The toys are different; The boxes are identical
If none of the boxes is to remain empty, then we can pack the toys in one of the following ways
a. 2, 2, 1
b. 3, 1, 1
Case a. Number of ways of achieving the first option 2 - 2 - 1
Two toys out of the 5 can be selected in ways. Another 2 out of the remaining 3 can be selected in ways and the last toy can be selected in way.
However, as the boxes are identical, the two different ways of selecting which box holds the first two toys and which one holds the second set of two toys will look the same. Hence, we need to divide the result by 2
Therefore, total number of ways of achieving the 2 - 2 - 1 option is ways = 15 ways
Case b. Number of ways of achieving the second option 3 - 1 - 1
Three toys out of the 5 can be selected in ways. As the boxes are identical, the remaining two toys can go into the two identical looking boxes in only one way.
Therefore, total number of ways of getting the 3 - 1 - 1 option is = 10 = 10 ways.
Total ways in which the 5 toys can be packed in 3 identical boxes
= number of ways of achieving Case a + number of ways of achieving Case b= 15 + 10 = 25 ways.
5% of A + 4% of B = | 2 | (6% of A + 8% of B) |
3 |
⟹ | 5 | A + | 4 | B | = | 2 | ❨ | 6 | A + | 8 | B | ❩ |
100 | 100 | 3 | 100 | 100 |
⟹ | 1 | A + | 1 | B | = | 1 | A + | 4 | B |
20 | 25 | 25 | 75 |
⟹ | ❨ | 1 | - | 1 | ❩ A = | ❨ | 4 | - | 1 | ❩ B |
20 | 25 | 75 | 25 |
⟹ | 1 | A = | 1 | B |
100 | 75 |
A | = | 100 | = | 4 | . |
B | 75 | 3 |
∴ Required ratio = 4 : 3
Speed = | ❨ | 240 | ❩m/sec = 10 m/sec. |
24 |
∴ Required time = | ❨ | 240 + 650 | ❩sec = 89 sec. |
10 |
Odd days in 1600 years = 0
Odd days in 300 years = (5 x 3) ≡ 1
97 years has 24 leap years + 73 ordinary years.
Number of odd days in 97 years ( 24 x 2 + 73) = 121 = 2 odd days.
Jan. Feb. March April May June (31 + 28 + 31 + 30 + 31 + 17) = 168 days
∴ 168 days = 24 weeks = 0 odd day.
Total number of odd days = (0 + 1 + 2 + 0) = 3.
Given day is Wednesday.
Other number = | ❨ | 11 x 7700 | ❩ | = 308. |
275 |
Let 1872/?N = 234.
Then ?N = 1872/234 = 8
? N = 8 x 8 = 64
Let distance covered by dog in 1 leap is x and
Distance covered by cat in 1 leap is y
Then, 3x = 4y
? x= 4/3y
Now, Ratio of speed of dog and cat = Ratio of distance covered by them in the same time = 4x : 5y
= 16/3y : 5y
= 16 : 15
Total volume of cuboid = (10 x 5 x 2) cm3
= 100 cm3
Volume curved = 1/3 x (22/7) x 3 x 3 x 7 cm3
= 66 cm3
% of wood wasted = (100 - 66)% = 34 %
Series pattern
12, 32, 52, 72, 92, 112
So missing term = 112 = 121
Angle of 360° is covered by hour hand in 12 h .
So, angle of 135° is covered by hour hand in 12/360° x 135° = 4.5 h
Thus, required time = (3 + 4.5)h = 7.5 h = 7 : 30
Try yourself. It was Wednesday.
Comments
There are no comments.Copyright ©CuriousTab. All rights reserved.