@bodhi_vriksha said:It'll be simply 1/4(4*pi*6^2 + 4*pi*4^2) + pi*6^2 = 88piTeam BV - Kamal Lohia
Got it! Perfect solution 
@bodhi_vriksha said:Though there is nothing like bold part in your post but your query is understandable.
See when I say a, b + 1, c + 2, d + 3 are four distinct positive integers from 1 to 12 such that a
- then the largest selection of four integers will be {9,10,11,12} for {a, b+1, c+2, d+3} which corresponds to {a,b,c,d} = {9,9,9,9} i.e. 9999 which is largest permissible number
- and the smallest selection of four integers will be {1,2,3,4} for {a, b+1, c+2, d+3} which corresponds to {a,b,c,d} = {1,1,1,1} i.e. 1111 which is smallest permissible number.
Does this make sense to you?
Team BV - Kamal Lohia
i m sorry 4 being a retard.....i have 2 doubts:
1)why {a,b,c,d} = {9,9,9,9} ...shud we not consider 6 in place of 9 in this problem as 6 is the max possible number possible in a dice...
2)even wen u take 9 9 9 9 wala case why12c4.... and not 9c4...
@Koushik98 said:why are we not taking plane surface area of smaller sphere???
It is just that ..
1/2 (pi*6^2) + 1/2 (pi*4^2) ------ for bottom surface
1/2 (pi*6^2) - 1/2 (pi*4^2) ------- for annular surface
so total would be (pi*6^2)
@bodhi_vriksha Is this true ?
1/2 (pi*6^2) + 1/2 (pi*4^2) ------ for bottom surface
1/2 (pi*6^2) - 1/2 (pi*4^2) ------- for annular surface
so total would be (pi*6^2)
@bodhi_vriksha Is this true ?
Directions for Questions 5 : Answer the questions on the basis of the information given below.
PQR is an equilateral triangle as shown in the figure given below. Let S be a point on QR. A semicircle is drawn having SR as diameter such that PQ is a tangent to the semicircle at the point T. Given that the center of the semicircle is at point O and the radius of the semicircle is 1 unit.
PQR is an equilateral triangle as shown in the figure given below. Let S be a point on QR. A semicircle is drawn having SR as diameter such that PQ is a tangent to the semicircle at the point T. Given that the center of the semicircle is at point O and the radius of the semicircle is 1 unit.
5)Given that the semicircle cuts PR at the point U. What is the ratio of length of the line segment PU to the radius of the semicircle?
a)1 : (2-√3)
b)1 : (√3-1)
c )3 : (√3+1)
d) 2 : √3
e)None of these
b)1 : (√3-1)
c )3 : (√3+1)
d) 2 : √3
e)None of these
@heylady said:Find the value of angle a in the triangle??
Sandeep
This is a very famous and old triangle/angle question. And researchers have found more than 8 different solutions to this..
I am posting just one of them..:)
First name the vertices as shown and draw BF such that angle(CBF) = 20.
Now observe that
angle(BCF) = angle(BFC) = 80
So BC = BF
Also, angle(BEC) = 50 = angle(BCE)
So BC = BE
Combining the two, we get
BE = BF
Now, angle(EBF) = 60
So triangle EBF is equilateral
i.e. BF = EF
Also, angle(DBF) = 60 - 20 = 40
and angle(BDF) = 180 - 100 - 40 = 40
So triangle BFD is isosceles
i.e. BF = FD
Combining above two, we get
EF = FD
Also, angle(EFD) = 180 - 80 - 60 = 40
So angle(DEF) = angle(EDF) = 70
i.e. a = 70 - angle(BDF) = 70 - 40 = 30 :)
Team BV - Kamal Lohia
This is a very famous and old triangle/angle question. And researchers have found more than 8 different solutions to this..
I am posting just one of them..:)
First name the vertices as shown and draw BF such that angle(CBF) = 20.
