Differential Equations of Class 12

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 is2 ⁿ .

It has been given that the coin is tossed 5 times so the total sample space is 2 ^s =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.

d/dx (e^logx) =

A: 1

B: x

C: x ² /2

D: - 1

Solution:

Explanation:

Correct option is (A)

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.

.