Algebra
- In how many ways can a committee schedule three speakers for three different meetings if they are all available on any of five possible dates?
-
View Hint View Answer Discuss in Forum
Required number of ways =
5P3 = 5 × 4 × 3 = 60Correct Option: C
Required number of ways =
5P3 = 5 × 4 × 3 = 60
- How many even three-digit numbers can be formed from the digits 1, 2, 5, 6 and 9 without repeating any of the digits ?
-
View Hint View Answer Discuss in Forum
The unit’s place will be occupied by 2 or 6 in three digit even numbers.
The remaining two places can be occupied by selecting from remaining four digits in 4P2 ways4P2 = 4! = 4 × 3 × 2 = 12 (4 - 2)! 2
∴ Total number of even three digit numbers = 2 × 12 = 24
Total ways = 3 × 4 × 2 = 24 ways.
{∵ Total available digits are 1, 2, 5, 6, 9.
Even digits = 2 and 6.
⇒ A can either be filled by 2 or 6
i.e. 2 ways.
B can either be filled by 4 ways
[∵ Total – digit used at A i.e. 5 – 1]}
and C can either be filled by 3 ways
[Total – digit used at A – digit used at B i.e. 5 – 1 – 1]Correct Option: D
The unit’s place will be occupied by 2 or 6 in three digit even numbers.
The remaining two places can be occupied by selecting from remaining four digits in 4P2 ways4P2 = 4! = 4 × 3 × 2 = 12 (4 - 2)! 2
∴ Total number of even three digit numbers = 2 × 12 = 24
Total ways = 3 × 4 × 2 = 24 ways.
{∵ Total available digits are 1, 2, 5, 6, 9.
Even digits = 2 and 6.
⇒ A can either be filled by 2 or 6
i.e. 2 ways.
B can either be filled by 4 ways
[∵ Total – digit used at A i.e. 5 – 1]}
and C can either be filled by 3 ways
[Total – digit used at A – digit used at B i.e. 5 – 1 – 1]
- If ten friends shake hands mutually, then the total number of hand shakes is
-
View Hint View Answer Discuss in Forum
It is to be noted that when two persons shake hands it is counted as one hand shake not two. So this is a problem on combination. The total number of hand shakes is
= The number of ways of selecting 2 persons out of 10 persons= 10C2 = 10 × 9 = 45 1 × 2 Correct Option: A
It is to be noted that when two persons shake hands it is counted as one hand shake not two. So this is a problem on combination. The total number of hand shakes is
= The number of ways of selecting 2 persons out of 10 persons= 10C2 = 10 × 9 = 45 1 × 2
-
If a = 2 and b = 4 then the tatio a + b equal to : b 3 c 5 b + c
-
View Hint View Answer Discuss in Forum
a = 2 = 8 b 3 12 b = 4 = 12 c 5 15
[Making B equal]∴ Required ratio = 8 + 12 = 20 12 + 15 27 Correct Option: A
a = 2 = 8 b 3 12 b = 4 = 12 c 5 15
[Making B equal]∴ Required ratio = 8 + 12 = 20 12 + 15 27
- The graph of linear equation y = x passes through the point
-
View Hint View Answer Discuss in Forum
Point (1, 1) satisfies the equation y = x.Correct Option: B
Point (1, 1) satisfies the equation y = x.
