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)