which of the folwing is maximum???
k110
k105
k216
k384????
kindly post the steps as well
k(n) denotes the no of ways in which n can be expressed as a difference of 2 perfct squares.
@anjali_sng said: k(n) denotes the no of ways in which n can be expressed as a difference of 2 perfct squares.which of the folwing is maximum???k110k105k216k384????kindly post the steps as well
Suppose the number is the difference of two squares a^2 - b^2. Hence it is nothing but the form (a + b)(a - b). Now either both a+b and a-b will be even, or both will be odd (think about it!)
Hence we should just see which one can be written as the product of two factors in the maximum number of ways as (even x even) or as (odd x odd).
The rest you figure out ;)
regards
scrabbler
Hence we should just see which one can be written as the product of two factors in the maximum number of ways as (even x even) or as (odd x odd).
The rest you figure out ;)
regards
scrabbler
in how many ways can we distribute 10 identical looking pencil to 4 students so that each student gets at least one pencil?
a)5040
b)210
c)84
d)none of these
@sameer-verma said:in how many ways can we distribute 10 identical looking pencil to 4 students so that each student gets at least one pencil? a)5040 b)210 c)84 d)none of these
option C- 84
@sameer-verma said:can u please provide the solution alslo....
err.. my bad ! i think it shud be 84
(a+1)+(b+1)+(c+1)+(d+1)=10
or, a+b+c+d= 6
therefore, (n+r-1)C(r-1)= 9C3= 84
There are 126 boxes containing apples.The number of apples in each box lies between 120 and 150,(both inclusive). let F(x) indicates the number of boxes containing x apples and f indicates the maximum value of F(x) for any x. What could be the minimum possible value of f ?............how to do this problem...any one..?
A dishonest dealer sells goods at 6*1/4 % loss on cost price but uses 12*1/2 % loss weight.What is his percentage profit or loss?
@clickwalker said:There are 126 boxes containing apples.The number of apples in each box lies between 120 and 150,(both inclusive). let F(x) indicates the number of boxes containing x apples and f indicates the maximum value of F(x) for any x. What could be the minimum possible value of f ?............how to do this problem...any one..?
Has to be 5. What's the OA?
@sameer-verma said:in how many ways can we distribute 10 identical looking pencil to 4 students so that each student gets at least one pencil?a)5040b)210c)84d)none of these
This can be reduced to
a+b+c+d=10
Nor for each to have at least one, the solution will be 9C3. Hence, 84.
puys, can someone give the formulae for solving CUBES (nxn cube painted in colours, no.of 2 face painted..?,3 side painted..?etc)..could save some time solving in the exam..
..will be also fine if someone directs me to the relevant thread..
thanx
..will be also fine if someone directs me to the relevant thread..
thanx
puys, can someone give the formulae for solving CUBES (nxn cube painted in colours, no.of 2 face painted..?,3 side painted..?etc)..could save some time solving in the exam..
..will be also fine if someone directs me to the relevant thread..
thanx
..will be also fine if someone directs me to the relevant thread..
thanx
@sarathbhumadi
In a cube or a cuboid there are six faces in each.
In a cube length, breadth and height are same while in cuboid these are different.
In a cube the number of unit cubes = (side)3.
In cuboid the number of unit cube = (l x b x h).
Example:
A cube of each side 4 cm, has been painted black, red and green on pars of opposite faces. It is then cut into small cubes of each side 1 cm.
The following questions and answers are based on the information give above:
The required number of such cubes is always 8, because there are 8 corners.
3. How many small cubes will have only two faces painted ?
Hence the no. of small cubes with two faces coloured = 12 x 2 = 24
(or)
No. of small cubes with two faces coloured = (x - 2) x No. of edges
where x = (side of big cube / side of small cube)
5. How many small cubes will have no faces painted ?
No. of small cubes will have no faces painted = No. of such small cubes
= (x - 2)3 [ Here x = (4/1) = 4 ]
= (4 - 2)3
= 8.
6. How many small cubes will have only two faces painted in black and green and all other faces unpainted ?
There are 4 small cubes in layer II and 4 small cubes in layer III which have two faces painted green and black.
Required no. of such small cubes = 4 + 4 = 8.
7. How many small cubes will have only two faces painted green and red ?
No. of small cubes having two faces painted green and red = 4 + 4 = 8.
8. How many small cubes will have only two faces painted black and red ?
No. of small cubes having two faces painted black and red = 4 + 4 = 8.
