AIMCAT 1613N question, please solve
STUDY BURNOUT......AARGGGHHHHH
AIMCAT
There is a circle in the x-y plane with its centre at the point C = (a, b) and radius 6 units. If a and b are integers, how many points with integer co-ordinates do not lie outside the circle?
OA-113
Plz explain
No of ways in which 576 can be written as -
1. Product of 3 distinct +ve integers.
2. Product of 3 distinct integers.
If X can complete a work in 2 days , Y can complete the same work in 3 days and Z can complete the same work in 4 days , in how many days will the work be completed
if X works with 1/2 of his efficiency , Y works with 1/3 of his efficiency and Z works with 1/4 of his efficiency. ( They are working together to complete the task )
f(x)=4x(x+1)(4x-1);x>3 . what is maximum by which divisible f(x) is divisible by
a.24
b.16
c.32
A task was given to a manager who had 14 members in his team. At any moment of time exactly 10 members worked simultaneously on the task. Since, the manager had to be fair in his work allocation, he allocated the task among the workers in such a way that each member worked on the task for exactly 't' minutes. If the task was completed in 210 minutes, then find the value of 't'. (Assume the efficiency of each of the members of the team is the same)??
Q. A particular month has 5 Tuesdays. The first and the last day of the month are not Tuesday. What day is the last day of the month?
a.Monday
b.Tuesday
c.Wednesday
d.Thursday
If 'x' is positive and x^4-62x^2+1 =0, find the value of x^3 + 1/x^3.??
In a right angled triangle the semi-perimeter is 126 cm and the shortest median is 53 cm. What is the area of a triangle has the largest median as its longest side ?
1)1262
2)1268
3)1259
4)1260
Algebra ke liye achha source bata do koi?
I am having my TIME material for CAT 2010... Though I can avail the CAT 2014/2015 material (second hand) from the market ...would it be much of difference in contents ? Please suggest.
The ratio of the lengths of the diagonals of a rhombus are 2:5, then the ratio of the area of the rhombus and the square on the shorter diagonal is :
1. 5:4
2. 5:2
3. 2:5
4. NOTA
An athlete has been asked to maintain ratio of carbohydrates to proteins in his diet in a 1:1 ratio. He has option to eat 2 dishes X having 1.7 carbohydrates for each unit of protein and Y which has 1.2 proteins for each unit of carbohydrates. In what ratio should he mix X and Y?
If x2 + (2m + 4) x + 9 is positive for all values of x, the range of m is____________.a)(-∞,-5) >∪> (1, ∞) b)(-∞,-1) >∪> (5, ∞) c)(-5, 1) d)(-5, -1)
Pls explain solution
2 vessels A and B contain 100 litre each of milk and water respectively. 40 litre is removed from A and inserted into B and 40 litre of the resulting solution is removed from B and inserted into A. This process is repeated indefinitely. Find the final % of milk in A
A serious doubt.
Consider the following statement.
There are two identical dice. The probability of obtaining the same number on both the dice is?
1st method: If the probability of obtaining (a,a) = x
Then probability of obtaining (a,b) = 2x (Since chances of getting (1,2) is more than than that of getting (1,1) or (2,2) because although (1,2) and (2,1) is the same but they are more likely to appear (or rather twice as likely).
The number of (a,a) pairs are 6 { (1,1),(2,2),(3,3),(4,4),(5,5),(6,6) } The number of (a,b) pairs are 15 ( 6C2 ) { (1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6) }
Therefore, Since total probability = 1
6(x) + 15(2x) = 1 => x = 1/36 => 6x = 1/6
P.S. Note: Although the number maybe the same for two difference dice, but the logic is different. [i.e. 6/6^2 ]
2nd method: This solution was given by Time in one of the Aimcats 2014:
Let the number of times 1 occurs on both dice be x1,
2 occurs on both dice be x2, ...
6 occurs on both dice be x6.
x1+x2+x3+x4+x5+x6 = 2
Therefore, Total number of ways = 2+6-1 C 6-1 = 7c5 = 21
Therefore probability of obtaining same number = 6/21
I think the latter approach fails to incorporate the difference in probability for (a,a) and (a,b) type.
As a matter of fact, consider two identical dice with only two numbers of both i.e. 1 and 2.
There are four possible outcomes: { (1,2),(2,1),(1,1),(2,2)}.
But even though (1,2) and (2,1) are same, the chances of getting them is twice as much as that of getting (2,2).
Therefore, Total probability in this case: 1(2x) + 2(x) = 1 4x=1 => x=1/4 The chances of getting (1,2) = ½, (1,1) = ¼ and (2,2) = ¼
What are your views on the same?
The range of a for which ax^2 -6x+9 >0 for all real values of x is ?
if a, b are the roots of x^2 - x +3= 0, then a^4 + b^4 =
i) 10
ii)7
iii)-10
iv) 8