Official Quant thread for CAT 2013

MBA CAT 2024
29105
@Buck.up said:
There are 25 points on a plane of which 7 are collinear , how many quadrilaterals can be formed from these points?a)5206b)2603c)13015d)none of these
Three possible cases:-

=> all 4 vertices are from the 18 non-collinear points
C(18, 4) ways

=> 3 vertices are from 18 non-collinear and one from remaining 7
7*C(18, 3) ways

=> 2 vertices from 18 non-collinear and two from remaining 7
C(7, 2)*C(18, 2) ways

Add to get, total as 11985 quadrilaterals

Alternatively:-

Total possible quadrilaterals = C(25, 4)
when all 4 points are collinear = C(7, 4)
When 3 are collinear = C(7, 3)*18

So, C(25, 4) - C(7, 4) - C(7, 3)*18 = 11985 quadrilaterals
29106
@Tusharrr said:
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?
21 ?
29107
@Buck.up said:
There are 25 points on a plane of which 7 are collinear , how many quadrilaterals can be formed from these points?a)5206b)2603c)13015d)none of these
18C4 + 18C3 * 7c1 + 18C2 * 7c2 = 3060 + 5712 + 3213 = 11985 ??
29108
@Tusharrr said:
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?
64 = 8 + 4a + 2b
28 = 2a + b

dy/dx = 3x^2 + 2ax + b
3 = 3 - 2a + b
b = 2a

b = 14 and a = 7

a + b = 21
@DeAdLy said:
Q:Find the sum of all possible distinct remainders which are obtained when squares of a prime number are divided by 6a.7, b.8, c.9, d.10
2^2 when divided by 6 is 4
3^2 when divided by 6 is 3
for rest (6k +/- 1)^2 when divided by 6 will be 1

Sum = 8
29109
@DeAdLy said:
Q:Find the sum of all possible distinct remainders which are obtained when squares of a prime number are divided by 6a.7, b.8, c.9, d.10
except 2,3 every prime number can be expressed in the form of 6k+1 and 6k-1 ;

(6k+/-1)^2 = 36k^2 +/- 12k + 1/6 ==> rem always 1;

rem for 2^2/6 = 4; 3^2/6 = 3 ;

distinct rems are 1,4,3 ; sum = 1+3+4 = 8??
29110
@DeAdLy said:
Q:Find the sum of all possible distinct remainders which are obtained when squares of a prime number are divided by 6a.7, b.8, c.9, d.10
8 ?
29111

As x ranges over all real values, what is the maximum value of root [ (x^2−44x+288) × (−x2+100x−2304) ]?

29112
@Tusharrr said:
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?
21
we get 2 equations:
b-2a=0______(1)
2b+4a=56_____(2)
we get a =7,b=14
29113
@Tusharrr said:
As x ranges over all real values, what is the maximum value of root [ (x^2−44x+288) × (−x2+100x−2304) ]?
0?
29114
@iLoveTorres said:
0?
Bhai yeh to minimum value hogi na.
29115
@DeAdLy said:
Q:Find the sum of all possible distinct remainders which are obtained when squares of a prime number are divided by 6a.7, b.8, c.9, d.10
A prime number can be expressed in 6K+1 form other than 2 and 3.
For 2 and 3 we get remainder as 4 and 3
For the other cases, it is 1
Hence 8
29116

A crew can row a certain course up the stream in 84 minutes, they can row the same course down stream in 9 minutes less than they can row in still water. How long would they take to row down with the same stream.

29117
@vbhvgupta

Is it 63 Mins?..Par 12 Mins bhi ho sakta hai..Options kya hai?
29118

Suppose there are 10 coins laid out in front of you. All of the coins are fair (i.e. have an equal chance of heads or tails) except one, which flips to heads every time. You draw one coin at random and flip it 5 times. If each of the 5 flips results in heads, then the probability that this coin is fair can be written as a/b, where a and bare coprime positive integers. What is the value of a+b?

29119
@Tusharrr said:
Suppose there are 10 coins laid out in front of you. All of the coins are fair (i.e. have an equal chance of heads or tails) except one, which flips to heads every time. You draw one coin at random and flip it 5 times. If each of the 5 flips results in heads, then the probability that this coin is fair can be written as a/b, where a and bare coprime positive integers. What is the value of a+b?
50?

9/41 I get...

regards
scrabbler
29120
@Tusharrr 4a+2b=56
y'=3x^2+2ax+b
2a=b
solving b=14
a=7
a+b=21
29121
@DeAdLy prime numbers gretaer than equal to 5
prime in the form of 6k+/- 1 will always give remainder 1 when divided by 6
4 mod 6=4
9 mod 6=3
4+3+1=8
29122
@Tusharrr
@Tusharrr said:
Suppose there are 10 coins laid out in front of you. All of the coins are fair (i.e. have an equal chance of heads or tails) except one, which flips to heads every time. You draw one coin at random and flip it 5 times. If each of the 5 flips results in heads, then the probability that this coin is fair can be written as a/b, where a and bare coprime positive integers. What is the value of a+b?
329?

29123
@Tusharrr said:
As x ranges over all real values, what is the maximum value of root [ (x^2−44x+288) × (−x2+100x−2304) ]?
is it 196 rt(3) ?
29124
@vbhvgupta speeds in AP..
TIME in HP

168*(x-9)/(x+75)=x
on solving 72 min