CAT 2012
A student is asked to form numbers between 3000 and 9000 with digits 2, 3, 5, 7 and 9. If no digit is to be repeated, in how many ways can the student do so?
(a) 24
(b) 120
(C) 60
(d) 72
CAT 2012
A, B and C can independently do a work in 15 days, 20 days and 30 days, respectively. They work together for some time after which Cleaves. A total of Rs.18000 is paid for the work and B gets Rs. 6000 more than C. For how many days did A work?
A. 2
B. 4
C. 6
D. 8
CAT 2014
Three identical cones with base radius r are placed on their bases so that each is touching the other two. The radius of the circle drawn through their vertices is
(a) smaller than r.
(b) equal to r.
(c) larger than r.
(d) depends on the height of the cones
CAT 2014
From each of the two given numbers, half the smaller number is subtracted. Of the resulting numbers, the larger one is three times as large as the smaller. What is the ratio of the two numbers?
(a) 2 : 1
(b) 3 : 1
(c) 3 : 2
(d) None
CAT 2017 SLOT 2
The average height of 22 toddlers increases by 2 inches when two of them leave this group. If the average height of these two
toddlers is one-third the average height of the original 22, then the average height, in inches, of the remaining 20 toddlers is
A) 30
B) 28
C) 32
D) 26
CAT 2019 SLOT 1
With rectangular axes of coordinates, the number of paths from (1,1) to (8,10) via (4,6), where each step from any point (x,y) is either to (x,y+1) or to (x+1,y) is [TITA]
CAT 2019 SLOT 1
Meena scores 40% in an examination and after review, even though her score is increased by 50%, she fails by 35 marks. If her post-review score is increased by 20%, she will have 7 marks more than the passing score. The percentage score needed for passing the examination is
A. 75
B. 80
C. 60
D. 70
CAT 2018 SLOT 1
The distance from A to B is 60 km. Partha and Narayan start from A at the same time and move towards B. Partha takes four hours more than Narayan to reach B. Moreover, Partha reaches the mid-point of A and B two hours before Narayan reaches B. The speed of Partha, in km per hour, is
A. 6
B. 3
C. 4
D. 5
CAT 2018 SLOT 1
Two types of tea, A and B, are mixed and then sold at Rs. 40 per kg. The profit is 10% if A and B are mixed in the ratio 3 : 2, and 5% if this ratio is 2 : 3. The cost prices, per kg, of A and B are in the ratio
A. 21 : 25
B. 19 : 24
C. 18 : 25
D. 17 : 25
CAT 2020 Slot 3
The area, in sq. units, enclosed by the lines x = 2, y = |x - 2| + 4, the X-axis and the Y-axis is equal to
A. 12
B. 8
C. 6
D. 10
CAT 2020 Slot 3
How many of the integers 1, 2, … , 120, are divisible by none of 2, 5 and 7?
A. 41
B. 42
C. 40
D. 43
CAT 2019 Slot 1
If (5.55)ˣ = (0.555)ʸ = 1000, then the value of 1/x - 1/y is
A. 1
B. 13
C. 23
D. 3
CAT 2019 Slot 2
Anil alone can do a job in 20 days while Sunil alone can do it in 40 days. Anil starts the job, and after 3 days, Sunil joins him. Again, after a few more days, Bimal joins them and they together finish the job. If Bimal has done 10% of the job, then in how many days was the job done?
A. 13
B. 12
C. 15
D. 14
CAT 2020 Slot 2
In a group of 10 students, the mean of the lowest 9 scores is 42 while the mean of the highest 9 scores is 47. For the entire group of 10 students, the maximum possible mean exceeds the minimum possible mean by
A. 5
B. 3
C. 4
D. 6
CAT 2020 Slot 2
Let the m-th and n-th terms of a Geometric progression be 3/4 and 12, respectively, when m < n. If the common ratio of the progression is an integer r, then the smallest possible value of r + n - m is
A. -4
B. -2
C. 6
D. 2
CAT 2019 Slot 1
A club has 256 members of whom 144 can play football, 123 can play tennis, and 132 can play cricket. Moreover, 58 members can play both football and tennis, 25 can play both cricket and tennis, while 63 can play both football and cricket. If every member can play at least one game, then the number of members who can play only tennis is
A. 32
B. 43
C. 38
D. 45
CAT 2019 Slot 2
Two ants A and B start from a point P on a circle at the same time, with A moving clock-wise and B moving anti-clockwise. They meet for the first time at 10:00 am when A has covered 60% of the track. If A returns to P at 10:12 am, then B returns to P at
A. 10:27 am
B. 10:25 am
C. 10:45 am
D. 10:18 am
CAT 2020 Slot 1
The number of real-valued solutions of the equation 2ˣ + 2⁻ˣ= 2 - (x - 2)² is
A. infinite
B. 0
C. 1
D. 2
CAT 2020 Slot 1Let A, B and C be three positive integers such that the sum of A and the mean of B and C is 5. In addition, the sum of B and the mean of A and C is 7. Then the sum of A and B is
A. 6
B. 4
C. 7
D. 5
CAT 2020 Slot 1The mean of all 4 digit even natural numbers of the form 'aabb', where a>0, is
A. 5544
B. 4466
C. 4864
D. 5050