GATE Questions

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Given 82.5% of 2360

 82.5100 x 2360 = 0.825 x 2360 = 1947

At least one black can be chosen in two ways from each box:
Now, probability of choosing at least one black ball from first box 

= 1/2 × [ (2C1× 2C1)/4C2 + 2C2/ 4C2 ]= 5/12

Probability of choosing at least one black ball from 2nd box
= 1/2 × [(4C1×12C1)/16C2 + 4C2/ 16C2] = 9/40

Final probability

= 5/12 + 9/40 = (50 + 27)/120 = 77/120

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

The following arrangements satisfy all 3 conditions.

Arrangement 1: 3 books in a row; 12 rows.

Arrangement 2: 4 books in a row; 9 rows.
Arrangement 3: 6 books in a row; 6 rows.
Arrangement 4: 9 books in a row; 4 rows.
Arrangement 5: 12 books in a row; 3 rows.

Therefore, the possible arrangements are 5.

We know 60 min = 1 hr
Total northward Laxmi's distance = 20kmph x 1hr = 20 km
Total southward Prasanna's distance = 30kmph x 1hr = 30 km
Total distance between Prasanna and Laxmi is = 20 + 30 = 50 km.

Principal = Rs.(100 x 5400)/(12 x 3)= Rs. 15000.

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.

These two events cannot be disjoint because P(K) + P(L) > 1.

P(AꓴB) = P(A) + P(B) - P(AꓵB).

An event is disjoint if P(A ꓵ B) = 0. If K and L are disjoint P(K ꓴ L) = 0.8 + 0.6 = 1.4

And Since probability cannot be greater than 1, these two mentioned events cannot be disjoint.