GATE Questions

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Let speed of train B be x m/s And length of train B be y m
Then length of train A is 2y m
Speed of train A = 84 × 5/18 = 210/9 m/s = 70/3 m/s
A.T.Q, (2y+y)/10 = 70/3 − x .............(i)
and (2y+y)/ 22.5 = 70/3 − 2x ................(ii)
solving (i) and (ii), y = 50 m

Time taken to fill 2/7 = 1
Then to fill full 1 = ?
? = 1/(2/7) = 7/2 minutes.

The clotting of blood is a chain reaction initiated by the enzyme thrombokinase produced by the platelets. This causes prothrombin to be converted into thrombin in the presence of Ca++ion.

Thrombin combines with fibrinogen  to produce fibrin threads which entangles the corpuscles to form the clot.

'&' is a Logical Symbol and is called as Ampersand.

^ is called Caret

- is called Bar

v is called Reversed Caret.

Let the Time be 'N' and Rate be 'R' 

J = (K x NR)/100 K = (L x NR)/100 

J/K = NR/100 K/L = NR/100 

J/K = K/L 

K x K = JL

Total number of possible ways = 

9C5 = 9 x 8 x 7 x 6 x 55 x 4 x 3 x 2 x 1 = 126

Number of favorable cases = 

$$\begin{gathered} 4C2 x 5C3 + 4C3 x 5C2 + 4C4 x 5C1 \\ 4 x 32 x 1 x 5 x 4 x 33 x 2 x 1 + 4 x 3 x 23 x 2 x 1 x 5 x 4 2 x 1 + 1 x 5 \\ = 6 x 10 + 4 x 10 + 5 \\ = 60 + 40 + 5 \\ = 105 \end{gathered}$$

Therefore, required probability = 105/126 = 5/6

The triangle is a caribbean shape that makes ships disappear.

Amount of work K can do in 1 day = 1/16

Amount of work L can do in 1 day = 1/12

Amount of work K, L and M can together do in 1 day = 1/4

Amount of work M can do in 1 day = 1/4 - (1/16 + 1/12) = 3/16 – 1/12 = 5/48

=> Hence M can do the job on 48/5 days = 9 (3/5) days