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CAT Standard Multiple-choice Question Papers 02 |
Geometry
Find the coordinates of the point which divides the line joining (5, -2) and (9, 6) internally in the ratio 1 : 3.
(6, 0)
(6, 3)
(0, 6)
(3, 6)
Ans : A
Find the number of triangles in an octagon.
326
120
56
Cannot be determined
Ans : C
Find the equation of a line whose intercepts are twice of the line 3x - 2y - 12 = 0
3x - 2y = 24
2x - 3y = 12
2x - 3y = 24
None of these
Ans : A
Find the area of the sector covered by the hour hand after it has moved through 3 hours and the length of the hour hand is 7cm.
77 sq.cm
38.5 sq.cm
35 sq.cm
70 sq.cm
Ans : B
Find the area of the triangle whose vertices are (-6, -2), (-4, -6), (-2, 5).
36
18
15
30
Ans : C
A stairway 10ft high is such that each step accounts for half a foot upward and one-foot forward. What distance will an ant travel if it starts from ground level to reach the top of the stairway?
30 ft
33 ft
10 ft
29 ft
Ans : D
Each interior angle of a regular polygon is 120 degrees greater than each exterior angle. How many sides are there in the polygon?
6
8
12
3
Ans : C
What is the area of the largest triangle that can be fitted into a rectangle of length 'l' units and width 'w' units?
lw/3
(2lw)/3
(3lw)/4
(lw)/2
Ans : D
Which of the following is inCorrect?
An incentre is a point where the angle bisectors meet.
The median of any side of a triangle bisects the side at right angle.
The point at which the three altitudes of a triangle meet is the orthocentre
The point at which the three perpendicular bisectors meet is the centre of the circumcircle.
Ans : B
A and B are two points with the co-ordinates (-2, 0) and (0, 5). What is the length of the diagonal AC if AB form one of the sides of the square ABCD?
units
units
units
units
Ans : B
Geometry
What is the measure of the circum radius of a triangle whose sides are 9, 40 and 41?
6
4
24.5
20.5
Ans : D
If the sum of the interior angles of a regular polygon measures up to 1440 degrees, how many sides does the polygon have?
10 sides
8 sides
12 sides
9 sides
Ans : A
If ABC is a right angle triangle with angle A = 900 and 2s = a + b + c, where a > b > c where notations have their usual meanings, then which one of the following is Correct?
(s - b) (s - c) > s (s - a)
(s - a) (s - c) > s (s - b)
(s - a) (s - b) < s (s - c)
4s (s - a) (s - b) (s - c) = bc
Ans : C
What is the measure of in radius of the triangle whose sides are 24, 7 and 25?
12.5
3
6
None of these
Ans : B
What is the circum radius of a triangle whose sides are 7, 24 and 25 respectively?
18
12.5
12
14
Ans : B
Quantitative Ability : Menstruation
A regular hexagon is inscribed in a circle of radius r cms. What is the perimeter of the regular hexagon?
3r
6r
r
9r
Ans : B
A 4 cm cube is cut into 1 cm cubes. What is the percentage increase in the surface area after such cutting?
4%
300%
75%
400%
Ans : B
If the diagonal and the area of a rectangle are 25 m and 168 m2, what is the length of the rectangle?
17 m
31 m
12 m
24 m
Ans : D
The surface area of the three coterminous faces of a cuboid are 6, 15, 10 sq.cm respectively. Find the volume of the cuboid.
30
20
40
35
Ans : A
If each interior angle of a regular polygon is 150 degrees, then it is
Octagon
Decagon
Dodecagon
Tetrahedron
Ans : C
Menstruation
A 5 cm cube is cut into as many 1 cm cubes as possible. What is the ratio of the surface area of the larger cube to that of the sum of the surface areas of the smaller cubes?
1 : 6
1 : 5
1 : 25
1 : 125
Ans : B
If the sides of a triangle measure 72, 75 and 21, what is the measure of its in radius?
37.5
24
9
15
Ans : C
The circumference of the front wheel of a cart is 30 ft long and that of the back wheel is 36 ft long. What is the distance travelled by the cart, when the front wheel has done five more revolutions than the rear wheel?
20 ft
25 ft
750 ft
900 ft
Ans : D
The area of a square field is 24200 sq m. How long will a lady take to cross the field diagonally at the rate of 6.6 km/hr?
3 minutes
2 minutes
2.4 minutes
2 minutes 40 seconds
Ans : B
Quantitative Ability : Trignometry
a and b are the lengths of the base and height of a right angled triangle whose hypotenuse is h. If the values of a and b are positive integers, which of the following cannot be a value of the square of the hypotenuse?
13
23
37
41
Ans : B
The angle of elevation of the top of a tower 30 m high, from two points on the level ground on its opposite sides are 45 degrees and 60 degrees. What is the distance between the two points?
30
51.96
47.32
81.96
Ans : C
What is the value of cot 15 o + cot 75 o + cot 135 o - cosec 30 o ?
3
Infinity
1
None of these
Ans : C
Ratio And Proportion
Rs.432 is divided amongst three workers A, B and C such that 8 times A's share is equal to 12 times B's share which is equal to 6 times C's share. How much did A get?
Rs.192
Rs.133
Rs.144
Rs.128
Ans : C
If 20 men or 24 women or 40 boys can do a job in 12 days working for 8 hours a day, how many men working with 6 women and 2 boys take to do a job four times as big working for 5 hours a day for 12 days?
