The corner of a cube has been cut by the plane passing through the mid-point of the three edges meeting at that corner. If the edge of the cube is of 2 cm length, then the volume of the pyramid thus cut off is
Volume = Area of base * HEIGHT * 1/3
AREA OF BASE = rt 3/2
The volume will be 1/3 * rt 3 /2 *1
height = perpendicular distance from the point (0,1,0) to the plane containing the points (0,0,0),(1,1,0) n (0,1,1). which is 1.
Volume = Area of base * HEIGHT * 1/3AREA OF BASE = rt 3/2 The volume will be 1/3 * rt 3 /2 *1 height = perpendicular distance from the point (0,1,0) to the plane containing the points (0,0,0),(1,1,0) n (0,1,1). which is 1.1/6 * rt 3= 0.289 cu units? @scrabbler bhai where i am going wrong??
The perimeter of the base of the cylinder is 6.28 cm. A part of this cylinder has been cut off. What is the volume of the remaining cylinder, as shown in the diagram? ( ˆ? = 3.14)
OA: 15.7The corner of a cube has been cut by the plane passing through the mid-point of the three edges meeting at that corner. If the edge of the cube is of 2 cm length, then the volume of the pyramid thus cut off is
recalculated..its 66..15 O - 110M 5A - 114O 1M ,13O 2M ,..............., 5O 10M = 1014O 1A,13O 1A,...................,10O 5A = 5we can visualize and count for rest as the possibilities will keep on increasing for o =13,12..9 and then decrease after some values as O =4,3,2,1what can be a shorter approach frnds???
Question reference: posted by techgeek2050 page 1383
Out of 5 apples, 10 mangoes, and 15 oranges, the number of ways of of distributing 15 fruits each to 2 persons isa- 56 b- 64 c- 66 d- 72
Guys m getting answer as 65... IN the solution mentioned above... u have considered (15O / 5A + 10M ) and (5A + 10M / 15O) as two different ways of distributing .... I think that only one way of distributing it... if we consider these as different then we would have to consider each combination twice........
Ithink ans is 65... but not in options...... can someone pls clarify....
Question reference: posted by techgeek2050 page 1383Out of 5 apples, 10 mangoes, and 15 oranges, the number of ways of of distributing 15 fruits each to 2 persons isa- 56b- 64c- 66d- 72 Guys m getting answer as 65... IN the solution mentioned above... u have considered (15O / 5A + 10M ) and (5A + 10M / 15O) as two different ways of distributing .... I think that only one way of distributing it... if we consider these as different then we would have to consider each combination twice........Ithink ans is 65... but not in options...... can someone pls clarify....
2 people are always considered as distinct. So I think this is a correct interpretation....A getting 15O and B getting (5A + 10M ) is distinct from A getting (5A + 10M) and B getting 15O)... regards scrabbler
2 people are always considered as distinct. So I think this is a correct interpretation....A getting 15O and B getting (5A + 10M ) is distinct from A getting (5A + 10M) and B getting 15O)...regardsscrabbler
Yes in that case ... the answer shud be 130.... cos each case can be made twice.....
example: 14O+ 1M to A being diff from 14O+1M to B... so then all 65 cases would be doubled.. to get 130....
case 1: 1 husband wife are on the table they can be selected in 5 ways.the remaining 2 people can be selected in 8*6=48 ways so totally 240 wayscase 2: no couple are on the table then 4 persons can be chosen in 10*8*6*4=1920Now they can be seated in 4! ways so totally 2160*4!?
Question reference:
@amresh_maverick said:2> 5 couples in a party .how many ways 4 persons can be seated on a table of 4 chairs such that no two husband wife are on the table ?
Hey You have multiplied with 4! for arrangement... but this is correct if they are sitting in a row what if they are sitting on 4 side of a square table.. then it would be 3!....
since its not given,... i guess we shud take it as 1920 only...
Yes in that case ... the answer shud be 130.... cos each case can be made twice..... example: 14O+ 1M to A being diff from 14O+1M to B... so then all 65 cases would be doubled.. to get 130....wot say ?
No.....I have no idea what you have done but I get 66... See my approach is different: Out of 5 apples, 10 mangoes, and 15 oranges, the number of ways of of distributing 15 fruits each to 2 persons is
Let us just see how many ways there are to give the apples and mangoes, the oranges can be used to fill up the balance so that each person gets 15.
The apples can be given to 2 people in 6 ways (0, 5), (1, 4), (2, 3) till (5, 0) and similarly the mangoes can be given in 11 ways. So overall 6 x 11 = 66 ways of distributing. For each of these, the oranges can be used to fill up the remaining capacity for each person. regards scrabbler
The corner of a cube has been cut by the plane passing through the mid-point of the three edges meeting at that corner. If the edge of the cube is of 2 cm length, then the volume of the pyramid thus cut off is
Volume = Area of base * HEIGHT * 1/3AREA OF BASE = rt 3/2 The volume will be 1/3 * rt 3 /2 *1 height = perpendicular distance from the point (0,1,0) to the plane containing the points (0,0,0),(1,1,0) n (0,1,1). which is 1.1/6 * rt 3= 0.289 cu units? @scrabbler bhai where i am going wrong??
no bhai height will be 1/_/3 there u r going wrong
No.....I have no idea what you have done but I get 66... See my approach is different:Out of 5 apples, 10 mangoes, and 15 oranges, the number of ways of of distributing 15 fruits each to 2 persons isLet us just see how many ways there are to give the apples and mangoes, the oranges can be used to fill up the balance so that each person gets 15.The apples can be given to 2 people in 6 ways (0, 5), (1, 4), (2, 3) till (5, 0) and similarly the mangoes can be given in 11 ways. So overall 6 x 11 = 66 ways of distributing. For each of these, the oranges can be used to fill up the remaining capacity for each person.regardsscrabbler
I get your approach..... mine was similar too....
I didnt realise that in doing so... we are already considering a combination twice.. once for person A then again for person B... so its fine... just the way i calculated... i thought the last option got repeated...
Making up for past sins I guess......I'm an Aero engineer, and you know what they say: "when the weight of the paperwork equals the weight of the plane, then and only then will the plane fly..."ObQuant: If a dozen oranges and 16 apples cost rupees 128 while 16 oranges and 5 apples cost rupees 89, what will be the cost of a dozen apples and 9 oranges? Do orally if possible!regardsscrabbler
as said did it orally
cost of 1 apple 5 rs
cost of 1 orange 4 rs
12*5+9*4=96
for doing it orally just seek the solutions of 3x+4y=32 in mind
side of the largest triangle that can be inserted in hexagon of side 1 cm.?
again on ur path scrabbler bhai did it orally too
_/3 it will be
join centre of hexagon with vertices ,now every length will be same as 1,from centre join the side ,half the side will come as _/3/2 as angle subtended is 60
