### Practice Exams ChE - 7

1. The probability of getting heads or tails in an unbiased toss coin is 1/2. If a coin is tossed 2 times, what is the probability of getting 2 consecutive heads?

a. 1/2

b. ???

c. 1/4

d. none of these

2. The probability of getting heads or tails in an unbiased toss coin is 1/2. If a coin is tossed thrice what is the probability of getting a tail on the third toss?

a. 1/8

b. ???

c. 1/2

d. none of these

3. The probability of a couple having a child with curly hair is 1/4, with thick lips is 1/3 and with both characteristics, 1/6. What is the probability of having two consecutive children with curly hair and thick lips if the two events are mutually exclusive?

a. 1/6

b. 25/144

c. ???

d. none of these

4. The probability that a good component is obtained from a sample is:

No. of good components in sample - probability

0 - 1/35

1 - 10/35

2 - 20/35

3 - 4/35

If a sample of 3 is taken infinite times, what is the average no. of good components in the sample?

a. 1.5

b. 1.77

c. 2.0

d. none of these

5. A box contains 5 red, 3 green, 2 white balls. What is the probability of not getting a white ball?

a. 0.2

b. ???

c. 0.8

d. none of these

6. Solve the differential equation:

dy = x^3 + 2x + 10

dx

7. Find dy for y = x

...........dx...........x-1

8. Given F(x) = x+1 find dy

....................................dx

9. Evaluate: 6x (x + 2x²) dx

10. Find dy given y= (y-7)

..............dx...............(y+2)

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