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- Question
In how many ways the letters of the word 'CIRCUMSTANCES' can be arranged such that all vowels came at odd places and N always comes at end?
Options- A. 1,51,200 ways.
- B. 5,04,020 ways
- C. 72,000 ways
- D. None of the above
- Correct Answer
- 1,51,200 ways.
ExplanationIn circumcstances word there are 3C's, 2S's, I, U,R, T, A, N, E
Total = 13 letters
But last letter must be N
Hence, available places = 12
In that odd places = 1, 3, 5, 7, 9, 11
Owvels = 4
This can be done in 6P4 ways
Remaining 7 letters can be arranged in 7!/3! x 2! ways
Hence, total number of ways = 6P4 x 7!/3! x 2! = 360 x 5040/12 = 1,51,200 ways.
- 1. An equilateral triangle is described on the diagonal of a square. What is the ratio of the area of the triangle to that of the square?
Options- A. 1:2
- B. 1:3
- C. 2:3
- D. 3^(1/2) :2 Discuss
- 2. The circumference of a circle, whose area is 24.64 sq.m
Options- A. 14.64
- B. 16.36
- C. 17.60
- D. 18.40 Discuss
- 3. Find the remainder when 1234 x 1235 x 1237 is divided by 8.
Options- A. 4
- B. 2
- C. 0
- D. 6 Discuss
- 4. If the parallel sides of a trapezium are 8 cm and 4 cm, M and N are the mid points of the diagonals of the trapezium, then length of MN is
Options- A. 12 cm
- B. 6 cm
- C. 1 cm
- D. 2 cm Discuss
- 5. If sum of upstream and downstream speed of a boat is 82 kmph, and the boat travels 105 km. upstream in 3 hr, Find the time taken by boat to cover 126 km downstream.
Options- A. 2.8 hrs
- B. 2.7 hrs
- C. 2.6 hrs
- D. 2.5 hrs Discuss
- 6. How many days are there in k weeks k days ?
Options- A. 8+k days
- B. 7+1k days
- C. 8k days
- D. 7/k days Discuss
- 7. A batsman scores 26 runs and increases his average from 14 to 15. Find the runs to be made if he wants top increasing the average to 19 in the same match ?
Options- A. 74
- B. 79
- C. 72
- D. 60 Discuss
- 8. There are 44 students in a hostel, due to the administration, 15 new students has joined. The expense of the mess increase by Rs. 33 per day. While the average expenditure per head diminished by Rs. 3, what was the original expenditure of the mess ?
Options- A. Rs. 404
- B. Rs. 514
- C. Rs. 340
- D. Rs. 616 Discuss
- 9. A motorist travels to a place 150 km away at an average speed of 50 km/hr and returns at 30 km/hr. His average speed for the whole journey in km/hr is :
Options- A. 35
- B. 36
- C. 37.5
- D. 38.2 Discuss
- 10. In one hour, a boat goes 12 km/hr along the stream and 6 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
Options- A. 9
- B. 8
- C. 7
- D. 7.5 Discuss
More questions
Correct Answer: 3^(1/2) :2
Explanation:
area of a square = a² sq cm
length of the diagonal = cm
area of equilateral triangle with side
=
required ratio =
Correct Answer: 17.60
Explanation:
Correct Answer: 6
Explanation:
When we divide 1234 by 8, remainder is 2
When we divide 1235 by 8, remainder is 3
When we divide 1237 by 8, remainder is 5
---> 2 x 3 x 5 = 30
As 30 will not be the remainder because it is greater than 8,
when 30 divided by 8, remainder = 6.
Correct Answer: 2 cm
Correct Answer: 2.7 hrs
Explanation:
Let Speed of boat in still water = b
Let Speed of still water = w
Then we know that,
Speed of Upstream = U = boat - water
Speed of Downstream = D = boat + water
Given, U + D = 82
b - w + b + w = 82
2b = 82
=> b = 41 kmph
From the given data,
41 - w = 105/3 = 35
w = 6 kmph
Now,
b + w = 126/t
=> 41 + 6 = 126/t
=> t = 126/47 = 2.68 hrs.
Correct Answer: 8k days
Explanation:
As we know that a week has 7 days,
k weeks k days = (7k + k) days = 8k days.
Correct Answer: 74
Explanation:
Number of runs scored more to increse the ratio by 1 is 26 - 14 = 12
To raise the average by one (from 14 to 15), he scored 12 more than the existing average.
Therefore, to raise the average by five (from 14 to 19), he should score 12 x 5 = 60 more than the existing average. Thus he should score 14 + 60 = 74.
Correct Answer: Rs. 616
Explanation:
Let the average expenditure per head be Rs. p
Now, the expenditure of the mess for old students is Rs. 44p
After joining of 15 more students, the average expenditure per head is decreased by Rs. 3 => p-3
Here, given the expenditure of the mess for (44+15 = 59) students is increased by Rs. 33
Therefore, 59(p-3) = 44p + 33
59p - 177 = 44p + 33
15p = 210
=> p = 14
Thus, the expenditure of the mess for old students is Rs. 44p = 44 x 14 = Rs. 616.
Correct Answer: 37.5
Explanation:
Average speed = (2xy) /(x + y) km/hr
= (2 * 50 * 30) / (50 + 30) km/hr.
37.5 km/hr.
Correct Answer: 9
Explanation:
Speed in still water = Average of Speed in Upstream and speed in Downstream
= 1/2 (12 + 6) kmph = 9 kmph.
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