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CAT Standard Multiple-choice Question Papers 04 |
There are 2 brothers among a group of 20 persons. In how many ways can the group be arranged around a circle so that there is exactly one person between the two brothers?
2 * 19!
18! * 18
19! * 18
2 * 18!
Ans : D
How many words can be formed by re-arranging the letters of the word ASCENT such that A and T occupy the first and last position respectively?
5!
4!
6! - 2!
6! / 2!
Ans : B
There are 12 yes or no questions. How many ways can these be answered?
1024
2048
4096
144
Ans : C
How many ways can 4 prizes be given away to 3 boys, if each boy is eligible for all the prizes?
256
12
81
None of these
Ans : C
A team of 8 students goes on an excursion, in two cars, of which one can seat 5 and the other only 4. In how many ways can they travel?
9
26
126
3920
Ans : C
How many numbers are there between 100 and 1000 such that atleast one of their digits is 6?
648
258
654
252
Ans : D
How many ways can 10 letters be posted in 5 post boxes, if each of the post boxes can take more than 10 letters?
5 10
10 5
10P5
10C5
Ans : A
In how many ways can the letters of the word EDUCATION be rearranged so that the relative position of the vowels and consonants remain the same as in the word EDUCATION?
9!/4
9!/(4!*5!)
4!*5!
None of these
Ans : C
In how many ways can 15 people be seated around two round tables with seating capacities of 7 and 8 people?
15!/(8!)
7!*8!
(15C8)*6!*7!
2*(15C7)*6!*7!
Ans : C
If the letters of the word CHASM are rearranged to form 5 letter words such that none of the word repeat and the results arranged in ascending order as in a dictionary what is the rank of the word CHASM?
24
31
32
30
Ans : C
Permutation and Combination
How many words of 4 consonants and 3 vowels can be made from 12 consonants and 4 vowels, if all the letters are different?
16C7 * 7!
12C4 * 4C3 * 7!
12C3 * 4C4
12C4 * 4C3
Ans : B
In how many ways can 5 letters be posted in 3 post boxes, if any number of letters can be posted in all of the three post boxes?
5C3
5P3
53
35
Ans : D
How many number of times will the digit '7' be written when listing the integers from 1 to 1000?
271
300
252
304
Ans : B
There are 6 boxes numbered 1, 2,...6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is
5
21
33
60
Ans : B
What is the value of 1*1! + 2*2! + 3!*3! + ............ n*n!, where n! means n factorial or n(n-A(n-2)...1
n(n-A(n-A!))
(n+A!)/(n(n-A))
(n+A! - n!)
(n + A! - 1!)
Ans : D
There are 5 Rock songs, 6 Carnatic songs and 3 Indi pop songs. How many different albums can be formed using the above repertoire if the albums should contain at least 1 Rock song and 1 Carnatic song?
15624
16384
6144
240
Ans : A
In how many ways can the letters of the word MANAGEMENT be rearranged so that the two As do not appear together?
10! - 2!
9! - 2!
10! - 9!
None of these
Ans : D
How many five digit numbers can be formed using the digits 0, 1, 2, 3, 4 and 5 which are divisible by 3, without repeating the digits?
15
96
216
120
Ans : C
How many words can be formed by re-arranging the letters of the word PROBLEMS such that P and S occupy the first and last position respectively?
8! / 2!
8! - 2!
6!
8! - 2*7!
Ans : C
Four dice are rolled simultaneously. What is the number of possible outcomes in which at least one of the die shows 6?
6! / 4!
625
671
1296
Ans : C
Percentage
A trader makes a profit equal to the selling price of 75 articles when he sold 100 of the articles. What % profit did he make in the transaction?
33.33%
75%
300%
150%
Ans : C
A merchant buys two articles for Rs.600. He sells one of them at a profit of 22% and the other at a loss of 8% and makes no profit or loss in the end. What is the selling price of the article that he sold at a loss?
