Loading....
Coupon Accepted Successfully!

Previous Year Paper

Open Flashcards

CAT-2008-Previous Years Paper

Question
25 out of 25
 

Consider a right circular cone of base radius 4 cm and height 10 cm. A cylinder is to be placed inside the cone with one of the flat surfaces resting on the base of the cone. Find the largest possible total surface area of the cylinder (in sq. cm).

 

 
A 100π/3
B 80π/3
C 120π/7
D 130π/9
E 110π/7
Ans. A

Consider the figures given below:

2h = 20 – 5 r

Surface area of cylinder = 2  r2+ 2rh
= 2
r2+ r (20 – 5r)

 

 

= 20 r – 2 r2= (20r – 3r2)

So, we have to maximize f(r) = 20r – 3r2

We know that that maximum of quadratic equation ax2+ bx + c = 0 arises for x = and the maximum value =

In this case

So the maximum surface area =

Hence, (a).

CAT-2008-Previous Years Paper Flashcard List

25 flashcards
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
15)
16)
17)
18)
19)
In a single elimination tournament, any player is eliminated with a single loss. The tournament is played in multiple rounds subject to the following rules:   A. If the number of players, say n, in any round is even, then the players are grouped in to n/2 pairs. The players in each pair play a match against each other and the winner moves on to the next round.   B. If the number of players, say it, in any round is odd, then one of them is given a bye, that is, he automatically moves on to the next round. The remaining (n-1) players are grouped into (n-l)/2 pairs. The players in each pair play a match against each other and the winner moves on to the next round. No player gets more than one bye in the entire tournament.   Thus, if n is even, then n/2 players move on to the next round while if n is odd, then (n+l)/2 players move on to the next round. The process is continued till the final round, which obviously is played between two players. The winner in the final round is the champion of the tournament. What is the number of matches played by the champion? A: The entry list for the tournament consists of 83 players. B: The champion received one bye. A If Question can be answered 1mm A alone but not from B alone. B If Question can be answered from B alone but not from A alone. C If Question can be answered from either of A or B alone. D If Question can be answered from A and B together but not from any of them alone. E If Question cannot be answered even from A and B together.
20)
In a single elimination tournament, any player is eliminated with a single loss. The tournament is played in multiple rounds subject to the following rules:   A. If the number of players, say n, in any round is even, then the players are grouped in to n/2 pairs. The players in each pair play a match against each other and the winner moves on to the next round.   B. If the number of players, say it, in any round is odd, then one of them is given a bye, that is, he automatically moves on to the next round. The remaining (n-1) players are grouped into (n-l)/2 pairs. The players in each pair play a match against each other and the winner moves on to the next round. No player gets more than one bye in the entire tournament.   Thus, if n is even, then n/2 players move on to the next round while if n is odd, then (n+l)/2 players move on to the next round. The process is continued till the final round, which obviously is played between two players. The winner in the final round is the champion of the tournament. If the number of players, say n, in the first round was between 65 and 128, then what is the exact value of n? A: Exactly one player received a bye in the entire tournament. B: One player received a bye while moving on to the fourth round from the third round A If Question can be answered 1mm A alone but not from B alone. B If Question can be answered from B alone but not from A alone. C If Question can be answered from either of A or B alone. D If Question can be answered from A and B together but not from any of them alone. E If Question cannot be answered even from A and B together.
21)
22)
23)
24)
25)