Official Quant thread for CAT 2013

@albiesriram said:
18 - B

As x ranges over all real values, what is the maximum value of

root [ (x^2−44x+288) × (−x^2+100x−2304) ]
The number of four digit numbers strictly greater than 4321 that can be formed from the digits 0,1,2,3,4,5 allowing for repetition of digits is
a)310 b)360 c)288 d)300

we have to purchase 100 birds in 100 rs. one sparrow equals - 1 rupee

20 crow for 1 rupee
one pigeon for 5 rupee.find the no of sparrows , crow & pigeon
?? ans not available
@Buck.up 288
@techgeek2050 said:
Find the maximum value of abc(b + c) if ab + bc + ca = 2
a(b+c)+bc=2,
abc(b+c)=2bc-b^2c^2,
now put a=1/2,b=1,c=1
so abc(b+c)=1
@rohit92 80 crows + 19 pigeOns + 1sparrow
@rohit92 said:
we have to purchase 100 birds in 100 rs. one sparrow equals - 1 rupee20 crow for 1 rupeeone pigeon for 5 rupee.find the no of sparrows , crow & pigeon?? ans not available
sparrow=1
crow=80
pigeon =19?
@Tusharrr said:
@Buck.up 288
No. OA 310

tushar wt is the basic technique to solve these kind of q


@albiesriram said:
cannot read the second qs properly. is angle(ACB) = pi/6 ?
@Buck.up said:
The number of four digit numbers strictly greater than 4321 that can be formed from the digits 0,1,2,3,4,5 allowing for repetition of digits isa)310 b)360 c)288 d)300
432_ ==> 4 nums ;
43_ _ ==> 3*6 = 18 nums ;
4_ _ _ ==> 2*6*6 = 72 nums ;

5 _ _ _ ==> 6*6*6 = 216 nums ;

Total = 310
@bullseyes said:
cannot read the second qs properly. is angle(ACB) = pi/6 ?
yup . a,b,c are the sides opposite to A , B n C angles..
@pakkapagal said:
How many of the first 1200 natural numbers are either prime to 6 or to 15?OA given is 400 bt m getting 720
number of numbers prime to 6= 1200(1-1/2)(1-1/3)=400
number of numbers prime to 15=1200(1-1/3)(1-1/5)=640
numbers which are prime to both=1200(1-1/2)(1-1/3)(1-1/5)=320
since question is either or,
so 400+640-320*2=400
@albiesriram said:
8 Students are arranged in a row. Find the probability that 2 of em, A n B are together..
_ _ _ _ _ _ _ _
A and b can sit it positions 1,2;2,3;3,4;4,5;5,6;6,7;7,8 in any order i.e A,B or B,A
ways of arranging other 6 people=8C6
SO net probability=2*8/8c6*2! =2/7
There are 25 points on a plane of which 7 are collinear , how many quadrilaterals can be formed from these points?
a)5206
b)2603
c)13015
d)none of these
@Buck.up said:
The number of four digit numbers strictly greater than 4321 that can be formed from the digits 0,1,2,3,4,5 allowing for repetition of digits isa)310 b)360 c)288 d)300
5_ _ _ you will get 6*6*6=216
432_ =4
43_ _ = 18
4 _ _ _ =2*6*6=72

SO totally 310

Let y=x^3+ax^2+bx. If (x,y)=(2,64) is a point on the curve and the slope of the tangent at x= ˆ'1 is 3, what is the value of a+b?

@iLoveTorres nicework..

Q:

Find the sum of all possible distinct remainders which are obtained when squares of a prime number are divided by 6
a.7, b.8, c.9, d.10