Official Quant thread for CAT 2013

MBA CAT 2024
41
@vijay_chandola said:
A function f is defined as f(n) = 6^n + 8^n for all integers n. Find the remainder when f(83) is divided by 49.



35..?
42
@krum said:
White balls, each of radius 6.5 cm, are floating in blue paint. While floating, the top of each ball is 4 cm above the paint surface. Now, if the paint is in a cuboid shaped vessel with base dimensions as 100 cm — 10 cm and height 10 cm; and there are 2 balls floating in this vessel, the total area in blue that a bird flying exactly above the vessel sees is:OPTIONS1) 2) 3) 4)
area of circular portion (top view) =2*pie*R^2 = 2*36 pie
where R= sqrt( 6.5^2 - 2.5^2) = 6
Therefore, required area = (1000-72pie) sq.cm.
43
@krum said:
Let P0(x) = x^3 + 313x^2 – 77x – 8.For integers n ≥1, define Pn(x) = Pn-1(x – n). Find the coefficient of x in P20(x)?OPTIONS1) 673 2) 763 3) 457 4) 856 5) None of these
NOT ??
44
@Brooklyn said:
NOT ??
p20(x)=p19(x-20)=p18((x-20)-19)...=p0(x-(20+19+18+17+..+1))=p0(x-210)


p20(x)=p0(x-210)=(x-210)^3 + 313(x-210)^2 €“ 77(x-210) €“ 8

coeff of x in (x-210)^3 = 3*(210)^2
coeff of x in 313(x-210)^2=-313*2*210
coeff of x in 77(x-210)=77

so 3*(210)^2-313*2*210-77=132300-131460-77=763
45
iss thread ka mera pehla question..kch tagda lata hu

The minimum value of |x-1| + |2x-1| + |3x-1| ............ + |119x -1| ?
a) 48
b)49
c) 52
d)53
46
@krum said:
Let P0(x) = x^3 + 313x^2 – 77x – 8.For integers n ≥1, define Pn(x) = Pn-1(x – n). Find the coefficient of x in P20(x)?OPTIONS1) 673 2) 763 3) 457 4) 856 5) None of these
P1=(x-1)^3+313(x-1)^2-77(x-1)-8
1+2+3+......+20=210
P20=(3*210*210-313*210*2-77)=763
47
@krum said:
Let P0(x) = x^3 + 313x^2 – 77x – 8.For integers n ≥1, define Pn(x) = Pn-1(x – n). Find the coefficient of x in P20(x)?OPTIONS1) 673 2) 763 3) 457 4) 856 5) None of these
763..??
48
@busar005 said:
763..??
to all , abse is thread pe sab approach daalenge ...plz koi ans nhi likhega only
49
@rkshtsurana said:
iss thread ka mera pehla question..kch tagda lata huThe minimum value of |x-1| + |2x-1| + |3x-1| ............ + |119x -1| ?a) 48b)49c) 52d)53
at x=1/119

|1/119-1|+|2/119-1|+|3/119-1|+..+|119/119-1|
=118/119+117/119+..+1/119+0
=1/119*118/2(119)
=59

kaise hoga bhai , ans kya hai?
50
@krum said:
at x=1/119|1/119-1|+|2/119-1|+|3/119-1|+..+|119/119-1|=118/119+117/119+..+1/119+0=1/119*118/2(119)=59kaise hoga bhai , ans kya hai?
59 is wrng...ans nhi bataunga...HINT : minimum value comes on median value..dnt take x = 1/119
51
@rkshtsurana said:
to all , abse is thread pe sab approach daalenge ...plz koi ans nhi likhega only
Sorry for spamming.. but ha yar... approach daldo... cos even if everyone here knows the solution.. when someone visits this later, he would feel so great to see such a beautiful thread... @krum bhai always does this.. i remember thinkace of last year.. he used to put solution for each and every question.. it would really help us all...
52
@rkshtsurana said:
iss thread ka mera pehla question..kch tagda lata huThe minimum value of |x-1| + |2x-1| + |3x-1| ............ + |119x -1| ?a) 48b)49c) 52d)53
( 1/60+....+59/60)*2
59???
53

hi all!
please post an explanation for this one-

the constt term in the expansion of
( x^2 + y +1/y +1/x^2)^8 is
4900;5000;5100;8000

54
@invincible2910 said:
hi all!please post an explanation for this one-the constt term in the expansion of ( x^2 + y +1/y +1/x^2)^8 is4900;5000;5100;8000
forming different pairs
as (a+b+c+d)^8
a^2*b^2*c^2*d^2 similarly every term below
8!/2!^4+8!/3!^2*2+8!/4!^2*2=4900 (Ans.)
55
@rkshtsurana said:
to all , abse is thread pe sab approach daalenge ...plz koi ans nhi likhega only


ok bhai....aage se sirf approaches..:D:)
56

Can somebody help me with Q's like something raise to paower something has which digit in some given place ............ for eg 3^2001 has which digit at ones place ........


Please give a detailed step by step approach .....
@krum @Brooklyn @chandrakant.k @anytomdickandhary
57
@Boson said:
Can somebody help me with Q's like something raise to paower something has which digit in some given place ............ for eg 3^2001 has which digit at ones place ........Please give a detailed step by step approach ..... @krum@Brooklyn@chandrakant.k@anytomdickandhary
you mean at tens place or units place??
58
@rkshtsurana said:
iss thread ka mera pehla question..kch tagda lata huThe minimum value of |x-1| + |2x-1| + |3x-1| ............ + |119x -1| ?a) 48b)49c) 52d)53
i am getting 59
for x=1/60
(1+2+3+....+59)*2/60
59
@Boson said:
Can somebody help me with Q's like something raise to paower something has which digit in some given place ............ for eg 3^2001 has which digit at ones place ........Please give a detailed step by step approach ..... @krum@Brooklyn@chandrakant.k@anytomdickandhary
SEE 3 has a unit digit pattern of 4
i mean
3^1 = 3
3^2 = 9
3^3 = x 7
3^4 = x 1
3^5 = xx 3
3^ 6 = xx 9
and so on
so just divide 2001 by 4
which leaves remainder of 1.. so it has last digit as 3
60
@Brooklyn Mera Sawaal bilkul general hai yaani kisi bhi place ke liye ...

Abhi ke liye maan lo units place par..