Rs. 404.80
Rs. 440
Rs. 536.80
Rs. 160
Ans : A
A trader professes to sell his goods at a loss of 8% but weights 900 grams in place of a kg weight. Find his real loss or gain per cent.
2% loss
2.22% gain
2% gain
None of these
Ans : B
Rajiv sold an article for Rs.56 which cost him Rs.x. If he had gained x% on his outlay, what was his cost?
Rs. 40
Rs. 45
Rs. 36
Rs. 28
Ans : A
A trader buys goods at a 19% Aount on the label price. If he wants to make a profit of 20% after allowing a Aount of 10%, by what % should his marked price be greater than the original label price?
+8%
-3.8%
+33.33%
None of these
Ans : A
If apples are bought at the rate of 30 for a rupee. How many apples must be sold for a rupee so as to gain 20%?
28
25
20
22
Ans : B
One year payment to the servant is Rs. 200 plus one shirt. The servant leaves after 9 months and recieves Rs. 120 and a shirt. Then find the price of the shirt.
Rs. 80
Rs. 100
Rs. 120
Cannot be determined
Ans : C
Two merchants sell, each an article for Rs.1000. If Merchant A computes his profit on cost price, while Merchant B computes his profit on selling price, they end up making profits of 25% respectively. By how much is the profit made by Merchant B greater than that of Merchant A?
Rs.66.67
Rs. 50
Rs.125
Rs.200
Ans : B
A merchant marks his goods in such a way that the profit on sale of 50 articles is equal to the selling price of 25 articles. What is his profit margin?
25%
50%
100%
66.67%
Ans : C
A merchant marks his goods up by 75% above his cost price. What is the maximum % Aount that he can offer so that he ends up selling at no profit or loss?
75%
46.67%
300%
42.85%
Ans : D
Speed, Time and Distance
Rajesh traveled from city A to city B covering as much distance in the second part as he did in the first part of this journey. His speed during the second part was twice as that of the speed during the first part of the journey. What is his average speed of journey during the entire travel?
His average speed is the harmonic mean of the individual speeds for the two parts.
His average speed is the arithmetic mean of the individual speeds for the two parts.
His average speed is the geometric mean of the individual speeds for the two parts.
Cannot be determined.
Ans : B
Two boys begin together to write out a booklet containing 535 lines. The first boy starts with the first line, writing at the rate of 100 lines an hour; and the second starts with the last line then writes line 534 and so on, backward proceeding at the rate of 50 lines an hour. At what line will they meet?
356
277
357
267
Ans : C
A man and a woman 81 miles apart from each other, start travelling towrds each other at the same time. If the man covers 5 miles per hour to the women's 4 miles per hour, how far will the woman have travelled when they meet?
27
36
45
None of these.
Ans : B
The speed of a motor boat itself is 20 km/h and the rate of flow of the river is 4 km/h. Moving with the stream the boat went 120 km. What distance will the boat cover during the same time going against the stream?
80 km
180 km
60 km
100 km
Ans : A
Two friends A and B run around a circular track of length 510 metres, starting from the same point, simultaneously and in the same direction. A who runs faster laps B in the middle of the 5th round. If A and B were to run a 3 km race long race, how much start, in terms of distance, should A give B so that they finish the race in a dead heat?
545.45 metres
666.67 metres
857.14 metres
Cannot be determined
Ans : B
I travel the first part of my journey at 40 kmph and the second part at 60 kmph and cover the total distance of 240 km to my destination in 5 hours. How long did the first part of my journey last?
4 hours
2 hours
3 hours
2 hours 24 minutes
Ans : C
By walking at 3/4th of his usual speed, a man reaches office 20 minutes later than usual. What is his usual time?
30 min
60 min
70 min
50 min
Ans : B
A passenger train covers the distance between stations X and Y, 50 minutes faster than a goods train. Find this distance if the average speed of the passenger train is 60 kmph and that of goods train is 20 kmph.