8 men
12 men
2 men
24 men
Ans : C
Two cogged wheels of which one has 32 cogs and other 54 cogs, work into each other. If the latter turns 80 times in three quarters of a minute, how often does the other turn in 8 seconds?
48
135
24
None of these
Ans : C
Ratio And Proportion
The monthly incomes of A and B are in the ratio 4 : 5, their expenses are in the ratio 5 : 6. If 'A' saves Rs.25 per month and 'B' saves Rs.50 per month, what are their respective incomes?
Rs.400 and Rs.500
Rs.240 and Rs.300
Rs.320 and Rs.400
Rs.440 and Rs.550
Ans : A
The proportion of milk and water in 3 samples is 2:1, 3:2 and 5:3. A mixture comprising of equal quantities of all 3 samples is made. The proportion of milk and water in the mixture is
2:1
5:1
99:61
227:133
Ans : D
A group of workers can do a piece of work in 24 days. However as 7 of them were absent it took 30 days to complete the work. How many people actually worked on the job to complete it?
35
30
28
42
Ans : C
A, B and C play cricket. A's runs are to B's runs and B's runs are to C's as 3:2. They get altogether 342 runs. How many runs did A make?
162
108
72
None of these
Ans : A
The monthly salaries of two persons are in the ratio of 4:7. If each receives an increase of Rs.25 in the salary, the ratio is altered to 3: 5. Find their respective salaries.
120 and 210
80 and 140
180 and 300
200 and 350
Ans : D
A fort has provisions for 60 days. If after 15 days 500 men strengthen them and the food lasts 40 days longer, how many men are there in the fort?
3500
4000
6000
None of these
Ans : B
The ratio of marks obtained by vinod and Basu is 6:5. If the combined average of their percentage is 68.75 and their sum of the marks is 275, find the total marks for which exam was conducted.
150
200
400
None of these.
Ans : B
The present ages of A and B are as 6 : 4. Five years ago their ages were in the ratio 5 : 3. Find their present ages.
42, 28
36, 24
30, 20
25, 15
Ans : C
A, B and C enter into a partnership by investing Rs.3600, Rs.4400 and Rs.2800. A is a working partner and gets a fourth of the profit for his services and the remaining profit is divided amongst the three in the rate of their investments. What is the amount of profit that B gets if A gets a total of Rs. 8000?
4888.88
9333.33
4000
3666.66
Ans : A
A, B and C, each of them working alone can complete a job in 6, 8 and 12 days respectively. If all three of them work together to complete a job and earn Rs.2340, what ill be C's share of the earnings?
Rs.520
Rs.1080
Rs.1170
Rs.630
Ans : A
Mixtures and Alligations
A 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2. 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more. At the end of the two removal and replacement, what is the ratio of milk and water in the resultant mixture?
17 : 3
9 : 1
3 : 17
5 : 3
Ans : B
In what ratio must a person mix three kinds of tea costing Rs.60/kg, Rs.75/kg and Rs.100 /kg so that the resultant mixture when sold at Rs.96/kg yields a profit of 20%?
1 : 2 : 4
3 : 7 : 6
1 : 4 : 2
None of these
Ans : C
A merchant mixes three varieties of rice costing Rs.20/kg, Rs.24/kg and Rs.30/kg and sells the mixture at a profit of 20% at Rs.30 / kg. How many kgs of the second variety will be in the mixture if 2 kgs of the third variety is there in the mixture?
1 kg
5 kgs
3 kgs
6 kgs
Ans : B
How many litres of water should be added to a 30 litre mixture of milk and water containing milk and water in the ratio of 7 : 3 such that the resultant mixture has 40% water in it?
7 litres
10 litres
5 litres
None of these
Ans : C
How many kgs of Basmati rice costing Rs.42/kg should a shopkeeper mix with 25 kgs of ordinary rice costing Rs.24 per kg so that he makes a profit of 25% on selling the mixture at Rs.40/kg?
20 kgs
12.5 kgs
16 kgs
200 kgs
Ans : A
How many litres of a 12 litre mixture containing milk and water in the ratio of 2 : 3 be replaced with pure milk so that the resultant mixture contains milk and water in equal proportion?
4 litres
2 litres
1 litre
1.5 litres
Ans : B
A sample of x litres from a container having a 60 litre mixture of milk and water containing milk and water in the ratio of 2 : 3 is replaced with pure milk so that the container will have milk and water in equal proportions. What is the value of x?
6 litres
10 litres
30 litres
None of these
Ans : B
A zookeeper counted the heads of the animals in a zoo and found it to be 80. When he counted the legs of the animals he found it to be 260. If the zoo had either pigeons or horses, how many horses were there in the zoo?
40
30
50
60
Ans : C
From a cask of milk containing 30 litres, 6 litres are drawn out and the cask is filled up with water. If the same process is repeated a second, then a third time, what will be the number of litres of milk left in the cask?
0.512 liters
12 liters
14.38 liters
15.36 liters
Ans : D
In a km race, A gives B a start of 20 seconds and beats him by 40m. However, when he gives B a start of 25 seconds they finish in a dead heat. What is A's speed in m/sec?
12.5 m/sec
20 m/sec
8 m/sec
10 m/sec
Ans : D
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