A speaks the truth 5 out of 7 times and B speaks truth 8 out of 9 times. What is the probability that they contradict each other in stating the same fact?

The average of five natural numbers is p. If the next three numbers are included then how much the average of these 8 numbers exceeds than the average p?

Directions : The graph shows the demand and production of different companies. Study the graph and answer the following questions.

The demand of company B is what percentage of the production of company F ?

P is 20 percent more than Q and Q is 30 percent less than R. If P is 420, then What is the value of R?

The value of $${3.157×4126×3.198\over63.972×2835.121}$$ is closest to : 

If Cos A + Cos² A = 1, then Sin² A + Sin⁴ A=?

Directions: Each of the questions consists of a question followed by three statements. You have to study the questions and the statements and decide which of the statements(s) is/are necessary to answer the question. 

What is the population of State ‘A’?
 I. After increasing the population of State A by 15% it becomes 1.61 lakhs
 II. Ratio of population of State A to that of State B is 7 : 8 respectively
 III. Population of State B is 1.6 lakhs

Cost of a diamond varies directly as the square of its weight. A diamond broke into four pieces with their weights in the ratio 1 : 2 : 3: 4. If the loss in the total value of the diamond was Rs.7000, the price of the original diamond was