Differential Equations of Class 12
Frequently Asked Questions
An unbiased coin is tossed 5 times Suppose that a variable X
is assigned the value k when k consecutive heads are obtained for k = 3,4,5,
otherwise X takes the value - 1 . Then the expected value of X , is :
A: 1/8
B: 316
C: - 18
D: - 316
Solution:
Explanation:
It is known that if a coin is tossed n times then the total sample space is2n .
It has been given that the coin is tossed 5 times so the total sample space is 2s=32.
Final Answer:
Hence, Option (A) is correct which is 1/8.
Define surjective function Give an example of function
Solution:
Explanation:
- Every element of the range set is a co-domain, hence the surjective function is defined with reference to the elements of the range set.
- A surjective function has an image that is the same as its co-domain.
- A surjective function's range, co-domain, and image are all the same.
-
We may also argue that a surjective function is an onto function if every
co-domain has at least one pre-image 
domain and 
- Let's have a look at surjective function in more detail.
- Assume and. A = {1, - 1,2,3} = {1,4,9}.
-
Because each element of has at least one pre-image in A,
is surjective.
Final Answer:
A surjective function is one in which each element in the domain of has at least one element in the domain of, resulting in 
.
Example: is surjective.
The transpose of a row matrix is
A: zero matrix
B: diagonal matrix
C: column matrix
D: row matrix
Solution:
Explanation:
Final Answer:
Hence, Option C column matrix is the correct answer.
It can take 12 hours to fill a swimming pool using two pipes
If the pipe of larger diameter is used for four hours and the pipe of smaller diameter for 9 hours,
only half of the pool can be filled. How long would it take for each pipe to fill the pool separately?
Solution:
Explanation:
The given data is,
The time required to fill the swimming pool using two pipes = 12 hours.
To fill the half of the pool,
The time for which the pipe of larger diameter is used = 4 hours.
The time for which the pipe of smaller diameter is used = 9 hours.
It is required to find the time that would take for each pipe to fill the pool separately.
Let the time taken by the larger pipe to fill the pool be x hours.
And, the time taken by the smaller pipe to fill the pool be y hours.
.
