Differential Equations of Class 12
Question
If for a curve ratio of the distance between the normal at any of its points and the origin to the distance between the same normal and the point (a, (B) is equal to the constant k (k >0, k ≠1), then the curve is a
Answer
Option 1 circle
Option 2 parabola
Option 3 ellipse
Option 4 hyperbola
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.
.
