Dialect and English Language
Name: Sanjeeb Thakali.
Subject name & code: Mathematics for IT (BT 0063)
Roll no.: 1308014090
Q.1 In a group of 50 people, 35 speak Hindi, 25 speak both English and Hindi and all the people speak at least one of the two languages. How many people only speak English and not Hindi? How many people speak English?
Solution:
Here, Let people speaking English language be ‘’E’’ and people speaking Hindi language be “H” respectively. E H 15 25 10
U= 50
Now by question, we have n(U) = 50 n(H) = 35 n(EᴨH) = 25 n₀(E) =? n(E) = ?
Now, n(U) = n(E) + n(H) - n(EᴨH) or, 50 = n(E) + 35 – 25 or, 50 = n(E) + 10 or, n(E) = 50 – 10 or, n(E) = 40
And,
n₀ (E) = n(E) – n(EᴨH) or, n₀ (E) = 40 – 25 or, n₀ (E) = 15
Therefore, the number of people speaking only English language is 15 and number of people speaking English language but not Hindi language is 40.
Q.2 Solve: (1 + y2) dx = (tan-1y-x) dy
Solution:
This equation contains y2 and tan-1y. Hence, it not a linear in y and can be written as :
(1+y2) = tan-1y-x + =
Which is Leibnitz’s equation in x. therefore, we have intermediately form I.F. as,
I.F. = = =
Thus, the solution is, x(I.F.) = or, x. = . Here, put t = and
Therefore,
x.et =
= t.-
= t. - + c
= + c
Or, x =
Q.3 Find the matrix of A such that 3A =
Solution:
Here, we have
3A =
Or, 3A = -
Or 3A =
Or A =
∴ A =
Q.4 A circular wheel is rotating at the rate of 25 revolutions per minute. If the radius of the wheel is 50 cm, find the distance covered by a point on the rim in one second (take π= 3.1416)
Solution:
Given,
Rate of revolutions of circular wheel = 25 revolutions per minute
Radius of the wheel = 50 cm
Distance covered by a point on the rim in one second =?
Here,
Angle through which the wheel
Subject name & code: Mathematics for IT (BT 0063)
Roll no.: 1308014090
Q.1 In a group of 50 people, 35 speak Hindi, 25 speak both English and Hindi and all the people speak at least one of the two languages. How many people only speak English and not Hindi? How many people speak English?
Solution:
Here, Let people speaking English language be ‘’E’’ and people speaking Hindi language be “H” respectively. E H 15 25 10
U= 50
Now by question, we have n(U) = 50 n(H) = 35 n(EᴨH) = 25 n₀(E) =? n(E) = ?
Now, n(U) = n(E) + n(H) - n(EᴨH) or, 50 = n(E) + 35 – 25 or, 50 = n(E) + 10 or, n(E) = 50 – 10 or, n(E) = 40
And,
n₀ (E) = n(E) – n(EᴨH) or, n₀ (E) = 40 – 25 or, n₀ (E) = 15
Therefore, the number of people speaking only English language is 15 and number of people speaking English language but not Hindi language is 40.
Q.2 Solve: (1 + y2) dx = (tan-1y-x) dy
Solution:
This equation contains y2 and tan-1y. Hence, it not a linear in y and can be written as :
(1+y2) = tan-1y-x + =
Which is Leibnitz’s equation in x. therefore, we have intermediately form I.F. as,
I.F. = = =
Thus, the solution is, x(I.F.) = or, x. = . Here, put t = and
Therefore,
x.et =
= t.-
= t. - + c
= + c
Or, x =
Q.3 Find the matrix of A such that 3A =
Solution:
Here, we have
3A =
Or, 3A = -
Or 3A =
Or A =
∴ A =
Q.4 A circular wheel is rotating at the rate of 25 revolutions per minute. If the radius of the wheel is 50 cm, find the distance covered by a point on the rim in one second (take π= 3.1416)
Solution:
Given,
Rate of revolutions of circular wheel = 25 revolutions per minute
Radius of the wheel = 50 cm
Distance covered by a point on the rim in one second =?
Here,
Angle through which the wheel