Quant Boosters by Hemant Malhotra  Set 14

hemant_malhotra
Director at ElitesGrid  CAT 2016  QA : 99.94, LRDI  99.70% / XAT 2017  QA : 99.975
Find numerically the greatest term in the expansion of (2+3x)^9 when x=3/2
(nr+1)/(r) *(a/x) >= 1
(10r)/r * (3x/2) >= 1
(10r)/r *(9/4)>= 1
909r> = 4r
so 13r< = 90
r < = 6. 9 so r=6
so 7th termIf a quadrilateral with sides 2, 3, 4 and 5 is inscribed in a circle and circumscribed to another circle then
find area of QuadrilateralDirect formula : If any quadrilateral with sides a, b, c and d inscribed in a circle and circumscribed to another circle then area of quadrilateral is sqrt(abcd). So here answer is sqrt(120)
Find remainder when 1^99+2^99+3^99+....99^99 is divided by 100
1 to 99 there are 99 terms
1^99+99^99 will be div by 100
2^99+98^99 will be div by 100
now 49^99+51^99 mod 100=0
but there will be one more term
50^99 mod 100
which is also divisible by 100
so OA=0How many integral solutions (a,b) does the equation a^b=a * b have
(1) 1
(2) 2
(3) 3
(4) 4
(5) More than foura^b = a * b
let b=1
then a=a
we can put any integral value of a here so More than 4
OA= 5What is the minimum value of 2x^2+3y^24x12y+18=0 for real x and y
Method1
partial differentiation
with respect to x
4x4=0 so x=1
now with respect to y
6y12=0 so y=2
now put x=1 and y=2
2+12424+18=4
so OA=4Method2
try to make perfect square form
2*(x1)^2+3*(y2)^2+4
so x=1 and y=2 will give us min valueF(x) and G(x) are two quadratic Functions such that
f(1)G(1)=1
f(2)G(2)=2
F(3)G(3)=5
Find value of F(4)G(4)
(1) 8
(2) 9
(3)10
(4)12Method1 f(x)=ax^2+bx+c
g(x)=dx^2+ex+m
now f(x)g(x)=x^2(ad)+x(be)+cm
let ad=M
be=N
cm=T
so f(x)g(x)= Mx^2+Nx+T
so M+N+T=1
4M+2N+T=2
9M+3N+T=5
now find M,N,T= M=1 N=2 and T=2
so F(x)g(x)=x^22x+2
so f(4)g(4)=10Quick approach = this is double difference AP if u are aware of this... it will take less than 20 seconds to solve. 1, 2, 5 so next will be 10
Centroid of triangle is at (1,1) while its orthocenter is at (5,3) then circumcentre of triangle could be
(1) (1,3)
(2) (8/3 , 0)
(3) (0,8/3)
(4) (7/3,1/3)Many Methods to tackle this, centroid bisect ortho and circum in 2:1 ratio
distance between (1,1) and (5,3) is sqrt(16+16)=sqrt32
so distance between centroid and circum should be sqrt32/2
check
sqrt(4+4)=sqrt8
so OA= AThere is a clock that has a special way of telling the time. It does not have any hands or numbers on it, but it has a chimer. If the time is 1 o'clock, it chimes once. If the time is 2 o'clock, it chimes twice, and so forth. The time gap between any two chimes is 4 seconds. How many seconds would it take you to know the time, after the first chime is heard, if it is 11 o'clock?
a) 40 seconds
b) 44 seconds
c) 42 seconds
d) none of theseOA=44 , 40+ extra 4 seconds u have to wait to confirm chimer rung no more
In triangle ABC, AB = 3000
BC = 875, CA = 3125
If I is the in center of the triangle, what is the ratio of AI:ID where AD is angle bisectorMethod1 AD is angle bisector
so AB/AC=BD/CD
so 3000/3125=BD/CD
let BD=x then CD=875x
so we can find x from here
now in triangle ABD AI is angle bisector
so BA/BD=AI/ID
3000/x=AI/IDAlternate 
AI/ID = (AB+AC)/BC, valid for every triangle
so ((6125/875)The average of three consecutive multiples of 3 is a.
The average of four consecutive multiples of 4 is a + 27.
The average of the smallest and largest of these seven integers is 42.
Determine the value of a.3(k+1) = a
4p+6 = a+27
4p+3k = 72
3 equations 3 variables.
k = 8 ; p = 12 and a = 27.