Official Quant thread for CAT 2013

Two circles of radii 'r' units and '2r' units intersect each other in such a way that their common chord is of the maximum possible length. What is the area (in square units) of the region that is common to the two circles?


1> pi*r^2/2
2> (7*pi*r^2)/6 -_/3*r^2
3>(11*pi*r^2)/6 -_/3/2*r^2
4>(
7*pi*r^2)/6 -_/3/2*r^2

find digit sum(till you get single digit number )of the smallest element in set p.The smallest element in set p can be represented as(8^x(25^300),which consists of 604-609 digits,where x is a natural number.


a.1 b.4 c.11 d.9 e.7

How many integers exist such that not only are they multiples 4016^4016 but are also the factors of 4016^4040 ?
A.4016^24
B.2425
C.4016^4040
D.2875


Please share approach

Q 57, 58

Consider the set S ={1,2,3...1000}. How many arithmetic progressions can be formed from the elements of S that start with 1 and end with 1000 and have at least 3 elements?

a.3

b.4

c.6

d.8

e.7

x is a set of 3 digit divisors which gives same remainder when it divides 2 numbers which are 12714 and 13914 what is the maximum possible elements in x


a) 1

b) 6

c) 8

d) none of these

(121212......300 Times)/99 - What is the remainder?

a) 18

b) 1

c) 98

d) none of these

permutation n combination sucks !! 😞

can this be left out ??

find the first non-zero digit from right in 25! ?


Plz give complete solution.

An ant is at one of the corners of a square prism with base 5 m × 5 m and height 10 m. What is the

minimum distance (in metres) that the ant has to crawl to reach the farthest corner on the prism?

(a) 150 (b) 125 (c) 200 (d) 250

plz help me with this one : options 23 ,22,24,26

Remainder when 12^107 is divided by 37??


a) 34
b) 36
c) 11
d) 3

Please post the approach as well

Sum of the third powers of the first hundred 100 natural numbers will have the units digit as


a) 3
b) 6
c) 9
d) 0

Q 60

Q- The number of factors of the square of a natural number is 105. The number of factors of the cube of the same number is 'F'. Find the maximum possible value of 'F'

ANS IS 280

PLZ TELL HOW TO DO

At how many points do the graphs of y = 1/x and y = x2 – 4 intersect each other?

ANS -3

apart frm making graphs can it be done some other way?

Mandeep has to create a password having 5 distinct characters using at least 2 digits (from 7 to 9) and at least 2 English vowels (from A, E, I, O and U). No character other than digits from 7 to 9 and vowels of English alphabets are allowed in that password. If the password starts with a digit, then it must end with an alphabet and if it starts with an alphabet, then it must end with a digit. Find the number of possible passwords that Mandeep can create.

a. 1260

b. 4480

c. 3620

d. 2880


pls reply with approach..

How many different ways can 15 identical apples to be distributed between R, M, B and H. If R cannot have more than 6 apples and M must have at least 3 apples.Please post your answer with the solution thanks

what is the present worth of rupees 132due in 2 years at 5% simple interest per annum?

Fresh fruits contain 68% water and dry fruits contain 20% water.How much dry fruit can be obtained from 100 kg of fresh fruits?

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