GATE Questions

---

Let P's speed = x km/hr. Then, Q's speed = (7 - x) km/ hr.

So, 24/x + 24/(7 - x) = 14

x2 - 98x + 168 = 0

(x - 3)(x - 4) = 0 => x = 3 or 4.

Since, P is faster than Q,

so P's speed = 4 km/hr and Q's speed = 3 km/hr.

Two men, three women and one child can be selected in ⁴C₂ x ⁶C₃ x ⁵C₁ ways = 600 ways.

The given words follow a relation that First arises from the second.

That is, fear arises from the threat. Similarly, anger arises from provocation.

Hence, Fear : Threat :: Anger : Provocation.

Choose 1 person for the single room & from the remaining choose 2 for the double room & from the remaining choose 4 people for the four person room, 

 Then, ⁷C₁ x ⁶C₂ x ⁴C₄ 

_{= 7 x 15 x 1 = 105}

The given puzzle follows a pattern that,

Number - <last digit> <sum of all digits>.

111 - 13

112 - 24

113 - 35

So 

117 - 79

1.12.91 is the first Sunday of December 91.
So, 3.12.91 is the first Tuesday of the month.
Clearly, 10.12.91, 17.12.91, 24.12.91 and 31.12.91 are also Tuesdays.
So, 24.12.91 is the fourth Tuesday.

Better is compared with worst and slower must be compared with quickest since fast is the extreme of it.

Hence, Better is to worst as slower is to quickest.