2
- C. 9
- D. 3n Discuss
- 10. G. C. D of 1.08, .36 and .9 is?
Options- A. .03
- B. .9
- C. .18
- D. .108 Discuss
More questions
Correct Answer: 24
Explanation:
This is an A.P. in which a = 6, d = 6 and S n = 1800
| Then, | n | [2a + (n - 1)d] = 1800 |
| 2 |
| ⟹ | n | [2 x 6 + (n - 1) x 6] = 1800 |
| 2 |
⟹ 3n (n + 1) = 1800
⟹ n(n + 1) = 600
⟹ n2 + n - 600 = 0
⟹ n2 + 25n - 24n - 600 = 0
⟹ n(n + 25) - 24(n + 25) = 0
⟹ (n + 25)(n - 24) = 0
⟹ n = 24
Number of terms = 24.
Correct Answer: 100
Explanation:
Given expression = [(0.05)2 + (0.41)2 +(0.073)2] / [(0.005)2 + (0.041)2 + (0.0073)2]
Which is in form of [(a2 + b2 + c2)] /[ (a/10)2 + (b/10)2 + (c/10)2] = 100 x (a2 + b2 + c2) / (a2+b2+c2)
= 100
Correct Answer: 46 minutes and 12 seconds
Explanation:
L.C.M. of 252, 308 and 198 = 2772.
So, A, B and C will again meet at the starting point in 2772 sec. i.e., 46 min. 12 sec.
Correct Answer: 0.625
Explanation:
Given expression = [(.356)2 -2 x .356 x .106 + (.106)2] / [(.632)2+2 x .632 x .368 +(.368)2]
= (a2 -2ab + b2) / (c2+2cd+d2)
= (a - b)2 / (c + d)2
= (.356 -.106)2 / (.632 + .368)2
= (.25)2
= .0625
Correct Answer: 4
Explanation:
| Given exp. = | (a + b)2 - (a - b)2 |
| ab |
| = | 4ab |
| ab |
= 4 (where a = 469, b = 174.)
Correct Answer: 1
Explanation:
Given expression
=[(3.65)2 + (2.35)2 -2 x 3.65 x 2.35 ] / 1.69
=a2 + b2 - 2ab / 1.69, Where a = 3.65 and b = 2.35
=(a - b)2 / 1.69
= (3.65 - 2.35)2 / 1.69
= (1.3)2 / 1.69
= 1.69 / 1.69
= 1
Correct Answer: 1
Explanation:
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Correct Answer: 100
Explanation:
Given expression = (0.01 - 0.0001) / (0.00001 + 1)
= (.0099 / .0001) + 1
= 99 + 1
= 100
Correct Answer: 9
Explanation:
| Given Expression |
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Correct Answer: .18
Explanation:
The Given Number are 1.08, .36 and 0.9
G. C. D of 108, 36 and 90 is 18
? Required G. C. D. = 0.18
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