9. How many small cubes will have only black painted ?
No. of small cubes having only black paint. There will be 8 small cubes which have only black paint. Four cubes will be form one side and 4 from the opposite side.
10. How many small cubes will be only red painted ?
No. of small cubes having only red paint = 4 + 4 = 8.
11. How many small cubes will be only green painted ?
No. of small cubes having only green paint = 4 + 4 = 8.
12. How many small cubes will have at least one face painted ?
No. of small cubes having at least one face painted = No. of small cubes having 1 face painted + 2 faces painted + 3 faces painted
= 24 + 24 + 8
= 56.
13. How many small cubes will have at least two faces painted ?
No. of small cubes having at least two faces painted = No. of small cubes having two faces painted + 3 faces painted
= 24 + 8
= 32.
In a cube or a cuboid there are six faces in each.
In a cube length, breadth and height are same while in cuboid these are different.
In a cube the number of unit cubes = (side)3.
In cuboid the number of unit cube = (l x b x h).
Example:
A cube of each side 4 cm, has been painted black, red and green on pars of opposite faces. It is then cut into small cubes of each side 1 cm.
The following questions and answers are based on the information give above:
1. How many small cubes will be there ?
Total no. of cubes = (sides)3 = (4)3 = 64
2. How many small cubes will have three faces painted ?
The required number of such cubes is always 8, because there are 8 corners.
3. How many small cubes will have only two faces painted ?
Hence the no. of small cubes with two faces coloured = 12 x 2 = 24
(or)
No. of small cubes with two faces coloured = (x - 2) x No. of edges
where x = (side of big cube / side of small cube)
Here , x = 4/1 = 4
4. How many small cubes will have only one face painted ?
The cubes which are painted on one face only are the cubes at the centre of each face of the big cube.
Since there are 6 faces in the big cube and each of the face of big cube there will be four small cubes.
Hence, in all there will be 6 x 4 = 24 such small cubes
The cubes which are painted on one face only are the cubes at the centre of each face of the big cube.
Since there are 6 faces in the big cube and each of the face of big cube there will be four small cubes.
Hence, in all there will be 6 x 4 = 24 such small cubes
(or)
(x - 2)2 x 6.
5. How many small cubes will have no faces painted ?
No. of small cubes will have no faces painted = No. of such small cubes
= (x - 2)3 [ Here x = (4/1) = 4 ]
= (4 - 2)3
= 8.
6. How many small cubes will have only two faces painted in black and green and all other faces unpainted ?
There are 4 small cubes in layer II and 4 small cubes in layer III which have two faces painted green and black.
Required no. of such small cubes = 4 + 4 = 8.
7. How many small cubes will have only two faces painted green and red ?
No. of small cubes having two faces painted green and red = 4 + 4 = 8.
8. How many small cubes will have only two faces painted black and red ?
No. of small cubes having two faces painted black and red = 4 + 4 = 8.
9. How many small cubes will have only black painted ?
No. of small cubes having only black paint. There will be 8 small cubes which have only black paint. Four cubes will be form one side and 4 from the opposite side.
10. How many small cubes will be only red painted ?
No. of small cubes having only red paint = 4 + 4 = 8.
11. How many small cubes will be only green painted ?
No. of small cubes having only green paint = 4 + 4 = 8.
12. How many small cubes will have at least one face painted ?
No. of small cubes having at least one face painted = No. of small cubes having 1 face painted + 2 faces painted + 3 faces painted
= 24 + 24 + 8
= 56.
13. How many small cubes will have at least two faces painted ?
No. of small cubes having at least two faces painted = No. of small cubes having two faces painted + 3 faces painted
= 24 + 8
= 32.
hope that helps
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Find the missing term in the series :
(2). 5 ? 4 7.5 17 45
1) length of sides of triangle are x+1,9-x,5x-3.the number of values of x for which the triangle is isoceles is
A)0
B)1
C)2
D)3
2)two people decide to meet between x and x+1 hours such dat each vl w8 no longer dan 20 mins for d other . find the probability(they will meet)
A)5/9
B)7/9
C)2/9
D)4/9
A circular wheel of circumference 600cms completes 12 revolutions in 12 minutes. Find its speed in m/sec.
A 0.1
B 0.2
c 0.3
D 0.4
Hie...althou m fr Cat 13...i think dis one shall help me a lot..:)
thanxx..