20 kms
25 kms
45 kms
40 kms
Ans : B
Yana and Gupta leave points x and y towards y and x respectively simultaneously and travel in the same route. After meeting each other on the way, Yana takes 4 hours to reach her destination, while Gupta takes 9 hours to reach his destination. If the speed of Yana is 48 km/hr, what is the speed of Gupta?
72 kmph
32 mph
20 mph
None of these
Ans : C
Ram covers a part of the journey at 20 kmph and the balance at 70 kmph taking total of 8 hours to cover the distance of 400 km. How many hours has been driving at 20 kmph?
2 hours
3 hours 20 minutes
4 hours 40 minutes
3 hours 12 minutes
Ans : D
Speed, Time and Distance
Train A traveling at 60 km/hr leaves Mumbai for Delhi at 6 P.M. Train B traveling at 90 km/hr also leaves Mumbai for Delhi at 9 P.M. Train C leaves Delhi for Mumbai at 9 P.M. If all three trains meet at the same time between Mumbai and Delhi, what is the speed of Train C if the distance between Delhi and Mumbai is 1260 kms?
60 km/hr
90 km/hr
120 km/hr
135 km/hr
Ans : C
Two trains, 200 and 160 meters long take a minute to cross each other while traveling in the same direction and take only 10 seconds when they cross in opposite directions. What are the speeds at which the trains are traveling?
21 m/s; 15 m/s
30 m/s; 24 m/s
18 m/s; 27 m/s
15 m/s; 24 m/s
Ans : A
An express train traveling at 72 km/hr speed crosses a goods train traveling at 45 km/hr speed in the opposite direction in half a minute. Alternatively, if the express train were to overtake the goods train, how long will it take to accomplish the task. Assume that the trains continue to travel at the same respective speeds as mentioned in case 1.
Cannot be determined
30 seconds
150 seconds
130 seconds
Ans : D
A train travels at an average speed of 90 km/hr without any stoppages. However, its average speed decrease to 60km/hr on account of stoppages. On an average, how many minutes per hour does the train stop?
12 minutes
18 minutes
24 minutes
20 minutes
Ans : D
Two trains A and B start simultaneously from stations X and Y towards each other respectively. After meeting at a point between X and Y, train A reaches station Y in 9 hours and train B reaches station X in 4 hours from the time they have met each other. If the speed of train A is 36 km/hr, what is the speed of train B?
24 km/hr
54 km/hr
81 km/hr
16 km/hr
Ans : B
A man moves from A to B at the rate of 4 km/hr. Had he moved at the rate of 3.67 km/hr, he would have taken 3 hours more to reach the destination. What is the distance between A and B?
33 kms
132 kms
36 kms
144 kms
Ans : B
A ship develops a leak 12 km from the shore. Despite the leak, the ship is able to move towards the shore at a speed of 8 km/hr. However, the ship can stay afloat only for 20 minutes. If a rescue vessel were to leave from the shore towards the ship, and it takes 4 minutes to evacuate the crew and passengers of the ship, what should be the minimum speed of the rescue vessel in order to be able to successfully rescue the people aboard the ship?
53 km/hr
37 km/hr
28 km/hr
44 km/hr
Ans : B
A man driving his bike at 24 kmph reaches his office 5 minutes late. Had he driven 25% faster on an average he would have reached 4 minutes earlier than the scheduled time. How far is his office?
24 km
72 km
18 km
Data Insufficient
Ans : C
When an object is dropped, the number of feet N that it falls is given by the formula N = ½gt2 where t is the time in seconds from the time it was dropped and g is 32.2. If it takes 5 seconds for the object to reach the ground, how many feet does it fall during the last 2 seconds?
64.4
96.6
161.0
257.6
Ans : D
If the wheel of a bicycle makes 560 revolutions in travelling 1.1 km, what is its radius?
31.25 cm
37.75 cm
35.15 cm
11.25 cm
Ans : A
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