Now observe that
angle(BCF) = angle(BFC) = 80
So BC = BF
Also, angle(BEC) = 50 = angle(BCE)
So BC = BE
Combining the two, we get
BE = BF
Now, angle(EBF) = 60
So triangle EBF is equilateral
i.e. BF = EF
Also, angle(DBF) = 60 - 20 = 40
and angle(BDF) = 180 - 100 - 40 = 40
So triangle BFD is isosceles
i.e. BF = FD
Combining above two, we get
EF = FD
Also, angle(EFD) = 180 - 80 - 60 = 40
So angle(DEF) = angle(EDF) = 70
i.e. a = 70 - angle(BDF) = 70 - 40 = 30 :)
Team BV - Kamal Lohia
Before starting to paint, Billu had 130 litres of blue paint, 164 litres of red paint, and 188 litres of white paint. Billu painted four equally sized stripes on a wall, making a blue stripe, a red stripe, a white stripe, and a pink stripe. Pink is a mixture of red and white, not necessarily in equal amounts. When he finished, he had equal amounts of blue, red, and white paint left. Find the total number of litres of paint Billu had left.?
@albiesriram said:Before starting to paint, Billu had 130 litres of blue paint, 164 litres of red paint, and 188 litres of white paint. Billu painted four equally sized stripes on a wall, making a blue stripe, a red stripe, a white stripe, and a pink stripe. Pink is a mixture of red and white, not necessarily in equal amounts. When he finished, he had equal amounts of blue, red, and white paint left. Find the total number of litres of paint Billu had left.?
114?
(130 - 92)*3
regards
scrabbler
(130 - 92)*3
regards
scrabbler
@Dexian said:i m sorry 4 being a retard.....i have 2 doubts:1)why {a,b,c,d} = {9,9,9,9} ...shud we not consider 6 in place of 9 in this problem as 6 is the max possible number possible in a dice...2)even wen u take 9 9 9 9 wala case why12c4.... and not 9c4...
Don't worry about that, I am way greater than you :)
1) yes..in the given/asked question involving dice it'll be 6 in place of 9.
9 came because I took an example of four digit number in which the digits varied up to 9.
2) Now for a four digit number abcd if all the digits are related like a But the case here is not simple as that.
It says 'a' is less than Or equal to 'b' which is less than Or equal to 'c' which is less than Or equal to 'd'
So to convert the mixed equality/inequality in pure inequality, I wrote 'a' is less than Or equal to 'b' corresponds to a
Try to grasp this one point. Everything else will be clear easily. :)
Team BV - Kamal Lohia
1) yes..in the given/asked question involving dice it'll be 6 in place of 9.
9 came because I took an example of four digit number in which the digits varied up to 9.
2) Now for a four digit number abcd if all the digits are related like a But the case here is not simple as that.
It says 'a' is less than Or equal to 'b' which is less than Or equal to 'c' which is less than Or equal to 'd'
So to convert the mixed equality/inequality in pure inequality, I wrote 'a' is less than Or equal to 'b' corresponds to a
Try to grasp this one point. Everything else will be clear easily. :)
Team BV - Kamal Lohia
@Koushik98 said:Directions for Questions 5 : Answer the questions on the basis of the information given below. PQR is an equilateral triangle as shown in the figure given below. Let S be a point on QR. A semicircle is drawn having SR as diameter such that PQ is a tangent to the semicircle at the point T. Given that the center of the semicircle is at point O and the radius of the semicircle is 1 unit. 5)Given that the semicircle cuts PR at the point U. What is the ratio of length of the line segment PU to the radius of the semicircle? a)1 : (2-√3) b)1 : (√3-1) c )3 : (√3+1) d) 2 : √3 e)None of these
can't find a way out......pls help
@Koushik98 said:Directions for Questions 5 : Answer the questions on the basis of the information given below. PQR is an equilateral triangle as shown in the figure given below. Let S be a point on QR. A semicircle is drawn having SR as diameter such that PQ is a tangent to the semicircle at the point T. Given that the center of the semicircle is at point O and the radius of the semicircle is 1 unit. 5)Given that the semicircle cuts PR at the point U. What is the ratio of length of the line segment PU to the radius of the semicircle? a)1 : (2-√3) b)1 : (√3-1) c )3 : (√3+1) d) 2 : √3 e)None of these
Just giving a hint out here...feeling lazy to draw the diagram and do the calculations part.
See that OQT is a 30-60-90 triangle such that OT is radius of semicircle = 1.
So QT = 1/rt(3) and OQ = 2/rt(3)
As OR = radius = 1, So QR = 1 + 2/rt(3) = PQ
And PT = 1 + 2/rt(3) - 1/rt(3) = 1 + 1/rt(3)
Now just use the secant tangent property of circles to get the answer.
Team BV - Kamal Lohia
See that OQT is a 30-60-90 triangle such that OT is radius of semicircle = 1.
