what is the maximum value of x^3y^3+3x*y
when x+y=8
ANSWER: 4144
x^3 * y^3 + 3x*y = (xy)^3 + 3xy
Now x+y=8 and we have to maximize xy
x=1 y=7 gives xy=7
x=2 y=6 gives xy=12
x=3 y=5 gives xy=15
x=4 y=4 gives xy=16 (MAXIMUM)
Hence x=4 and y=4
Solve 16(256+3)= 4144
x^3 * y^3 + 3x*y = (xy)^3 + 3xy
Now x+y=8 and we have to maximize xy
x=1 y=7 gives xy=7
x=2 y=6 gives xy=12
x=3 y=5 gives xy=15
x=4 y=4 gives xy=16 (MAXIMUM)
Hence x=4 and y=4
Solve 16(256+3)= 4144
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There are a number of chocolates in a bag. If they were to be equally divided among 14 children, there are 10 chocolates left. If they were to be equally divided among 15 children, there are 8 chocolates left. Obviously, this can be satisfied if any multiple of 210 chocolates are added to the bag. What is the remainder when the minimum feasible number of chocolates in the bag is divided by 9?
from the queston n=14x+10 and n= 15x+8. by solving these two equations we get x=2
by substitung this x in any one of the equation we get n=38 nd acc to question n=38+210=249 and ans is 249%9=5
by substitung this x in any one of the equation we get n=38 nd acc to question n=38+210=249 and ans is 249%9=5
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Let f(m,n) = 45*m + 36*n, where m and n are integers (positive or negative). What is the minimum positive value for f(m,n) for all values of m and n (this may be achieved for various values of m and n)?
The greatest common divisor (gcd) of non-zero integers a and b is the smallest positive integer that can be written as (with as integers).
So now, the smallest positive value(say d), that can be written as is the greatest common divisor of 45 and 36.
Therefore, the minimum positive value for for all integer values of is equal to 9.
So now, the smallest positive value(say d), that can be written as is the greatest common divisor of 45 and 36.
Therefore, the minimum positive value for for all integer values of is equal to 9.
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We have an equal arms two pan balance and need to weigh objects with integral weights in the range 1 to 40 kilo grams. We have a set of standard weights and can place the weights in any pan. . (i.e) some weights can be in a pan with objects and some weights can be in the other pan. The minimum number of standard weights required is:
a. 4
b. 10
c. 5
d. 6
Option a) 4 → three std weights of 2 kg each and one std wt. of 5 kg
We just need to factorize the magnitude of the highest weight, i.e., 40.
40 = 2x2x2x5
to weigh 1kg → 2x2 kg in one pan and 5 on the other
to weigh 3 kgs → 2 kg in one pan and 5 kg on the other, and so on.
We just need to factorize the magnitude of the highest weight, i.e., 40.
40 = 2x2x2x5
to weigh 1kg → 2x2 kg in one pan and 5 on the other
to weigh 3 kgs → 2 kg in one pan and 5 kg on the other, and so on.
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If n is the sum of two consecutive odd integers and less than 100, what is the greatest possibility of n?
a)98
b)94
c)96
d)99
aking greatest possibility
we take 51 + 49 but 51 + 49 = 100, we need x + y < 100
so we take 47 + 49 = 96 (ANS)
we take 51 + 49 but 51 + 49 = 100, we need x + y < 100
so we take 47 + 49 = 96 (ANS)
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A call center agent has a list of 305 phone nos of people in alphabetic order of names (but she does not have any of the names). she needs to quickly contacts deepak sharma to convey a message to him.If each call takes 2 minutes to complete, and every call is answered, what is the minimum amount of time in which she can guarantee to deliver the message to Mr.Sharma.
t is actually based on Binary search. Since, the numbers are in alphabetical order of names, she can call the last number and ask his name. Based on the response, she picks up 305/2 = 152 nd number. Then, 152/2 = 76 th number, then 76/2 = 38th number, 38/2 = 19 th number, 19/2 = 9th number, 9/2 = 4th number, 4/2 = 2nd number, 2/2 = 1st number. So, she has to make minimum 9 calls. Each call duration is 2 minutes. So, she takes 18 minutes.
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Eric throws two dice, and his score is the sum of the values shown. Sandra throws one die, and her score is the square of the value shown. What is the probability that Sandra’s score will be strictly higher than Eric’s score?
What is the largest number that will divide 90207, 232585 and 127986 without leaving a
remainder?
a) 257 b) 905 c) 351 d) 498
232585 - 127986 =104599
127986 - 90207 = 37779
since 37779 < 104599
v use 37779
1st 37779/257=147
37779/905=41.74....
37779/351=107.6....
37779/498=75.8....
so ans is 257
127986 - 90207 = 37779
since 37779 < 104599
v use 37779
1st 37779/257=147
37779/905=41.74....
37779/351=107.6....
37779/498=75.8....
so ans is 257
we understand that answer is the HCF of all the numbers, but we need not to actually calculate the HCF, just a little observation will help you to get through in seconds by reducing the options.. first check the numbers, and the options, as 498 is one of the options, that means, all the numbers should be even number as 498 is also an even number, but only 127986 is even so 498 is not the option, then we check the divisibility by 3, so 232585 is not divisible by 3, that means amongst the options, one which is divisible by is not the correct one, 351 is not the answer, then for being divisible by 905, numbers should be divisible by 5 as well, but only 232585 is divisible...so 905 is also not the correct answer, so we are left with 257 as correct answer... :) :)
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a. 3-sqrt(7)
What is the distance of BC in cms if two circles of radii 5 cm and 3 cm touch each other at A and also touch a line at B and C?
If r1, r2 are the radii of two circles and d is distance between their centers, then
(i) the length of a direct common tangent =
(ii) the length of a transverse common tangent =
Thus, 60^0.5
(i) the length of a direct common tangent =
(ii) the length of a transverse common tangent =
Thus, 60^0.5
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In the polynomial f(x) = x^5 + a*x^3 + b*x^4 +c*x + d, all coefficients a, b, c, d are integers. If 3 + sqrt(7) is a root, which of the following must be also a root?(Note that x^n denotes the x raised to the power n, or x multiplied by itself n times. Also sqrt(u) denotes the square root of u, or the number which when multiplied by itself, gives the number u)?
a. 3-sqrt(7)
b. 3+sqrt(21)
c. 5
d. sqrt(7) + sqrt(3)
Sol: Option A
here,
taking option a.
sum of roots=(-a/1)=(3+sqrt7)+(3-sqrt7)=6....therefore a=-6(an integer value)
and product of roots=(-d/1)=(3+sqrt7)(3-sqrt7)=9-7=2....therefore d=-2(an integer value)
No other options satisfy the condition of a and d to be integer values.
taking option a.
sum of roots=(-a/1)=(3+sqrt7)+(3-sqrt7)=6....therefore a=-6(an integer value)
and product of roots=(-d/1)=(3+sqrt7)(3-sqrt7)=9-7=2....therefore d=-2(an integer value)
No other options satisfy the condition of a and d to be integer values.
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