HSC Commerce (English Medium) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Determine the order and degree of the following differential equation:

(y''')² + 3y'' + 3xy' + 5y = 0

Determine the order and degree of the following differential equation:

`(("d"^2"y")/"dx"^2)^2 + cos ("dy"/"dx") = 0`

Determine the order and degree of the following differential equation:

`[1 + (dy/dx)^2]^(3/2) = 8(d^2y)/dx^2`

Determine the order and degree of the following differential equation:

`(("d"^3"y")/"dx"^3)^(1/2) - ("dy"/"dx")^(1/3) = 20`

Determine the order and degree of the following differential equation:

`"x" + ("d"^2"y")/"dx"^2 = sqrt(1 + (("d"^2"y")/"dx"^2)^2)`

Integrate the following w.r.t.x: `(3x + 1)/sqrt(-2x^2 + x + 3)`

Choose the correct option from the given alternatives:

The order and degree of the differential equation `sqrt(1 + ("dy"/"dx")^2) = (("d"^2"y")/"dx"^2)^(3/2)` are respectively.

Determine the order and degree of the following differential equation:

`("d"^2"y")/"dx"^2 + 5 "dy"/"dx" + "y" = "x"^3`

Determine the order and degree of the following differential equation:

`"dy"/"dx" = 3"y" + root(4)(1 + 5 ("dy"/"dx")^2)`

Determine the order and degree of the following differential equation:

`("d"^4"y")/"dx"^4 + sin ("dy"/"dx") = 0`

Determine the order and degree of the following differential equation:

`(("d"^3"y")/"dx"^3)^2 = root(5)(1 + "dy"/"dx")`

Express the following statement in symbolic form.

e is a vowel or 2 + 3 = 5

Express the following statement in symbolic form.

Mango is a fruit but potato is a vegetable.

Express the following statement in symbolic form.

Milk is white or grass is green.

Express the following statement in symbolic form.

I like playing but not singing.

Express the following statement in symbolic form.

Even though it is cloudy, it is still raining.

Write the truth value of the following statement.

Earth is a planet and Moon is a star.

Write the truth value of the following statement.

16 is an even number and 8 is a perfect square.

Write the truth value of the following statement.

A quadratic equation has two distinct roots or 6 has three prime factors.

Write the truth value of the following statement.

The Himalayas are the highest mountains but they are part of India in the North East.