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- Question
- In how many ways can the letters of the word 'Director' be arranged so that the three vowels are never together?
Options- A. 1800
- B. 18000
- C. 16000
- D. 1600
- Correct Answer
- 18000
ExplanationTotal number of letters = 8
Number of vowels = 3 and r occurs twice.
Total number of arrangements when there is no restriction = 8!/2!
When three vowels are together, regarding them as one letter, we have only 5 + 1 = 6 letters
These six letters can be arranged in 6!/2! ways, since r occurs twice.
But the three vowels can be arranged among themselves in 3! ways.
Hence number of arrangement when the three vowels are together = 6! /(2 !x 3!)
? Required number = 8!/2! - {6! / (2! x 3!)} = 18,000 - 1. A can complete a piece of work in 10 days, while B alone can complete it in 15 days. They work together for 5 days and rest of the work is done by C in 2 days. If they receive $ 450 for the whole work, how should they divide the money?
Options- A. $250, $100, $100
- B. $225, $150, $75
- C. $200, $150, $100
- D. $175, $175, $100 Discuss
- 2. The angle of elevation of a tower from a distance 50 m from its foot is 30°. The height of the tower is :
Options- A. 50 ?3 m
- B. 50 m ?3
- C. 75 ?3 m
- D. 75 m ?3 Discuss
- 3. If 30% of A = 20 % of B, then find the value of A : B?
Options- A. 1 : 3
- B. 3 : 2
- C. 3 : 1
- D. 2 : 3 Discuss
- 4. 80 litre mixture of milk and water contains 10% milk. How much milk (in litres) must be added to make water percentage in the mixture as 80%?
Options- A. 8
- B. 9
- C. 10
- D. 12 Discuss
- 5. If log 5 (x 2 + x) - log 5 x = 2 then the value of x is?
Options- A. 24
- B. 25
- C. 23
- D. 120 Discuss
- 6. The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?
Options- A. 0
- B. 1
- C. 10
- D. 19 Discuss
- 7. Two trains A and B travel from points X to Y and the ratio of the speeds of A to that of B is 2 : 7. Find the ratio of time taken by A and B to reach From X to Y.
Options- A. 2 : 5
- B. 3 : 5
- C. 3 : 8
- D. 7 : 2 Discuss
- 8. Walking with 3/4 of his usual speed, Sachin covers a certain distance in 2 h more than the time he takes to cover the distance at his usual speed. Find the time taken by him to cover this distance with usual speed.
Options- A. 5 h
- B. 6 h
- C. 9 h
- D. 4 h Discuss
- 9. If ? 2 n = 64, then the value of n is?
Options- A. 2
- B. 4
- C. 6
- D. 12 Discuss
- 10. Ram and Sita are walking towards each other with the speed of 8 km/h and 2 km/h, respectively over a road 160 km long. How soon will they meet?
Options- A. 16 h
- B. 8 h
- C. 10 h
- D. 20 h Discuss
More questions
Correct Answer: $225, $150, $75
Explanation:
Correct Answer: 50 m ?3
Explanation:
Correct Answer: 2 : 3
Explanation:
Given that, 30 % of A = 20 % of B
? A/B = 20/30 = 2/3
? A : B = 2 : 3
Correct Answer: 10
Explanation:
Let initial quantity be Q, and final quantity be F
F = Q(1 - 8/Q)
=> Q = 20
Correct Answer: 24
Explanation:
? log5[(x2 + x ) / x] = 2
? log10(x + 1) = 2
? x + 1 = 25
? x = 24
Correct Answer: 19
Explanation:
Average of 20 numbers = 0.
∴ Sum of 20 numbers (0 x 20) = 0.
It is quite possible that 19 of these numbers may be positive and if their sum is a then 20th number is (-a).
Correct Answer: 7 : 2
Explanation:
We know that speed is inversely proportional to time.
Given that, (Speed of A ) : (speed of B ) = 2 : 7
?(Time taken by A ) : (Time taken by B ) = 1/2 : 1/7 = 7 : 2
Correct Answer: 6 h
Explanation:
Let th distance = D
and usual speed = V
According to the question,
D/(3V/4) - D/V = 2
? D/V = 3 x 2 = 6
Time taken to cover the distance with usual speed = 6 h
Correct Answer: 12
Explanation:
?2n = 64
? 2n/2 = 26
? n/2 = 6
? n = 12
Correct Answer: 16 h
Explanation:
Distance = 160 km
Relative Speed = 8 + 2 = 10
Time = Distance/Relative speed = 160/10 = 16 h
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