Bihar Board 12th Maths Important Questions Short Answer Type Part 2 in English

Bihar Board 12th Maths Important Questions Short Answer Type Part 2 in English

BSEB 12th Maths Important Questions Short Answer Type Part 2 in English

Differential Equation

Question 1.
determine order and degree of following differential equations:

Question 2.
Form a differential equation of family of curve. y² = a(a² – x²)
Answer:
Given equation
y² = a(a² – x²)
Diff. w.r. to x

Question 3.
Form a differential equation of the family of curve.
y² + y² = 2ax
Answer:
Given equation
y² + y² = 2ax ……….. (i)
Diff. w.r. to x

Vector Algebra

Question 1.

Question 2.
Find unit vector in the direction of vector :

Question 3.

Question 4.

Question 5.

Answer:

Question 6.

Question 7.

Question 8.

Question 9.

Question 10.

Question 11.
Find the area of a parallelogram whose adjacent sides are given by the vectors

Probability

Question 1.

Question 2.
A family has two children. What is the probabiity that both the children are boys given that at lest one of them is a boy?
Solution:
Let b stand for boy and g for girl.
The sample space of the experiment is
S = ((b, b),(g, b),(b, g), (g, g))
Let E and F denote the following events.
E: ‘both the children are boys’
F:’ atleast on the child is a boy’ ,
Then, E = {(b,b)} and F = {(b,b),(g,b),(b,gi}
Noi, E ∩ F = {(b, b)} .
Thus P(F) = 3/4 and P(E∩F) = 1/4

Question 3.
A die is thrown If E is the eient the number appearing is a multiple of 3’ and F be the event ‘the number appearing is evem Then find whether E and F are independent.
Solution:
We know the sample space is S = { 1, 2, 3,4, 5, 6}
Now E = {3,6},
F = {2,4,6) and E ∩ F = {6}
Then, P(E) = 2/6 = 1/3
P(F) = 3/6 = 1/2
and P(E∩F) = 1/6
Clearly P(E∩F)= P(E).P(F)
Hence E and F are independent events.

Question 4.
An unbaised dic is thrown twice, Let the event A be odd number on the first throw and B thc event ‘odd number on the second throw.
Check the independence of the events A and B.
Solution:
If all the 36 elementary events of the experiment are consided to be equally likely.
We have,

CIçarly, P(A∩B) = P(A) x P(B)
Thus A and B are independènt events.