So QT = 1/rt(3) and OQ = 2/rt(3)
As OR = radius = 1, So QR = 1 + 2/rt(3) = PQ
And PT = 1 + 2/rt(3) - 1/rt(3) = 1 + 1/rt(3)
Now just use the secant tangent property of circles to get the answer.
Team BV - Kamal Lohia
@pankaj1988 said:An intelligence agency forms two digit code consisting of distinct digits selected from 0 through 9 such that first digit is not 0. Some codes, when hand written on slip, can however potentially create confusion when read upside down- for example 61 may appear as 19. Find the number of codes for which there is no confusion.a)73 b)70 c)71 d)67No OA
total codes = 9*10= 90
digits that can cause confusion 0,1,6,8,9
5C2 = 10ways.
and they can be mirrored so .... 10*2 = 20
but here 69 when mirrored is 69 only.
90-20 +1 = 71 numbers?
EDIT : 11, 88 should also be considered just like 69..
total 73?
digits that can cause confusion 0,1,6,8,9
5C2 = 10ways.
and they can be mirrored so .... 10*2 = 20
but here 69 when mirrored is 69 only.
90-20 +1 = 71 numbers?
EDIT : 11, 88 should also be considered just like 69..
total 73?
@Koushik98 said:can't find a way out......pls help
I guess it will be 2 : rt3. Can't draw a figure right now, (wrong comp, office:) but consider that:
(a) QTO is a 30-60-90 triangle. So we can find length of PT and PR through this.
(b) PT * PT = PU * PR. We can now use this to find PU.
regards
scrabbler
(a) QTO is a 30-60-90 triangle. So we can find length of PT and PR through this.
(b) PT * PT = PU * PR. We can now use this to find PU.
regards
scrabbler
@bodhi_vriksha said:Just giving a hint out here...feeling lazy to draw the diagram and do the calculations part.See that OQT is a 30-60-90 triangle such that OT is radius of semicircle = 1.So QT = 1/rt(3) and OQ = 2/rt(3)As OR = radius = 1, So QR = 1 + 2/rt(3) = PQAnd PT = 1 + 2/rt(3) - 1/rt(3) = 1 + 1/rt(3)Now just use the secant tangent property of circles to get the answer.Team BV - Kamal Lohia
yeah got it...thanx
@albiesriram said:Before starting to paint, Billu had 130 litres of blue paint, 164 litres of red paint, and 188 litres of white paint. Billu painted four equally sized stripes on a wall, making a blue stripe, a red stripe, a white stripe, and a pink stripe. Pink is a mixture of red and white, not necessarily in equal amounts. When he finished, he had equal amounts of blue, red, and white paint left. Find the total number of litres of paint Billu had left.?
130-x=164-(x+y)=188-(x+z)
y=34
z=58
x=y+z=92
total=482-92*4=114
@heylady said:Find the value of angle a in the triangle??
My take on this... Using sine rule in triangle with angles 80 and 40 and triangle with angles a and 160-a:
sina /sin(a+20) = sin40/sin80 = > 2sin50*sina=sin(a+20)=> a=30
Team BV - Vineet
@uditultimate said:for geometry freaksQ there is a isosceles triangle : base =6 c.m., altitude = 1 c.m.find the area of maximum square that can be extracted from this triangle...
36/49
just use similar triangles
Find the number of integer quadruples (a,b,c,d) with 0 ≤ a,b,c,d ≤ 100, such that a and b are the roots of the quadratic equation x^2 − cx + d = 0, while c and d are the roots of the quadratic equation x^2 − ax + b = 0.
@albiesriram said:Before starting to paint, Billu had 130 litres of blue paint, 164 litres of red paint, and 188 litres of white paint. Billu painted four equally sized stripes on a wall, making a blue stripe, a red stripe, a white stripe, and a pink stripe. Pink is a mixture of red and white, not necessarily in equal amounts. When he finished, he had equal amounts of blue, red, and white paint left. Find the total number of litres of paint Billu had left.?
130 - x = 164 - (x+a) = 188-(2x-a)
x= 92
a = 34
34*3 = 114
@jain4444 said:Find the number of integer quadruples (a,b,c,d) with 0 ≤ a,b,c,d ≤ 100, such that a and b are the roots of the quadratic equation x^2 − cx + d = 0, while c and d are the roots of the quadratic equation x^2 − ax + b = 0.
a=c
==> 101 solutions (including both 0 and 100)
:neutral: